Time Europa Brussels K2 K3 K4 K5 K6 K7+8 K9 Berlin 3 Amsterdam Foyer K1

## Sunday, June 25

09:30-13:00     Su1-1: Tutorial: Codes for Distributed Computing Su1-2: Tutorial: Information Limits on Finding and Hiding Message Sources on Networks: Social Media and Cryptocurrencies
14:00-17:30     Su2-1: Tutorial: Statistical Foundations of Interactive Learning Su2-2: Tutorial: Information Theoretic Cryptography for Information Theorists
18:00-21:00                       SuW: Welcome Reception

## Monday, June 26

08:30-08:45 Opening Ceremony
08:45-09:45 MoP: Plenary Talk: Reading and Hiding Data in Quantum Systems - Andreas Winter
10:10-11:10 Mo1-1: Algebraic Coding Mo1-2: Convolutional Codes Mo1-3: Multiple Access 1 Mo1-4: Entropy 1 Mo1-5: Optical Communications Mo1-6: Precoding Mo1-7: Quantization Mo1-8: Rate Distortion Theory 1 Mo1-9: Hypothesis Testing 1 Mo1-A: Age of Information 1
11:30-12:50 Mo2-1: Coding Techniques 1 Mo2-2: Locally Repairable Codes 1 Mo2-3: Broadcast Channels 1 Mo2-4: Feedback Mo2-5: Reconstruction Mo2-6: Complexity Mo2-7: ARQ Mo2-8: Quantum IT 1 Mo2-9: Source Coding 1 Mo2-A: Age of Information 2
12:50-14:40                         Mo: WITHITS Event
14:40-16:20 Mo3-1: Reed-Solomon Codes Mo3-2: LDPC Codes 1 Mo3-3: Caching 1 Mo3-4: Channel Capacity 1 Mo3-5: Detection and Estimation 1 Mo3-6: Wireless Networks 1 Mo3-7: Communications 1 Mo3-8: Compressed Sensing 1 Mo3-9: MIMO 1 Mo3-A: Age of Information 3
16:40-18:20 Mo4-1: Coding Theory 1 Mo4-2: Coding for Storage Mo4-3: Interference Channels 1 Mo4-4: Shannon Inequalities Mo4-5: Bounds 1 Mo4-6: Multiterminal Source Coding Mo4-7: Security 1 Mo4-8: Privacy 1 Mo4-9: Subspace and LDPC Codes Mo4-A: Energy Harvesting 1
18:30-20:00                       MoM: Mentoring Event

## Tuesday, June 27

08:30-09:30 TuP: Plenary Talk: Biological Systems as Communication Networks - Urbashi Mitra
09:50-11:10 Tu1-1: Array Codes Tu1-2: Polar Codes 1 Tu1-3: Multiple Access 2 Tu1-4: Information Measures Tu1-5: Joint Source-Channel Coding 1 Tu1-6: Strong Converses Tu1-7: Crypto 1 Tu1-8: Wireless Communication Tu1-9: Hypothesis Testing 2
11:30-12:50 Tu2-1: Coding Techniques 2 Tu2-2: Locally Repairable Codes 2 Tu2-3: Broadcast Channels 2 Tu2-4: Channel Capacity 2 Tu2-5: Massive MIMO Tu2-6: MIMO 2 Tu2-7: Energy Harvesting 2 Tu2-8: Compressed Sensing 2 Tu2-9: Source Coding 2
14:40-16:20 Tu3-1: Network Coding 1 Tu3-2: LDPC Codes 2 Tu3-3: Caching 2 Tu3-4: Second Order Tu3-5: Detection and Estimation 2 Tu3-6: Sequences 1 Tu3-7: Communications 2 Tu3-8: Information Theory and Statistics 1 Tu3-9: Machine Learning 1
16:40-18:20 Tu4-1: Coding Theory 2 Tu4-2: Coding for Distributed Storage 1 Tu4-3: Interference Channels 2 Tu4-4: Entropy 2 Tu4-5: Bounds 2 Tu4-6: Sequences 2 Tu4-7: Security 2 Tu4-8: Quantum IT 2 Tu4-9: Compression 1
18:30-19:15   MoF: Fano Memorial

## Wednesday, June 28

08:30-09:30 WeP: Shannon Lecture: The Spirit of Information Theory - David Tse
09:50-11:10 We1-1: Iterative Decoding 1 We1-2: Student Paper Awards Candidate Talks 1 We1-3: Coding for Storage and Streaming We1-4: Zero Error Capacity We1-5: Joint Source-Channel Coding 2 We1-6: Spatial Coupling We1-7: Security 3 We1-8: Quantum IT 3 We1-9: Source Coding 3
11:30-12:30 We2-1: Coding Techniques (Focus Session) We2-2: Student Paper Awards Candidate Talks 2 We2-3: Crypto (Focus Session) We2-4: Security (Focus Session)   We2-5: Network Information Theory (Focus Session)           We2-P: Recent Results Posters
12:45-13:45 WeA: Awards Session

## Thursday, June 29

08:30-09:30 ThP: Plenary Talk: The Flesh of Polar Codes - Emre Telatar
09:50-11:10 Th1-1: Lattice Codes 1 Th1-2: Polar Codes 2 Th1-3: Broadcast Channels 3 Th1-4: Private Information Retrieval Th1-5: Rate Distortion Theory 2 Th1-6: Coding for Insertion and Deletion Channels 1 Th1-7: Security 4 Th1-8: Quantum IT 4 Th1-9: Source Coding 4
11:30-12:50 Th2-1: Coding Techniques 3 Th2-2: Locally Repairable Codes 3 Th2-3: Multicell and Cloud Radio Th2-4: Channel Capacity 3 Th2-5: Estimation 1 Th2-6: MIMO 3 Th2-7: Security 5 Th2-8: Compressed Sensing 3 Th2-9: Statistics 1
12:50-13:20                         ThL: Student Lunch
13:30-14:30   ThI: Interview with the Shannon Awardee
14:40-16:20   Th3-2: Coding for Distributed Storage 2 Th3-3: Relaying Th3-4: Guessing Th3-5: Detection and Estimation 3 Th3-6: Multiple Access Feedback Th3-7: Communications 3 Th3-8: Compressed Sensing 4 Th3-9: Signal Processing   Th3-1: Coding Theory 3
16:40-18:20   Th4-2: Coded Computation Th4-3: Coded Caching 1 Th4-4: Shannon Theory and Molecular Th4-5: Bounds 3 Th4-6: Wireless Networks 2 Th4-7: Random Access Channels Th4-8: Index Coding 1 Th4-9: Compression 2   Th4-1: Network Coding 2
19:30-23:00 ThB: Banquet

## Friday, June 30

08:30-09:30 FrP: Plenary Talk: Information Theory Out of its Box - Cédric Villani
09:50-11:10 Fr1-1: Lattice Codes 2 Fr1-2: Polar Codes 3 Fr1-3: Multiple Access 3 Fr1-4: Information Retrieval Fr1-5: Information Dynamics Fr1-6: Coding for Insertion and Deletion Channels 2 Fr1-7: Security 6 Fr1-8: Multiple Access Fr1-9: Channel Identification
11:30-12:50 Fr2-1: Rank Metric Codes Fr2-2: Iterative Decoding 2 Fr2-3: Coded Caching 2 Fr2-4: Channel Capacity 4 Fr2-5: Communications 4 Fr2-6: Coding and Decoding Fr2-7: Privacy and Security Fr2-8: Computation
14:40-16:20 Fr3-1: Codes and Graphs Fr3-2: LDPC Codes 3 Fr3-3: Caching 3 Fr3-4: Entropy 3 Fr3-5: Machine Learning 2 Fr3-6: Estimation 2 Fr3-7: Information Theory and Statistics 2 Fr3-8: Index Coding 2 Fr3-9: Statistics 2
16:40-18:00 Fr4-1: Coding Theory 4 Fr4-2: DNA and Coding Fr4-3: Error Exponents Fr4-4: Bounds 4 Fr4-5: Shannon Theory and Applications Fr4-6: Quantum IT 5 Fr4-7: Source Coding 5

## Sunday, June 25

### Sunday, June 25, 09:30 - 13:00

Room: K2

#### Su1-2: Tutorial: Information Limits on Finding and Hiding Message Sources on Networks: Social Media and Cryptocurrencies

Giulia Fanti, Pramod Viswanath
Room: K3

### Sunday, June 25, 14:00 - 17:30

#### Su2-1: Tutorial: Statistical Foundations of Interactive Learning

Kamalika Chaudhuri, Tara Javidi
Room: K2

#### Su2-2: Tutorial: Information Theoretic Cryptography for Information Theorists

Himanshu Tyagi, Shun Watanabe
Room: K3

Room: Foyer

## Monday, June 26

### Monday, June 26, 08:30 - 08:45

#### Opening Ceremony

Room: Europa
Chairs: Gerhard Kramer (Technical University of Munich, Germany), Rudolf Mathar (RWTH Aachen University, Germany)

### Monday, June 26, 08:45 - 09:45

#### MoP: Plenary Talk: Reading and Hiding Data in Quantum Systems - Andreas Winter

Andreas Winter
Room: Europa
Chair: Martin Bossert (Ulm University, Germany)

### Monday, June 26, 10:10 - 11:10

#### Mo1-1: Algebraic Coding

Room: Europa
Chair: Christian Senger (University of Stuttgart, Germany)
10:10 Constructions of Partial MDS Codes over Small Fields
Eitan Yaakobi (Technion, Israel); Ryan Gabrys (UIUC, USA); Mario Blaum (IBM Almaden Research Center & Universidad Complutense, Madrid, USA); Paul H. Siegel (University of California, San Diego, USA)
Partial MDS (PMDS) codes are a class of erasure-correcting array codes which combine local correction of the rows with global correction of the array. An $m\times n$ array code is called an $(r;s)$ PMDS code if each row belongs to an $[n,n-r,r+1]$ MDS code and the code can correct erasure patterns consisting of $r$ erasures in each row together with $s$ more erasures anywhere in the array. While a recent construction by Calis and Koyluoglu generates $(r;s)$ PMDS codes for all $r$ and $s$, its field size is exponentially large. In this paper, a family of PMDS codes with field size $\mathcal{O}\left( \max\{m,n^{r+s}\}^s \right)$ is presented.
pp. 1-5
10:30 Attaining Capacity with iterated (U|U+V) codes based on AG codes and Koetter-Vardy soft decoding
Jean-Pierre Tillich (INRIA, France); Irene Márquez-Corbella (University of La Laguna, Spain)
In this paper we show how to attain the capacity of discrete symmetric channels with polynomial time decoding complexity by considering iterated (U|U+V) constructions with algebraic geometry (AG) code components. These codes are decoded with a recursive computation of the a posteriori probabilities of the code symbols together with decoding the AG components with the Koetter-Vardy algorithm. We show that, when the number of levels of the iterated (U|U+V) construction tends to infinity, we attain the capacity of any discrete symmetric channel. Moreover the error probability decays quasi-exponentially with the codelength in the case of Reed-Solomon code constituents and exponentially with Tsfasman-Vladuts-Zink code constituents.
pp. 6-10
10:50 An Algebraic-Combinatorial Proof Technique for the GM-MDS Conjecture
Anoosheh Heidarzadeh and Alex Sprintson (Texas A&M University, USA)
This paper considers the problem of designing maximum distance separable (MDS) codes over small fields with constraints on the support of their generator matrices. For any given $m\times n$ binary matrix $M$, the GM-MDS conjecture, due to Dau et al., states that if $M$ satisfies the so-called MDS condition, then for any field $\mathbb{F}$ of size $q\geq n+m-1$, there exists an $[n,m]_q$ MDS code whose generator matrix $G$, with entries in $\mathbb{F}$, fits $M$ (i.e., $M$ is the support matrix of $G$). Despite all the attempts by the coding theory community, this conjecture remains still open in general. It was shown, independently by Yan et al. and Dau et al., that the GM-MDS conjecture holds if the following conjecture, referred to as the TM-MDS conjecture, holds: if $M$ satisfies the MDS condition, then the determinant of a transformation matrix $T$, such that $TV$ fits $M$, is not identically zero, where $V$ is a Vandermonde matrix with distinct parameters. In this work, we generalize the TM-MDS conjecture, and present an algebraic-combinatorial approach based on polynomial-degree reduction for proving this conjecture. Our proof technique's strength is based primarily on reducing inherent combinatorics in the proof. We demonstrate the strength of our technique by proving the TM-MDS conjecture for the cases where the number of rows ($m$) of $M$ is upper bounded by $5$. For this class of special cases of $M$ where the only additional constraint is on $m$, only cases with $m\leq 4$ were previously proven theoretically, and the previously used proof techniques are not applicable to cases with $m > 4$.
pp. 11-15

#### Mo1-2: Convolutional Codes

Room: Brussels
Chair: Michael Lentmaier (Lund University, Sweden)
10:10 On the Code Distance of a Woven Block Code Construction
Igor V. Zhilin and Alexey Kreshchuk (Institute for Information Transmission Problems, Russia); Victor V. Zyablov (Institute for Information Transmission Problems (IITP) RAS, Russia)
In this paper we propose a woven block code construction based on two convolutional outer codes and a single inner code. We proved lower and upper bounds on this construction's code distance. The lower bound is shown to be higher than the product of the free distances of inner and outer constituent codes. Since this construction uses well-developed convolutional constituent codes, we believe that it would be competitive to turbo codes in the future mobile communication systems.
pp. 16-20
10:30 Generalized column distances for convolutional codes
Sara D. Cardell (University of Campinas, Brazil); Marcelo Firer (State University of Campinas - UNICAMP, Brazil); Diego Napp (University of Aveiro, Portugal)
In this work, we adapt the notion of generalized Hamming weight of block codes to introduce the novel concept of generalized column distances for convolutional codes. This can be considered an extension of the work done by J. Rosenthal and E. York on the generalized Hamming weights for free distance of convolutional codes. We also introduce the concept of Almost-MDP and Near- MDP convolutional code. The problem of constructing convolutional codes with design generalized column distance remains an interesting open problem that requires further research.
pp. 21-25
10:50 A Unified Ensemble of Concatenated Convolutional Codes
Saeedeh Moloudi and Michael Lentmaier (Lund University, Sweden); Alexandre Graell i Amat (Chalmers University of Technology, Sweden)
We introduce a unified ensemble for turbo-like codes (TCs) that contains the four main classes of TCs: parallel concatenated codes, serially concatenated codes, hybrid concatenated codes, and braided convolutional codes. We show that for each of the original classes of TCs, it is possible to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. We also derive the density evolution (DE) equations for this ensemble over the binary erasure channel. The thresholds obtained from the DE indicate that the TC ensembles from the unified ensemble have similar asymptotic behavior to the original TC ensembles.
pp. 26-30

#### Mo1-3: Multiple Access 1

Room: K2
Chair: Aydin Sezgin (RUB, Germany)
10:10 Cooperative Binning for Semi-deterministic Channels with Non-causal State Information
Ido Binyamin Gattegno and Haim H Permuter (Ben-Gurion University, Israel); Shlomo (Shitz) Shamai (The Technion, Israel); Ayfer Özgür (Stanford University, USA)
The capacity of two semi-deterministic channels with the presence of non-causal channel state information (CSI) is characterized. The first channel is a state-dependent semi-deterministic relay channel. The CSI is available only at the transmitter and receiver, but not at the relay. The second channel is a state-dependent multiple access channel (MAC) with partial cribbing and CSI only at one transmitter and the receiver. In the semi-deterministic relay channel without states, the capacity can be achieved using partial-decode-forward scheme. The transmission is split to blocks; in each block, the relay decodes a part of the message and cooperation is established using those bits. When the channel depends on a state, the decoding procedure at the relay reduces the transmission rate. The cooperative-bin-forward is a coding scheme that establishes cooperation based on random bins. The deterministic output is mapped into bins, and the relay chooses the transmission sequence based the bin index. This scheme achieves the capacity when the CSI is available causally. In this work, we present a variation of the cooperative-bin-forward scheme that achieves capacity for non-causal CSI. The bin index of the deterministic output is selected by the transmitter, such that the relay's transmission is coordinated with the states. This coding scheme also applies for the MAC with partial cribbing and non-causal CSI at one transmitter and receiver. The capacity is achieved by the new variation of cooperative bin-forward. On top of that, we show an example in which the capacity with non-causal CSI is strictly greater than with causal CSI.
pp. 31-35
10:30 A New Achievable Rate Region for Multiple-Access Channel with States
Mohsen Heidari Khoozani and Farhad Shirani (University of Michigan, USA); Sandeep Pradhan (University Michigan, USA)
The problem of reliable communication over the multiple-access channel (MAC) with states is investigated. We propose a new coding scheme for this problem which uses \textit{quasi-group} codes (QGC). We derive a new computable single-letter characterization of the achievable rate region. As an example, we investigate the problem of \textit{doubly-dirty} MAC with modulo-$4$ addition. It is shown that the sum rate $R_1+R_2=1$ bits per channel use is achievable using the new scheme. Whereas, the natural extension of the Gel'fand-Pinsker scheme, sum-rates greater than $0.32$ are not achievable.
pp. 36-40
10:50 The Benefit of Encoder Cooperation in the Presence of State Information
Parham Noorzad and Michelle Effros (California Institute of Technology, USA); Michael Langberg (State University of New York at Buffalo, USA)
In many communication networks, the availability of channel state information at various nodes provides an opportunity for network nodes to work together, or cooperate. This work studies the benefit of cooperation in the multiple access channel with a cooperation facilitator, distributed state information at the encoders, and full state information available at the decoder. Under various causality constraints, sufficient conditions are obtained such that encoder cooperation through the facilitator results in a gain in sum-capacity that has infinite slope in the information rate shared with the encoders. This result extends the prior work of the authors on cooperation in networks where none of the nodes have access to state information.
pp. 41-45

#### Mo1-4: Entropy 1

Room: K3
Chair: Holger Boche (Technical University Munich, Germany)
10:10 A lower bound on the differential entropy for log-concave random variables with applications to rate-distortion theory
Arnaud Marsiglietti and Victoria Kostina (California Institute of Technology, USA)
We derive a lower bound on the differential entropy for symmetric log-concave random variable $X$ in terms of the $p$-th absolute moment of $X$, which shows that entropy and $p$-th absolute moment of a symmetric log-concave random variable are comparable. We apply our bound to study the rate distortion function under distortion measure $| x - \hat x|^r$ for sources that follow a log-concave probability distribution. In particular, we establish that the difference between the rate distortion function and the Shannon lower bound is at most $\log(\sqrt{2}e) \approx 1.9$ bits, independently of $r$ and the target distortion $d$. For mean-square error distortion, the difference is at most $\log\sqrt{\pi e} \approx 1.55$ bits, regardless of $d$. Our results generalize to the case of vector $X$. Our proof technique leverages tools from convex geometry.
pp. 46-50
10:30 H(X) vs. H(f(X))
Ferdinando Cicalese (University of Verona, Italy); Luisa Gargano (University of Salerno, Italy); Ugo Vaccaro (University of Salerno, USA)
It is well known that the entropy H(X) of a finite random variable is always greater or equal to the entropy H(f(X)) of a function f of X, with equality if and only if the function f is one-to-one. In this paper, we give tights bounds on H(f(X)) when the function f is not one-to-one, and we illustrate a few scenarios where this matters. As an intermediate step towards our main result, we prove a lower bound on the entropy of a probability distribution, when only a bound on the ratio between the maximum and the minimum probability is known. Our lower bound improves previous results in the literature, and it is likely to find applications outside the scenario considered in this paper.
pp. 51-55
10:50 Concavity of Entropy Power: Equivalent Formulations and Generalizations
Thomas Courtade (University of California, Berkeley, USA)
We investigate extensions of Costa's entropy power inequality (EPI). In particular, we show that Costa's EPI, when appropriately formulated, can be precisely generalized to non-Gaussian additive perturbations. This reveals fundamental links between the Gaussian logarithmic Sobolev inequality and the convolution inequalities for entropy and Fisher information. Various consequences including a reverse entropy power inequality and information-theoretic central limit theorems are discussed.
pp. 56-60

#### Mo1-5: Optical Communications

Room: K4
Chair: Frank R. Kschischang (University of Toronto, Canada)
10:10 On Time-Bandwidth Product of Multi-Soliton Pulses
Alexander Span (University of Stuttgart, Germany); Vahid Aref and Henning Buelow (Nokia Bell Labs, Germany); Stephan ten Brink (University of Stuttgart, Germany)
Multi-soliton pulses are potential candidates for fiber optical transmissions where the information is modulated and recovered in the so-called nonlinear Fourier domain. While this is an elegant technique to account for the channel nonlinearity, the obtained spectral efficiency, so far, is not competitive with the classic Nyquist-based schemes. In this paper, we study the evolution of the time-bandwidth product of multi-solitons as they propagate along the optical fiber. For second and third order soliton pulses, we numerically optimize the pulse shapes to achieve the smallest time-bandwidth product when the phase of the spectral amplitudes is used for modulation. Moreover, we analytically estimate the pulse-duration and bandwidth of multi-solitons in some practically important cases. Those estimations enable us to approximate the time-bandwidth product for higher order solitons.
pp. 61-65
10:30 A Novel Demodulation Scheme for a Memoryless Optical Interference Channel
Kamran Keykhosravi and Erik Agrell (Chalmers University of Technology, Sweden)
Matched filtering and sampling, which is known to be the optimal receiver for the linear additive white Gaussian noise channel, is in general suboptimal for a nonlinear medium. Nonetheless, it is commonly used in fiber-optical communication systems with nonlinear distortion. In this paper, a novel demodulation scheme is proposed for a two-user memoryless interference channel, with a type of nonlinear crosstalk that occurs in wavelength-multiplexed optical transmission. We show by simulations that by using this demodulation scheme, unlike matched filtering and sampling, the symbol error rate decreases to zero in the high-power regime.
pp. 66-70
10:50 Optical MISO IM/DD Channels: Optimality of Spatial Repetition Codes among DC-offset STBCs
Yerzhan Sapenov (KAUST & Nazarbayev University, Saudi Arabia); Anas Chaaban (King Abdullah University of Science and Technology, Saudi Arabia); Zouheir Rezki (University of Idaho, USA); Mohamed-Slim Alouini (King Abdullah University of Science and Technology (KAUST), Saudi Arabia)
In this paper, an optical wireless multiple-input single-output communication system employing intensity-modulation direct-detection is considered. Subject to a per transmit-aperture power constraint, the performance of direct current (DC) offset space-time block codes (STBC) is studied in terms of pairwise error probability (PEP). It is shown that among the class of DC-STBCs, the worst case PEP, i.e., the one corresponding to the minimum distance between two codewords, is minimized by repetition coding (RC) for any channel state. Therefore, it follows that among all DC-STBCs, RC is optimal in terms of worst case PEP under any turbulence statistics. This result agrees with previously published numerical results showing the superiority of RC in such systems. It also agrees with previously published analytical results on this topic under log- normal turbulence and further extends it to arbitrary turbulence statistics. Numerical results provided to verify this result also indicate that RC is not only optimal in terms of worst case PEP, but also in terms of average error probability.
pp. 71-75

#### Mo1-6: Precoding

Room: K5
Chair: Jinyuan Chen (Louisiana Tech University, USA)
10:10 Beamforming Codebook Compensation for Beam Squint with Channel Capacity Constraint
Mingming Cai and J. Nicholas Laneman (University of Notre Dame, USA); Bertrand Hochwald (Notre Dame University, USA)
Analog beamforming with phased arrays is a promising technique for 5G wireless communication in millimeter wave bands. A beam focuses on a small range of angles of arrival or departure and corresponds to a set of fixed phase shifts across frequency due to practical hardware constraints. In switched beamforming, a discrete codebook consisting of multiple beams is used to cover a larger angle range. However, for sufficiently large bandwidth, the gain provided by the phased array is frequency dependent even if the radiation pattern of the antenna elements is frequency independent. The effect is called beam squint. This paper shows that the beam squint reduces channel capacity of a uniform linear array (ULA). The beamforming codebook is designed to compensate for the beam squint by imposing a channel capacity constraint. For example, our codebook design algorithm can improve the channel capacity by 17.8% for a ULA with 64 antennas operating at bandwidth of 2.5 GHz and carrier frequency of 73 GHz. Analysis and numerical examples suggest that a denser codebook is required to compensate for the beam squint. Furthermore, the effect of beam squint is shown to increases as the growth of bandwidth, and the beam squint limits the bandwidth given the number of antennas in the array.
pp. 76-80
10:30 Asymptotics of Nonlinear LSE Precoders with Applications to Transmit Antenna Selection
Ali Bereyhi (Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany); Mohammad Ali Sedaghat (Friedrich Alexander University of Erlangen-Nürnberg, Germany); Ralf R. Müller (Friedrich-Alexander Universität Erlangen-Nürnberg, Germany)
This paper studies the large-system performance of Least Square Error (LSE) precoders which minimize the input-output distortion over an arbitrary support subject to a general penalty function. The asymptotics are determined via the replica method in a general form which encloses the Replica Symmetric (RS) and Replica Symmetry Breaking (RSB) ans\"atze. As a result, the marginal decoupling property'' of LSE precoders for $b$-steps of RSB is derived. The generality of the studied setup enables us to address special cases in which the number of active transmit antennas are constrained. Our numerical investigations depict that the computationally efficient forms of LSE precoders based on $\ell_1$-norm'' minimization perform close to the cases with zero-norm'' penalty function which have a considerable improvements compared to the random antenna selection. For the case with BPSK signals and restricted number of active antennas, the results show that RS fails to predict the performance while the RSB ansatz is consistent with theoretical bounds.
pp. 81-85
10:50 MIMO IBC Beamforming with Combined Channel Estimate and Covariance CSIT
Wassim Tabikh and Dirk Slock (EURECOM, France); Yi Yuan-Wu (Orange Labs, France)
This work deals with beamforming for the MIMO Interfering Broadcast Channel (IBC), i.e. the Multi-Input Multi-Output (MIMO) Multi-User Multi-Cell downlink (DL). The novel beamformers are here optimized for the Expected Weighted Sum Rate (EWSR) for the case of Partial Channel State Information at the Transmitters (CSIT). Gaussian (Posterior) partial CSIT can optimally combine channel estimate and channel covariance information. We introduce the first large system analysis for optimized beamformers with partial CSIT, here for the Massive MISO (MaMISO) case. In the case of Gaussian partial CSIT, the beamformers only depend on the means and covariances of the channels. The large system analysis furthermore allows to predict the EWSR performance on the basis of the channel statistics only.
pp. 86-90

#### Mo1-7: Quantization

Room: K6
Chair: Ioannis Kontoyiannis (Athens UniversityEcon & Business, Greece)
10:10 How to Quantize n Outputs of a Binary Symmetric Channel to n-1 Bits?
Wasim Huleihel and Or Ordentlich (MIT, USA)
Suppose that $Y^n$ is obtained by observing a uniform Bernoulli random vector $X^n$ through a binary symmetric channel with crossover probability $\alpha$. The most informative Boolean function" conjecture postulates that the maximal mutual information between $Y^n$ and any Boolean function $\mathrm{b}(X^n)$ is attained by a dictator function. In this paper, we consider the complementary" case in which the Boolean function is replaced by $f:\left\{0,1\right\}^n\mapsto\left\{0,1\right\}^{n-1}$, namely, an $n-1$ bit quantizer, and show that $I(f(X^n);Y^n)\leq (n-1)\cdot\left(1-h(\alpha)\right)$ for any such $f$. Thus, in this case, the optimal function is of the form $f(x^n)=(x_1,\ldots,x_{n-1})$.
pp. 91-95
10:30 Information-Distilling Quantizers
Bobak Nazer (Boston University, USA); Or Ordentlich and Yury Polyanskiy (MIT, USA)
Let $X$ and $Y$ be dependent random variables. We consider the problem of designing a scalar quantizer for $Y$ to maximize the mutual information between its output and $X$, and study fundamental properties and bounds for this form of quantization. Our main focus is the regime of low $I(X;Y)$, where we show that for a binary $X$, there always exist an $M$-level quantizer attaining mutual information of $\Omega(-M\cdot I(X;Y)/\log(I(X;Y))$ and that there exists pairs of $X,Y$ for which the mutual information attained by any $M$-level quantizer is $\mathcal{O}(-M\cdot I(X;Y)/\log(I(X;Y)))$.
pp. 96-100

#### Mo1-8: Rate Distortion Theory 1

Room: K7+8
Chair: Shigeaki Kuzuoka (Wakayama University, Japan)
10:10 Distortion bounds for source broadcasting and asymmetric data transmission with bandwidth expansion
Shraga Bross and Hagai Zalach (Bar-Ilan University, Israel)
We consider the broadcasting of a single Gaussian source over a two-user Gaussian broadcast channel with bandwidth expansion. In addition to the source broadcasting the encoder sends a message reliably to the higher quality'' user. Conditioned on the message rate, we derive an outer bound on the set of attainable mean-squared error distortion pairs at the two users which extends the Reznic-Feder-Zamir bound. Based on the outer bound and an inner bound that we derive we characterize the set of achievable energy-distortion exponents for this problem.
pp. 101-105
10:30 Rate-Distortion Region of a Gray-Wyner Problem with Side-Information
Meryem Benammar (HUAWEI Technologies France, France); Abdellatif Zaidi (Université Paris-Est Marne La Vallée, France)
In this work, we establish a full single-letter characterization of the rate-distortion region of an instance of the Gray-Wyner model with side information at the decoders. In this model an encoder observes a pair of memoryless sources $(S^n_1,S^n_2)$ and communicates with two receivers over a common error-free rate-limited link of capacity $R_0$, as well as two individual error-free rate-limited links of capacities $R_1$ and $R_2$. Both receivers reproduce the source component $S^n_2$ losslessly; and Receiver 1 also reproduces the source component $S^n_1$ lossily, to within some prescribed distortion level $D_1$. Also, Receiver 1 and Receiver 2 observe each a memoryless side information sequence, $Y^n_1$ and $Y^n_2$, assumed to be arbitrarily correlated among them, and with the source pair $(S^n_1,S^n_2)$.
pp. 106-110
10:50 A Multiple Description CEO Problem with Log-Loss Distortion
Georg Pichler (Vienna University of Technology, Austria); Pablo Piantanida (CentraleSupélec-CNRS-Université Paris-Sud, France); Gerald Matz (Vienna University of Technology, Austria)
This paper investigates the Multiple Description (MD) Chief Executive Officer (CEO) problem under logarithmic-loss distortion. The setup extends previous work of Courtade and Weissman (2014) by requiring the CEO to obtain a useful reconstruction also from a reduced set of descriptions. A single-letter characterization of the achievable region is derived under a suitable conditional independence assumption. Surprisingly, the resulting rate requirement is in general less than that required to ensure successful typicality decoding of the corresponding description.
pp. 111-115

#### Mo1-9: Hypothesis Testing 1

Room: K9
Chair: Gregory Wornell (MIT, USA)
10:10 Neyman-Pearson Test for Zero-Rate Multiterminal Hypothesis Testing
Shun Watanabe (Tokyo University of Agriculture and Technology, Japan)
The problem of zero-rate multiterminal hypothesis testing is revisited. A Neyman-Pearson-like test is proposed and its non-asymptotic performance is clarified; for short blocklength, it is numerically examined that the proposed test is superior to a previously known Hoeffding-like test proposed by Han-Kobayashi. For the large deviation regime, it is shown that our proposed test achieves the optimal trade-off between the type I and type II exponents shown by Han-Kobayashi. The information geometry method plays an important role in the analysis as well as the construction of the test.
pp. 116-120
10:30 Using data-compressors for statistical analysis of problems on homogeneity testing and classification
Boris Ryabko (Institute of Computational Technologies of SB RAS & Novosibirsk State University, Russia); Andrey Guskov and Irina Selivanova (The State Public Scientific Technological\\ Library of SB RAS, Novosibirsk, Russia)
Nowadays data compressors are applied to many problems of text analysis, but many such applications are developed outside of the framework of mathematical statistics. In this paper we overcome this obstacle and show how several methods of classical mathematical statistics can be developed based on applications of the data compressors.
pp. 121-125
10:50 First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources with General Mixture
Te Sun Han (University of Electro-Communications, Japan); Ryo Nomura (Senshu University, Japan)
The first- and second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under constraints that the type I error probability is allowed asymptotically up to $\varepsilon$, is called the $\varepsilon$-optimum exponent. In this paper, we first give the second-order $\varepsilon$-exponent in the case where the null hypothesis and the alternative hypothesis are a mixed memoryless source and a stationary memoryless source, respectively. We next generalize this setting to the case where the alternative hypothesis is also a mixed memoryless source. We address the first-order $\varepsilon$-optimum exponent in this setting.
pp. 126-130

#### Mo1-A: Age of Information 1

Room: Berlin 3
Chair: Yin Sun (the Ohio State University, USA)
10:10 Status updates through M/G/1/1 queues with HARQ
Elie Najm (Ecole Polytechnique Fédérale de Lausanne, Switzerland); Roy Yates and Emina Soljanin (Rutgers University, USA)
We consider a system where randomly generated updates are to be transmitted to a monitor, but only a single update can be in the transmission service at a time. Therefore, the source has to prioritize between the two possible transmission policies: preempting the current update or discarding the new one. We consider Poisson arrivals and general service time, and refer to this system as the M/G/1/1 queue. We start by studying the average status update age and the optimal update arrival rate for these two schemes under general service time distribution. We then apply these results on two practical scenarios in which updates are sent through an erasure channel using (a) an infinite incremental redundancy (IIR) HARQ system and (b) a fixed redundancy (FR) HARQ system. We show that in both schemes the best strategy would be not to preempt. Moreover, we also prove that, from an age point of view, IIR is better than FR.
pp. 131-135
10:30 Information Freshness and Popularity in Mobile Caching
Clement Kam, Sastry Kompella and Gam Nguyen (Naval Research Laboratory, USA); Jeffrey Wieselthier (Wieselthier Research, USA); Anthony Ephremides (University of Maryland, USA)
We propose a model for mobile caching in which the rate of requests for content is dependent on the popularity and the freshness of the information. We model popularity based on the history of requests and freshness based on the age of the content. We consider a discrete time (slotted) system in which new packets arrive at a limited capacity cache at discrete times. We prove that the optimal policy for choosing the set of packets to reside in a full cache when a packet arrives is to reject the one with the lowest request rate in that particular slot. Thus, there is no advantage to separately knowing the history of requests or the age of the content. Since the optimal policy depends on the profile of the request process, we also study the expected behavior of the request model. We provide a sufficient condition under which the change in the request rate goes to zero and provide some numerical examples that illustrate this behavior. We also consider a slight alteration to the model, in which only the recent history of requests is used for determining the request rate. In this case, we provide a sufficient condition for when the rate is equal to zero, which approximates the duration of requests for content.
pp. 136-140
10:50 Age-Optimal Constrained Cache Updating
Roy Yates (Rutgers University, USA); Philippe Ciblat (Telecom ParisTech, France); Aylin Yener (Pennsylvania State University, USA); Michele A Wigger (Telecom ParisTech, France)
We consider a system where a local cache maintains a collection of N dynamic content items that are randomly requested by local users. A capacity-constrained link to a remote network server limits the ability of the cache to hold the latest version of each item at all times, making it necessary to design an update policy. Using an age of information metric, we show under a relaxed problem formulation that an asymptotically optimal policy updates a cached item in proportion to the square root of the item's popularity. We then show experimentally that a physically realizable policy closely approximates the asymptotic optimal policy.
pp. 141-145

### Monday, June 26, 11:30 - 12:50

#### Mo2-1: Coding Techniques 1

Room: Europa
Chair: Jos H. Weber (Delft University of Technology, The Netherlands)
Simon R Blackburn (Royal Holloway University of London, United Kingdom (Great Britain)); Tuvi Etzion (Technion-Israel Institute of Technology, Israel); Maura B Paterson (Birkbeck, University of London, United Kingdom (Great Britain))
Shah, Rashmi and Ramchandran recently considered a model for Private Information Retrieval (PIR) where a user wishes to retrieve one of several $R$-bit messages from a set of $n$ non-colluding servers. Their security model is information-theoretic. Their paper is the first to consider a model for PIR in which the database is not necessarily replicated, so allowing distributed storage techniques to be used. Shah et al.\ show that at least $R+1$ bits must be downloaded from servers, and describe a scheme with linear total storage (in $R$) that downloads between $2R$ and $3R$ bits. For any positive $\epsilon$, we provide a construction with the same storage property, that requires at most $(1+\epsilon)R$ bits to be downloaded; moreover one variant of our scheme only requires each server to store a bounded number of bits (in the sense of being bounded by a function that is independent of $R$). We also provide variants of a scheme of Shah et al which downloads exactly $R+1$ bits and has quadratic total storage. Finally, we simplify and generalise a lower bound due to Shah et al.\ on the download complexity a PIR scheme. In a natural model, we show that an $n$-server PIR scheme requires at least $nR/(n-1)$ download bits in many cases, and provide a scheme that meets this bound.
pp. 146-150
11:50 Nearly Optimal Constructions of PIR and Batch Codes
Hilal Asi (Technion - Israel Institute of Technology, Israel); Eitan Yaakobi (Technion, Israel)
In this work we study two families of codes with availability, namely private information retrieval (PIR) codes and batch codes. While the former requires that every information symbol has $k$ mutually disjoint recovering sets, the latter asks this property for every multiset request of $k$ information symbols. The main problem under this paradigm is to minimize the number of redundancy symbols. We denote this value by $r_P(n,k), r_B(n,k)$, for PIR, batch codes, respectively, where $n$ is the number of information symbols. Previous results showed that for any constant $k$, $r_P(n,k) = \Theta(\sqrt{n})$ and $r_B(n,k)=\mathcal{O}(\sqrt{n}\log(n)$. In this work we study the asymptotic behavior of these codes for non-constant $k$ and specifically for $k=\Theta(n^\epsilon)$. We also study the largest value of $k$ such that the rate of the codes approaches 1, and show that for all $\epsilon<1$, $r_P(n,n^\epsilon) = o(n)$, while for batch codes, this property holds for all $\epsilon< 0.5$.
pp. 151-155
12:10 Cyclone Codes
Christian Schindelhauer (University of Freiburg & Rechnernetze und Telematik an der Albert-Ludwigs-Universität Freiburg, Germany); Andreas Jakoby (Bauhaus-Universität Weimar, Germany); Sven Köhler (University of Freiburg, Germany)
We introduce Cyclone codes which are rateless erasure resilient codes. They combine Pair codes with Luby Transform (LT) codes by computing a code symbol from a random set of data symbols using bitwise XOR and cyclic shift operations. The number of data symbols is chosen according to the Robust Soliton distribution. XOR and cyclic shift operations establish a unitary commutative ring if data symbols have a length of p − 1 bits, for some prime number p. We consider the graph given by code symbols combining two data symbols. If n/2 such random pairs are given for n data symbols, then a giant component appears, which can be resolved in linear time. We can extend Cyclone codes to data symbols of arbitrary even length, provided the Goldbach conjecture holds. Applying results for this giant component, it follows that Cyclone codes have the same encoding and decoding time complexity as LT codes, while the overhead is upper-bounded by those of LT codes. Simulations indicate that Cyclone codes significantly decreases the overhead of extra coding symbols.
pp. 156-160
12:30 Approaching Capacity Using Incremental Redundancy without Feedback
Haobo Wang, Sudarsan Vasista Srinivasan Ranganathan and Richard Wesel (University of California, Los Angeles, USA)
Variable-length codes with incremental redundancy controlled by feedback allow a system to approach capacity with short average blocklengths and thus relatively low-complexity decoders. This paper shows how to use those same variable-length codes with incremental redundancy to approach capacity without feedback. The general principle is to provide a common pool of redundancy that can be accessed by exactly the variable-length codes that need it. We provide example implementations using both regular and irregular low-density generator matrix (LDGM) codes to provide this common pool of redundancy, utilizing the inter-frame coding approach that Zeineddine and Mansour used to combat rate variation due to fading in broadcast transmissions. Obtaining the LDGM degree distributions requires a new design methodology involving differential evolution for a generalized peeling decoder. Monte-Carlo simulations using a 2dB binary-input additive white Gaussian noise channel confirm the feasibility of this new approach. For a frame error rate of $10^{-3}$, the irregular LDGM code achieves 96% of the throughput of the corresponding feedback system.
pp. 161-165

#### Mo2-2: Locally Repairable Codes 1

Room: Brussels
Chair: Iwan Duursma (University of Illinois at Urbana-Champaign, USA)
11:30 Rate Optimal Binary Linear Locally Repairable Codes with Small Availability
Swanand Kadhe (Texas A&M University, USA); Robert Calderbank (Duke University, USA)
A locally repairable code with availability has the property that every code symbol can be recovered from multiple, disjoint subsets of other symbols of small size. In particular, a code symbol is said to have $(r,t)$-availability if it can be recovered from $t$ disjoint subsets, each of size at most $r$. A code with availability is said to be 'rate optimal', if its rate is maximum among the class of codes with given locality, availability, and alphabet size. This paper focuses on rate-optimal binary, linear codes with small availability, and makes three contributions. First, it establishes tight upper bounds on the rate of binary linear codes with $(r,2)$ and $(2,3)$ availability. Second, it establishes a uniqueness result for binary rate-optimal codes, showing that for certain classes of binary linear codes with $(r,2)$ and $(2,3)$-availability, any rate-optimal code must be a direct sum of shorter rate-optimal codes. Finally, it derives properties of locally repairable codes associated with convex polyhedra, especially, focusing on the codes associated with the Platonic solids. It demonstrates that these codes are locally repairable with $t = 2$, and that the codes associated with (geometric) dual polyhedra are (coding theoretic) duals of each other.
pp. 166-170
11:50 On Optimal Ternary Locally Repairable Codes
Jie Hao and Shutao Xia (Tsinghua University, P.R. China); Bin Chen (South China Normal University, P.R. China)
In an $[n,k,d]$ linear code, a code symbol is said to have locality $r$ if it can be repaired by accessing at most $r$ other code symbols. For an $(n,k,r)$ locally repairable code (LRC), the minimum distance satisfies the well-known Singleton-like bound $d\le n-k-\lceil k/r\rceil +2$. In this paper, we study optimal ternary LRCs meeting this Singleton-like bound by employing a parity-check matrix approach. It is proved that there are only $8$ classes of possible parameters with which optimal ternary LRCs exist. Moreover, we obtain explicit constructions of optimal ternary LRCs for all these $8$ classes of parameters, where the minimum distance could only be 2, 3, 4, 5 and 6.
pp. 171-175
12:10 A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes
Nikhil Krishnan Muralee Krishnan and Bhagyashree Puranik (Indian Institute of Science, India); P Vijay Kumar (Indian Institute of Science & University of Southern California, India); Itzhak Tamo (Tel Aviv University, Israel); Alexander Barg (University of Maryland, USA)
In this paper, we study the impact of locality on the decoding of binary cyclic codes under two approaches, namely ordered statistics decoding (OSD) and trellis decoding. Given a binary cyclic code having locality or availability, we suitably modify the OSD to obtain gains in terms of Signal-To-Noise ratio, for a given reliability and essentially the same level of decoder complexity. With regard to trellis decoding, we show that careful introduction of locality results in the creation of cyclic subcodes having lower maximum state complexity. We also present a simple upper-bounding technique on the state complexity profile, based on the zeros of the code. Finally, it is shown how the decoding speed can significantly be increased in the presence of locality, in the moderate-to-high SNR regime, by making use of a quick-look decoder that often returns the ML codeword.
pp. 176-180
12:30 Locally Repairable Codes with the Optimum Average Information Locality
Locally repairable codes (LRCs) have been proposed and used in practice as effective coding methods for distributed storage systems (DSSs). In a DSS, information block recovery is a critical task performed in the case of data node permanent failure or temporal unavailability. Temporal node unavailability accounts for 90% of all block recoveries triggered in DSS. Since parity blocks are not needed to be recovered during a temporal node unavailability, special attention should be given to reconstruction of information blocks when trying to minimize the average bandwidth needed for block recovery. Motivated by this, in this work, we study the average locality of information blocks. We obtain a lower bound on the average locality of information blocks of LRCs and design LRCs that achieve the bound. In addition to obtaining the optimal average locality for the information blocks, our codes achieve the optimal maximum locality for all the information blocks as well as some parity blocks (in some cases all the parity blocks).
pp. 181-185

Room: K2
Chair: Chandra Nair (Chinese University of Hong Kong, Hong Kong)
11:30 Error Exponent of the Common-Message Broadcast Channel with Variable-Length Feedback
Lan V. Truong and Vincent Y. F. Tan (National University of Singapore, Singapore)
We derive upper and lower bounds on the reliability function for the discrete memoryless broadcast channel with common message and variable-length feedback. We show that the bounds are tight when the broadcast channel is stochastically degraded. We adapt and supplement new ideas to Yamamoto and Itoh's two-phase coding scheme for the direct part and Burnashev's proof technique for the converse part.
pp. 186-190
11:50 Exact Random Coding Exponents and Universal Decoders for the Degraded Broadcast Channel
Ran Averbuch and Neri Merhav (Technion, Israel)
This work contains two main contributions concerning the degraded broadcast channel. The first is an analysis of the exact random coding error exponents for both users, and the second is the derivation of universal decoders for both users. These universal decoders are certain variants of the maximum mutual information (MMI) universal decoder, and which achieve the corresponding random coding exponents. In addition, we introduce some lower bounds, which involve optimization over very few parameters, unlike the original, exact exponents, which involve minimizations over auxiliary probability distributions. Numerical results for the binary symmetric broadcast channel are given as well, which show improvements over previously derived error exponents for the same model.
pp. 191-195
12:10 Feedback Halves the Dispersion for Some Two-User Broadcast Channels with Common Message
Kasper F Trillingsgaard (Aalborg University, Denmark); Wei Yang (Princeton University, USA); Giuseppe Durisi (Chalmers University of Technology, Sweden); Petar Popovski (Aalborg University, Denmark)
We investigate the maximum coding rate achievable on a two-user broadcast channel for the case where a common-message is transmitted using fixed-blocklength codes with feedback. Specifically, we focus on a family of broadcast channels composed of two antisymmetric Z-channels. For this setup, we obtain matching upper and lower bounds on the dispersion term in the asymptotic expansion of the maximum coding rate. These bounds reveal that the dispersion is halved compared to the no-feedback case.
pp. 196-200
12:30 A New Capacity-Approaching Protocol for General 1-to-K Broadcast Packet Erasure Channels with ACK/NACK
Chih-Hua Chang and Chih-Chun Wang (Purdue University, USA)
The capacity region of 1-to-$K$ broadcast packet erasure channels with ACK/NACK is known for some scenarios, e.g., $K\leq 3$, etc. However, existing achievability schemes either require knowing the target rate $\vec{R}$ in advance, and/or have a complicated description of the achievable rate region that is difficult prove whether it matches the capacity or not. This work proposes a new network coding protocol with the following unique set of features: (i) Its achievable rate region is identical to the capacity region for all the scenarios in which the capacity is known; (ii) Its achievable rate region is much more tractable that existing works and has been used to derive new capacity rate vectors; (iii) It employs {\em sequential encoding} that naturally handles dynamic packet arrivals; (iv) It automatically adapts to unknown packet arrival rates $\vec{R}$; (v) It is based on $GF(q)$ with $q>K$. Numerically, for $K=4$, it admits an average control overhead 2--4\% (assuming each packet has 1000 bytes), average encoding memory usage 48.5 packets, and average per-packet delay 94.8 time slots, when operating at 95\% of the capacity.
pp. 201-205

#### Mo2-4: Feedback

Room: K3
Chair: Gerhard Kramer (Technical University of Munich, Germany)
11:30 On the Capacity of Burst Noise-Erasure Channels With and Without Feedback
A class of burst noise-erasure channels which incorporate both errors and erasures during transmission is studied. The channel, whose output is explicitly expressed in terms of its input and a stationary ergodic noise-erasure process, is shown to satisfy a so-called quasi-symmetry'' condition under certain invertibility conditions. As a result, it is proved that a uniformly distributed input process maximizes the channel's block mutual information, resulting in a closed-form formula for its non-feedback capacity in terms of the noise-erasure entropy rate and the entropy rate of an auxiliary erasure process. The feedback channel capacity is also characterized, showing that feedback does not increase capacity and generalizing prior related results.
pp. 206-210
11:50 The ARMA(k) Gaussian Feedback Capacity
Tao Liu and Guangyue Han (The University of Hong Kong, Hong Kong)
Using Kim's variational formulation (with a slight yet important modification), we derive the ARMA(k) Gaussian feedback capacity, i.e., the feedback capacity of an additive channel where the noise is a k-th order autoregressive moving average Gaussian process. More specifically, the ARMA(k) Gaussian feedback capacity is expressed as a simple function of a solution to a system of polynomial equations, which proves to have only finitely many solutions for the cases k = 1,2 and possibly beyond.
pp. 211-215
12:10 An Optimal Coding Scheme for the BIBO Channel with a No-Repeated-Ones Input Constraint
Oron Sabag and Haim H Permuter (Ben-Gurion University, Israel); Navin Kashyap (Indian Institute of Science, India)
A binary-input binary-output (BIBO) channel is investigated in the presence of feedback and input constraints. The feedback capacity and the optimal input distribution of this setting are presented for the case where the input sequence contains no consecutive ones. A simple coding scheme is designed based on the principle of posterior matching, which was introduced by Shayevitz and Feder for memoryless channels. The posterior matching scheme for our input-constrained setting is shown to achieve capacity using two new ideas: \textit{message history}, which captures the memory embedded in the setting, and \textit{message splitting}, which simplifies the scheme analysis. Additionally, in the special case of an S-channel, we give a very simple zero-error coding scheme that achieves capacity.
pp. 216-220

#### Mo2-5: Reconstruction

Room: K4
Chair: Urbashi Mitra (University of Southern California, USA)
11:30 Compressed Sensing with Prior Information via Maximizing Correlation
Xu Zhang, Wei Cui and Yulong Liu (Beijing Institute of Technology, P.R. China)
Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via maximizing the correlation between the prior knowledge and the desired signal. We then present a geometric analysis for the proposed method under sub-gaussian measurements. Our results reveal that if the prior information is good enough, then the proposed approach can improve the performance of the standard CS. Simulations are provided to verify our results.
pp. 221-225
11:50 Low Dimensional Atomic Norm Representations in Line Spectral Estimation
Maxime Ferreira Da Costa (Imperial College London, United Kingdom (Great Britain)); Wei Dai (Imperial College, United Kingdom (Great Britain))
The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. As opposed to discretization-based methods for inverse problems, line spectral estimation reconstructs signals whose spectral supports lie continuously in the Fourier domain. If recent advances have shown that atomic norm relaxation produces highly robust estimates in this context, the computational cost of this approach remains, however, the major flaw for its application to practical systems. In this work, we aim to bridge the complexity issue by studying the atomic norm minimization problem from low dimensional projection of the signal samples. We derive conditions on the sub-sampling matrix under which the partial atomic norm can be expressed by a low-dimensional semidefinite program. Moreover, we illustrate the tightness of this relaxation by showing that it is possible to recover the original signal in poly-logarithmic time for two specific sub-sampling patterns.
pp. 226-230
12:10 Analysis of Approximate Message Passing with a Class of Non-Separable Denoisers
Yanting Ma (North Carolina State University, USA); Cynthia Rush (Columbia University, USA); Dror Baron (North Carolina State University, USA)
Approximate message passing (AMP) is a class of low-complexity scalable algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal $\beta_0$ from noisy, linear measurements y = A $\beta_0$ + w. AMP has the attractive feature that its performance (for example, the mean squared error of its estimates) can be accurately tracked by a simple, scalar iteration referred to as state evolution when the unknown signal has independent and identically distributed (i.i.d.) entries. However, in many real-world applications, like image or audio signal reconstruction, the unknown signal contains dependencies between entries and so a coordinate-wise independence structure is not a good approximation for the prior of the unknown signal. In this paper we study the case where the unknown signal has dependent entries using a class of non-separable sliding-window denoisers and prove that a new form of state evolution still accurately predicts AMP performance in this scenario. This is an early step in understanding the role of non-separable denoisers within AMP, and will lead to a characterization of more general denoisers in problems including compressive image reconstruction.
pp. 231-235
12:30 Inexact Projected Gradients on Unions of Subspaces
Thomas Wiese, Lorenz Weiland and Wolfgang Utschick (Technische Universität München, Germany)
We prove convergence of the projected gradient algorithm with inexact projections when applied to linear inverse problems with constraint sets that are unions of subspaces. Such an algorithm is useful for joint angle and delay estimation in MIMO radar, where classical estimators for angle estimation can be integrated into compressive sensing methods for range estimation.
pp. 236-240

#### Mo2-6: Complexity

Room: K5
Chair: Pulkit Grover (Carnegie Mellon University, USA)
11:30 Analysis and Enhancements of a Cognitive Based Complexity Measure
Dilshan I De Silva and Nuwan Kodagoda (Sri Lanka Institute of Information Technology, Sri Lanka); Saluka Kodituwakku and Amalka J. Pinidiyaarachchi (University of Peradeniya, Sri Lanka)
As stated by Tom DeMacro, something that cannot be measured is uncontrollable. Thus, a number of metrics have been developed to measure the complexity associated with software by considering various aspects such as size, control flow and data flow between modules, cognitive informatics etc. Amongst these aspects, cognitive informatics is recognized as a promising aspect in measuring software complexity. Thus, majority of the complexity metrics that were proposed after the introduction of cognitive informatics have been proposed mainly based on the cognitive aspect. Amongst them, Chhillar and Bhasins' weighted composite complexity measure is one of the few metrics that had attempted to measure the complexity of a program by considering more than three or more complexity factors. After a thorough analysis, in a previous study, the authors identified that the weighted composite complexity measure could be further improved by considering more complexity factors. This paper extends the previous study to identify the most appropriate factors that could be considered by the weighted composite complexity measure. Using the opinions of the industry experts, the authors were able to discover that compound conditional statements, threads and recursion could also be considered by the weighted composite complexity measure. Accordingly, the weighted composite complexity measure was enhanced to capture the complexities that arise due to those factors. The paper also includes a demonstration of the complexity calculation method of the improved weighted composite complexity measure with the use of three sample java programs, which were written by incorporating the above mentioned factors. In addition, an application of the weighted composite complexity measure to the same programs are also given in the paper, to illustrate the changes in complexity values of the two measures.
pp. 241-245
11:50 Generic Cospark of a Matrix Can Be Computed in Polynomial Time
Sichen Zhong (SUNY Stony Brook, USA); Yue Zhao (Stony Brook University, USA)
The cospark of a matrix is the cardinality of the sparsest vector in the column space of the matrix. Computing the cospark of a matrix is well known to be an NP hard problem. Given the sparsity pattern (i.e., the locations of the non-zero entries) of a matrix, if the non-zero entries are drawn from independently distributed continuous probability distributions, we prove that the cospark of the matrix equals, with probability one, to a particular number termed the generic cospark of the matrix. The generic cospark also equals to the maximum cospark of matrices consistent with the given sparsity pattern. We prove that the generic cospark of a matrix can be computed in polynomial time, and offer an algorithm that achieves this.
pp. 246-250
12:10 Enumeration of Boolean Functions of Sensitivity Three and Inheritance of Nondegeneracy
Kazuyuki Amano (Gunma University, Japan)
The sensitivity of a Boolean function is the maximum, over all inputs, of the number of input bits which when flipped change the output of the function. We enumerate all Boolean functions of sensitivity at most three and investigate their properties with the aid of computers. The number of NPN equivalence classes of nondegenerate $n$-variable Boolean functions of sensitivity three is 7, 80, 4215, 190221, 65694, 8873, 848, 64 and 8 for $n=3,4,\ldots, 11$ and zero for $n\geq 12$. We verify that, over all these functions, the maximum of block sensitivity, certificate complexity, decision tree complexity and degree is 6, 6, 9 and 9, respectively. A key to making this enumeration possible is the fact that, for every nondegenerate Boolean function $f$, a subfunction $f|_{x_i=0}$ or $f|_{x_i=1}$ is nondegenerate for some variable $x_i$, which is recently shown by Lee, Lokam, Tsai and Yang [in Proc. of ISIT '15, pages 501-505]. We extend this result by showing that, the minimum number of nondegenerate subfunctions in $\{f|_{x_i=0}, f|_{x_i=1}\}_{1 \leq i\leq n}$ is, in fact, four.
pp. 251-255
12:30 On the Complexity of Estimating Renyi Divergences
Maciej Skorski (IST Austria, Austria)
This paper studies the complexity of estimating Rényi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known a priori. Extending the results of Acharya et al. (SODA'15) on estimating Rényi entropy, we present improved estimation techniques together with upper and lower bounds on the sample complexity. We show that, contrarily to estimating Rényi entropy where a sublinear (in the alphabet size) number of samples suffices, the sample complexity is heavily dependent on \emph{events occurring unlikely} in $q$, and is unbounded in general (no matter what an estimation technique is used). For any divergence of integer order bigger than $1$, we provide upper and lower bounds on the number of samples dependent on probabilities of $p$ and $q$ (the lower bounds hold for non-integer orders as well). We conclude that the worst-case sample complexity is polynomial in the alphabet size if and only if the probabilities of $q$ are non-negligible. This gives theoretical insights into heuristics used in the applied literature to handle numerical instability, which occurs for small probabilities of $q$. Our result shows that they should be handled with care not only because of numerical issues, but also because of a blow up in the sample complexity.
pp. 256-260

#### Mo2-7: ARQ

Room: K6
Chair: Zouheir Rezki (University of Idaho, USA)
11:30 An Information Density Approach to Analyzing and Optimizing Incremental Redundancy with Feedback
Haobo Wang, Nathan Wong, Alexandar M Baldauf, Christopher K Bachelor and Sudarsan Vasista Srinivasan Ranganathan (University of California, Los Angeles, USA); Dariush Divsalar (Jet Propulsion Laboratory, USA); Richard Wesel (University of California, Los Angeles, USA)
This paper uses a case study of a tail-biting convolutional code (with successful decoding indicated by the reliability output Viterbi algorithm) to present an information density approach for analyzing and optimizing the throughput of systems using incremental redundancy controlled by feedback. Polyanskiy's normal approximation combined with a linear model for the information gap of a rate-compatible code family provides a simple and accurate characterization of the behavior of feedback systems employing practical codes, such as convolutional or low-density parity-check codes. Especially for short message lengths on the order of k < 50 message bits, the newly proposed model is more accurate than Vakilinia's model in which the rate of first successful decoding has a Gaussian probability density function.
pp. 261-265
11:50 Outage Effective Capacity of Buffer-Aided Diamond Relay Systems Using HARQ-IR
Deli Qiao (East China Normal University, P.R. China)
In this paper, transmission over buffer-aided diamond relay systems under statistical quality of service (QoS) constraints is studied. The statistical QoS constraints are imposed as limitations on delay violation probabilities. In the absence of channel state information (CSI) at the transmitter, truncated hybrid automatic repeat request-incremental redundancy (HARQ-IR) is incorporated to make better use of the wireless channel and the resources for each communication link. The packets that cannot be successfully received upon the maximum number of transmissions will be removed from buffer, i.e., outage occurs. The outage effective capacity is defined as the maximum constant arrival rate to the source that can be supported by the goodput departure processes, i.e., the departure that can be successfully received by the receiver. The outage effective capacity for the buffer-aided diamond relay system is obtained for HARQ-IR incorporated transmission strategy under the end-to-end delay constraints. In comparison with the decode-and-forward (DF) protocol with perfect CSI at the transmitters, it is shown that HARQ-IR can achieve better performance when the delay constraints are stringent.
pp. 266-270
12:10 Constraints for coded tunnels across long latency bottlenecks with ARQ-based congestion control
Ulrich Speidel (University of Auckland, New Zealand); Sven Puchinger and Martin Bossert (Ulm University, Germany)
This paper considers capacity and delay constraints for coded tunnels across an erasure channel which occurs on shared Internet satellite links. Such links are long latency bottlenecks with a limited capacity input queue which drops packets when it overflows. The latency delays ARQ ACK feedback to senders, making it difficult for them to tune their packet transmission rate. This can cause the input queue to oscillate between empty and overflow. Queue oscillation leaves the link underutilised during the empty phases and slows down large packet flows. Channel coding can in principle provide goodput improvement in this scenario by letting senders accelerate to higher packet rates before burst losses occur and by mitigating exponential backoff after losses. However, this is only possible if the codes preserve sufficient channel capacity for the improved goodput to expand into. We formulate capacity and delay constraints that such block codes must meet. Using loss data obtained on a purpose-built simulator network, we show that such coding is feasible in a practical scenario and that partial unit memory (PUM) codes are particularly suitable for this task. In this context, we propose a part-systematic encoding for PUM codes, which performs slightly better than non-systematic encoding.
pp. 271-275
12:30 Throughput of HARQ-IR with Finite Blocklength Codes and QoS Constraints
Yi Li, M. Cenk Gursoy and Senem Velipasalar (Syracuse University, USA)
In this paper, throughput of hybrid automatic repeat request (HARQ) schemes with finite blocklength codes is studied for both constant-rate and ON-OFF discrete-time Markov arrivals under statistical queuing constraints and deadline limits. After analyzing the decoding error probability and outage probability, the distribution of transmission period is characterized, and the throughput expressions are obtained for both arrival models. Analytical results are verified via Monte Carlo simulations. In the numerical results, the impact of deadline constraints, fixed transmission rate, coding blocklength, and queuing constraints on the throughput is analyzed.
pp. 276-280

#### Mo2-8: Quantum IT 1

Room: K7+8
Chair: Marco Dalai (University of Brescia, Italy)
11:30 Polar Codes for Arbitrary Classical-Quantum Channels and Arbitrary cq-MACs
Rajai Nasser (École Polytechnique Fédérale de Lausanne, Switzerland); Joseph M. Renes (ETH Zurich, Switzerland)
We prove polarization theorems for arbitrary classical-quantum (cq) channels. The input alphabet is endowed with an arbitrary Abelian group operation and an Ar{\i}kan-style transformation is applied using this operation. It is shown that as the number of polarization steps becomes large, the synthetic cq-channels polarize to deterministic homomorphism channels that project their input to a quotient group of the input alphabet. This result is used to construct polar codes for arbitrary cq-channels and arbitrary classical-quantum multiple access channels (cq-MAC). The encoder can be implemented in $O(N\log N)$ operations, where $N$ is the blocklength of the code. A quantum successive cancellation decoder for the constructed codes is proposed. It is shown that the probability of error of this decoder decays faster than $2^{-N^{\beta}}$ for any $\beta<\frac{1}{2}$.
pp. 281-285
11:50 Sphere-Packing Bound for Symmetric Classical-Quantum Channels
Hao-Chung Cheng (National Taiwan University, Taiwan); Min-Hsiu Hsieh and Marco Tomamichel (University of Technology Sydney, Australia)
We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of the subexponential to the polynomial, The established pre-factor is arguably optimal because it matches the best known random coding upper bound in the classical case. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function.
pp. 286-290
12:10 A meta-converse for private communication over quantum channels
Mark M Wilde (Louisiana State University, USA); Marco Tomamichel (University of Technology Sydney, Australia); Mario Berta (California Institute of Technology, USA)
We establish a converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for simplifying the tripartite picture of privacy involving local operations and public classical communication to a bipartite picture of quantum privacy involving local operations and classical communication. This approach has previously led to some of the strongest upper bounds on secret key rates, including the squashed entanglement and the relative entropy of entanglement. Here we use this approach along with a 'privacy test to establish a general meta-converse bound for private communication.
pp. 291-295
12:30 Moderate Deviations for Classical-Quantum Channels
Hao-Chung Cheng (National Taiwan University, Taiwan); Min-Hsiu Hsieh (University of Technology Sydney, Australia)
We show that the reliable communication through a classical-quantum channel is possible when the transmission rate approaches the channel capacity sufficiently slowly. This scenario exists between the non-vanishing error probability regime, where the rate tends to capacity with a fixed error, and the small error probability regime, where the error vanishes given a rate below capacity. The proof employs a sharp concentration bound in strong large deviation theory, and the asymptotic expansions of the error-exponent functions.
pp. 296-300

#### Mo2-9: Source Coding 1

Room: K9
Chair: Lele Wang (Stanford University & Tel Aviv University, USA)
11:30 Entropy of Some General Plane Trees
Zbigniew Golebiewski (Wroclaw University of Science and Technology, Poland); Abram Magner (UIUC, USA); Wojciech Szpankowski (Purdue University, USA)
We continue developing the information theory of advanced data structures. In our previous work, we introduced structural entropy of unlabeled graphs and designed lossless compression algorithms for {\it binary} trees (with structure-correlated vertex names). In this paper, we consider $d$-ary trees ($d\ge 2$) and trees with unrestricted degree for which we compute the entropy (the first step to design optimal compression algorithms). It turns out that extending from binary trees to general trees is mathematically quite challenging and leads to new recurrences that find ample applications in the information theory of structures.
pp. 301-305
11:50 On Optimality and Redundancy of Side Information Version of SWLZ
Ayush Jain (Indian Institute of Technology Kanpur); Rakesh K. Bansal (Indian Institute of Technology Kanpur & India, India)
In this work, we establish the pointwise optimality of side information version of SWLZ algorithm for stationary ergodic sources. We also obtain a pointwise upper bound on the redundancy rate of this side information version of SWLZ algorithm for a subclass of $\phi-$mixing sources, which includes Markov sources as a special case. This upper bound obtained differs only by a constant factor from the best bound that has been obtained on redundancy rate for the original SWLZ algorithm itself.
pp. 306-310
12:10 Two-Dimensional Source Coding by Means of Subblock Enumeration
Takahiro Ota (Nagano Prefectural Institute of Technology, Japan); Hiroyoshi Morita (The University of Electro-Communications, Japan)
A technique of lossless compression via substring enumeration (CSE) is a well-known lossless compression algorithm for a one-dimensional (1D) source. The CSE uses a probabilistic model built from the circular string of an input source for encoding the source. The CSE is applicable to two-dimensional (2D) sources such as images by dealing with a line of pixels of 2D source as a symbol of an extended alphabet. At the initial step of the CSE encoding process, we need to output number of occurrences of all symbols of the extended alphabet, so that the time complexity increases exponentially when the size of source becomes large. To reduce the time complexity, we propose a new CSE which can encode a 2D source in block-by-block instead of line-by-line. The proposed algorithm uses the flat torus of an input 2D source as a probabilistic model instead of the circular string of the source. Moreover, we prove the asymptotic optimality of the proposed algorithm for 2D general sources.
pp. 311-315

#### Mo2-A: Age of Information 2

Room: Berlin 3
Chair: Michele A Wigger (Telecom ParisTech, France)
11:30 Timely Updates over an Erasure Channel
Roy Yates (Rutgers University, USA); Elie Najm (Ecole Polytechnique Fédérale de Lausanne, Switzerland); Emina Soljanin and Jing Zhong (Rutgers University, USA)
Using an age of information (AoI) metric, we examine the transmission of coded updates through a binary erasure channel to a monitor/receiver. We start by deriving the average status update age of an infinite incremental redundancy (IIR) system in which the transmission of a k-symbol update continues until k symbols are received. This system is then compared to a fixed redundancy (FR) system in which each update is transmitted as an n symbol packet and the packet is successfully received if and only if at least k symbols are received. If fewer than k symbols are received, the update is discarded. Unlike the IIR system, the FR system requires no feedback from the receiver. For a single monitor system, we show that tuning the redundancy to the symbol erasure rate enables the FR system to perform as well as the IIR system. As the number of monitors is increased, the FR system outperforms the IIR system that guarantees delivery of all updates to all monitors.
pp. 316-320
11:50 Remote Estimation of the Wiener Process over a Channel with Random Delay
Yin Sun (the Ohio State University, USA); Yury Polyanskiy (MIT, USA); Elif Uysal-Biyikoglu (METU)
In this paper, we consider a problem of sampling a Wiener process, with samples forwarded to a remote estimator via a channel that consists of a queue with random delay. The estimator reconstructs a real-time estimate of the signal from causally received samples. Motivated by recent research on age-of-information, we study the optimal sampling strategy that minimizes the mean square estimation error subject to a sampling frequency constraint. We prove that the optimal sampling strategy is a threshold policy, and find the optimal threshold. This threshold is determined by the sampling frequency constraint and how much the Wiener process varies during the channel delay. An interesting consequence is that even in the absence of the sampling frequency constraint, the optimal strategy is not zero-wait sampling in which a new sample is taken once the previous sample is delivered; rather, it is optimal to wait for a non-zero amount of time after the previous sample is delivered, and then take the next sample. Further, if the sampling times are independent of the observed Wiener process, the optimal sampling problem reduces to an age-of-information optimization problem that has been recently solved. Our comparisons show that the estimation error of the optimal sampling policy is much smaller than those of age-optimal sampling, zero-wait sampling, and classic uniform sampling.
pp. 321-325
12:10 Age and Value of Information: Non-linear Age Case
Antzela Kosta and Nikolaos Pappas (Linköping University, Sweden); Anthony Ephremides (University of Maryland, USA); Vangelis Angelakis (Linköping University, Sweden)
We consider a real-time status update system consisting of a source-destination network. A stochastic process is observed at the source, and samples, so called status updates, are extracted at random time instances, and delivered to the destination. In this paper, we expand the concept of information ageing by introducing the Cost of Update Delay (CoUD) metric to characterize the cost of having stale information at the destination. We introduce the Value of Information of Update (VoIU) metric that captures the reduction of CoUD upon reception of an update. The importance of the VoIU metric lies on its tractability which enables an alternative performance criterion in status update systems.
pp. 326-330
12:30 Status Updates Over Unreliable Multiaccess Channels
Sanjit Kaul (IIIT Delhi, India); Roy Yates (Rutgers University, USA)
Applications like environmental sensing, and health and activity sensing, are supported by networks of devices (nodes) that send periodic packet transmissions over the wireless channel to a sink node. We look at simple abstractions that capture the following commonalities of such networks (a) the nodes send periodically sensed information that is temporal and must be delivered in a timely manner, (b) they share a multiple access channel and (c) channels between the nodes and the sink are unreliable (packets may be received in error) and differ in quality. We consider scheduled access and slotted ALOHA-like random access. Under scheduled access, nodes take turns and get feedback on whether a transmitted packet was received successfully by the sink. During its turn, a node may transmit more than once to counter channel uncertainty. For slotted ALOHA-like access, each node attempts transmission in every slot with a certain probability. For these access mechanisms we derive the age of information (AoI), which is a timeliness metric, and arrive at conditions that optimize AoI at the sink. We also analyze the case of symmetric updating, in which updates from different nodes must have the same AoI. We show that ALOHA-like access, while simple, leads to AoI that is worse by a factor of about $2e$, in comparison to scheduled access.
pp. 331-335

Room: K1

### Monday, June 26, 14:40 - 16:20

#### Mo3-1: Reed-Solomon Codes

Room: Europa
Chair: Alexander Vardy (University of California San Diego, USA)
14:40 Twisted Reed-Solomon Codes
Peter Beelen (Technical University of Denmark, Denmark); Sven Puchinger (Ulm University, Germany); Johan S. H. Rosenkilde (Technical University of Denmark, Denmark)
We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the new codes are not equivalent to a Reed--Solomon code.
pp. 336-340
15:00 Iterative Soft-Decision Decoding of Reed-Solomon Codes of Prime Lengths
Shu Lin (UC Davis, USA); Khaled Abdel-Ghaffar (University of California, USA); Juane Li (University of California at Davis, USA); Keke Liu (Broadcom, USA)
A novel scheme is presented for encoding and decoding of Reed-Solomon codes of prime lengths. Encoding is performed on a collection of codewords which are mapped through Galois Fourier transform into a codeword in a low-density parity-check code with a binary parity-check matrix for transmission. Using this matrix, a binary iterative soft-decision decoding algorithm is applied to jointly decode a collection of codewords in the Reed-Solomon code. By allowing information sharing among the received vectors corresponding to the codewords in the collection, the proposed decoding scheme achieves superior performance over algorithms decoding individual Reed-Solomon codewords including maximum likelihood decoding.
pp. 341-345
15:20 Optimal Repair Schemes for Some Families of Full-Length Reed-Solomon Codes
Hoang Dau (University of Illinois at Urbana-Champaign, USA); Olgica Milenkovic (University of Illinois at Urbana-Champaign (UIUC), USA)
Reed-Solomon codes have found many applications in practical storage systems, but were until recently considered unsuitable for distributed storage applications due to the widely-held belief that they have poor repair bandwidth. The work of Guruswami and Wootters (STOC'16) has shown that one can actually perform bandwidth-efficient linear repair with Reed-Solomon codes: When the codes are over the field $\mathbb{F}_{q^t}$ and the number of parities $r \geq q^s$, where $(t-s)$ divides $t$, there exists a linear scheme that achieves a repair bandwidth of $(n-1)(t-s)\log_2 q$ bits. We extend this result by showing the existence of such a linear repair scheme for every $1 \leq s < t$. Moreover, our new schemes are optimal among all linear repair schemes for Reed-Solomon codes when $n = q^t$ and $r = q^s$. Additionally, we improve the lower bound on the repair bandwidth for Reed-Solomon codes, also established in the work of Guruswami and Wootters.
pp. 346-350
15:40 Repairing Reed-Solomon Codes With Two Erasures
Hoang Dau and Iwan Duursma (University of Illinois at Urbana-Champaign, USA); Han Mao Kiah (Nanyang Technological University, Singapore); Olgica Milenkovic (University of Illinois at Urbana-Champaign (UIUC), USA)
Despite their exceptional error-correcting properties, Reed-Solomon codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the whole file to be reconstructed in order to recover a single erased codeword symbol. In a recent work, Guruswami and Wootters (STOC'16) proposed a single-erasure repair method for Reed-Solomon codes that achieves the optimal repair bandwidth amongst all linear encoding schemes. We extend their trace collection technique to cope with two erasures.
pp. 351-355
16:00 Decoding of Interleaved Reed-Solomon Codes Using Improved Power Decoding
Sven Puchinger (Ulm University, Germany); Johan S. H. Rosenkilde (Technical University of Denmark, Denmark)
We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code length $n$. For $m>2$, this is an asymptotic improvement over the previous state-of-the-art for all rates, and the first improvement for $R>1/3$ in the last $20$ years. The method combines collaborative decoding of IRS codes with power decoding up to the Johnson radius.
pp. 356-360

#### Mo3-2: LDPC Codes 1

Room: Brussels
Chair: Paul H. Siegel (University of California, San Diego, USA)
14:40 Average Spectra for Ensembles of LDPC Codes and Applications
Irina Bocharova and Boris D. Kudryashov (St. Petersburg University of Information Technologies, Mechanics and Optics, Russia); Vitaly Skachek and Yauhen Yakimenka (University of Tartu, Estonia)
The exact values of finite length average weight distributions for both binary ensembles and binary images of nonbinary ensembles of regular LDPC codes are computed. The exact average stopping set distribution for the binary ensemble is also obtained. The computed spectra are applied in order to bound from above the average stopping redundancy of the ensemble of binary regular LDPC codes. The exponents both of the average weight distribution for the binary image of the ensemble of nonbinary regular LDPC codes and of the average stopping weight distribution for the binary regular LDPC codes are also presented.
pp. 361-365
15:00 Time-invariant LDPC convolutional codes
Dimitris Achlioptas (University of california, USA); Hamed Hassani (University of Pennsylvania, USA); Wei Liu and Ruediger L Urbanke (EPFL, Switzerland)
Spatially coupled codes have been shown to universally achieve the capacity for a large class of channels. Many variants of such codes have been introduced to date. We discuss a further such variant that is particularly simple and is determined by a very small number of parameters. More precisely, we consider time-invariant low-density convolutional codes with very large constraint lengths. We show via simulations that, despite their extreme simplicity, such codes still show the threshold saturation behavior known from the spatially coupled codes discussed in the literature. Further, we show how the typical minimum stopping set size is related to basic parameters of the code. Due to their simplicity and good performance, these codes might be attractive from an implementation perspective.
pp. 366-370
15:20 On LDPC Code Ensembles with Generalized Constraints
Yanfang Liu, Pablo M. Olmos and Tobias Koch (Universidad Carlos III de Madrid & Gregorio Marañón Health Research Institute, Spain)
In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and Maximum Likelihood (ML) decoding at GC nodes into our analysis without resorting on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoder (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a success probability that depends on the GC block code and its decoding algorithm. The P-PD asymptotic performance can be predicted using standard techniques for LDPC codes. Further, we propose a class of GLDPC ensembles for which the simulated P-PD performance numerically coincides with the actual performance of the GLPDC code. The methodology presented may serve as a reference for the design of coding systems based on spare graphs with generalized constraints
pp. 371-375
15:40 Non-Uniformly Coupled LDPC Codes: Better Thresholds, Smaller Rate-loss, and Less Complexity
Laurent Schmalen, Vahid Aref and Fanny Jardel (Nokia Bell Labs, Germany)
We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing the amount of coupling between spatial positions, we show that we can construct codes with excellent thresholds and small rate loss, even with the lowest possible smoothing parameter and large variable node degrees, which are required for low error floors. We also establish that the decoding convergence speed is faster with non-uniformly coupled codes, which we verify by density evolution of windowed decoding with a finite number of iterations. We also show that by only slightly increasing the smoothing parameter, practical codes with potentially low error floors and thresholds close to capacity can be constructed. Finally, we give some indications on protograph designs.
pp. 376-380
16:00 Reed-Solomon Based Nonbinary Globally Coupled LDPC Codes: Correction of Random Errors and Bursts of Erasures
Juane Li (University of California at Davis, USA); Keke Liu (Broadcom, USA); Shu Lin (UC Davis, USA); Khaled Abdel-Ghaffar (University of California, USA)
This paper presents a special type of nonbinary LDPC codes which are constructed based on Reed-Solomon codes. For a code of this type, its Tanner graph is composed of a set of disjoint and identical Tanner graphs, which are coupled together by a group of global check-nodes. Such a code is called a globally coupled LDPC code. This type of codes are capable of correcting random symbol errors, multiple phased bursts of erasures, and a single long burst of erasures.
pp. 381-385

#### Mo3-3: Caching 1

Room: K2
Chair: Osvaldo Simeone (King's College London, United Kingdom (Great Britain))
14:40 Characterizing the Rate-Memory Tradeoff in Cache Networks within a Factor of 2
Qian Yu (University of Southern California, USA); Mohammad Ali Maddah-Ali (Bell Labs, Alcatel Lucent, USA); Salman Avestimehr (University of Southern California, USA)
We consider a basic caching system, where a single server with a database of $N$ files (e.g. movies) is connected to a set of $K$ users through a shared bottleneck link. Each user has a local cache memory with a size of $M$ files. The system operates in two phases: a placement phase, where each cache memory is populated up to its size from the database, and a following delivery phase, where each user requests a file from the database, and the server is responsible for delivering the requested contents. The objective is to design the two phases to minimize the load (peak or average) of the bottleneck link. We characterize the rate-memory tradeoff of the above caching system within a factor of 2.00884 for both the peak rate and the average rate (under uniform file popularity), where the best proved characterization in the current literature gives a factor of 4 and 4.7 respectively. Moreover, in the practically important case, where the number of files ($N$) is large, we exactly characterize the tradeoff for systems with no more than 5 users, and characterize the tradeoff within a factor of 2 otherwise. We establish these results by developing novel information theoretic outer-bounds for the caching problem, which improves the state of the art and gives tight characterization in various cases.
pp. 386-390
15:00 A Computer-Aided Investigation on the Fundamental Limits of Caching
Chao Tian (University of Tennessee Knoxville, USA)
We present our recent effort, in the context of the caching systems, in developing a computer-aided approach in the investigation of information systems. Yeung's linear programming (LP) outer bound of the entropy space is our starting point, however our effort goes significantly beyond using it to prove information inequalities. A symmetry-reduced linear program is used to identify the boundary of the memory-transmission-rate tradeoff for several simple cases, for which we can obtain a set of tight outer bounds. General hypotheses on the optimal tradeoff are formed from these computed data, which are then analytically proved. This leads to a complete characterization of the optimal tradeoff for caching systems with only two users, and a partial characterization for systems with only two files. Next, we show that by carefully analyzing the joint entropy structure of the outer bounds for certain cases, a novel code construction can be reverse-engineered, and unachievability of linear codes can be proved for some other cases. Finally, we show that strong outer bounds can be computed through strategically relaxing the LP, which allows us to compute outer bounds for larger problem cases, despite the seemingly impossible computation scale.
pp. 391-395
15:20 Capacity Scaling of Wireless Device-to-Device Caching Networks under the Physical Model
An Liu and Vincent Lau (Hong Kong University of Science and Technology, Hong Kong); Giuseppe Caire (Technische Universität Berlin, Germany)
We study the capacity scaling law of a device-to-device (D2D) caching network where n nodes are placed on a regular grid of area n. Each node caches some (coded) bits from a content library and requests a file from the library independently according to the Zipf popularity distribution. We propose a cache-induced hierarchical cooperation scheme which achieves the optimal capacity scaling law under a commonly used "physical model". When the path loss exponent $\alpha<3$, the capacity scaling law can be significantly better than the throughput scaling laws achieved by the existing state-of-the-art schemes. To the best of our knowledge, this is the first work that completely characterizes the capacity scaling law for wireless caching networks under the physical model.
pp. 396-400
15:40 Wireless Coded Caching: A Topological Perspective
Jingjing Zhang and Petros Elia (EURECOM, France)
We explore the performance of coded caching in a SISO BC setting where some users have higher link capacities than others. Focusing on a binary and fixed topological model where strong links have a fixed normalized capacity 1, and where weak links have reduced normalized capacity $\tau < 1$, we identify — as a function of the cache size and $\tau$ — the optimal throughput performance, within a factor of at most 8. The transmission scheme that achieves this performance, employs a simple form of interference enhancement, and exploits the property that weak links attenuate interference, thus allowing for multicasting rates to remain high even when involving weak users. This approach ameliorates the negative effects of uneven topology in multicasting, now allowing all users to achieve the optimal performance associated to $\tau = 1$, even if $\tau$ is approximately as low as $\tau \leq 1-(1-w)^g$ where $g$ is the coded-caching gain, and where $w$ is the fraction of users that are weak. This leads to the interesting conclusion that for coded multicasting, the weak users need not bring down the performance of all users, but on the contrary to a certain extent, the strong users can lift the performance of the weak users without any penalties on their own performance. Furthermore for smaller ranges of $\tau$, we also see that achieving the near-optimal performance comes with the advantage that the strong users do not suffer any additional delays compared to the case where $\tau = 1$.
pp. 401-405
16:00 Multiplex Conductance and Gossip Based Information Spreading in Multiplex Networks
Yufan Huang (North Carolina State University, USA); Huaiyu Dai (NC State University, USA)
In this work, we study the information spreading time in multiplex networks, adopting the gossip (random-walk) based information spreading model. A new metric called multiplex conductance is defined based on the multiplex network structure and used to quantify the information spreading time in a general multiplex network in the idealized setting. Multiplex conductance is then evaluated for some interesting multiplex networks to facilitate understanding in this new area. Finally, the tradeoff between the information spreading efficiency improvement and the layer cost is examined to explain the user's social behavior and motivate effective multiplex network designs.
pp. 406-410

#### Mo3-4: Channel Capacity 1

Room: K3
Chair: Min Li (The University of Newcastle, Australia)
14:40 Capacity of Discrete-Time Wiener Phase Noise Channels to Within a Constant Gap
Luca Barletta (Politecnico di Milano, Italy); Stefano Rini (National Chiao Tung University, Taiwan)
The capacity of the discrete-time channel affected by both additive Gaussian noise and Wiener phase noise is studied. Novel inner and outer bounds are presented, which differ of at most $6.65$ bits per channel use for all channel parameters. The capacity of this model can be subdivided in three regimes: (i) for large values of the frequency noise variance, the channel behaves similarly to a channel with circularly uniform iid phase noise; (ii) when the frequency noise variance is small, the effects of the additive noise dominate over those of the phase noise, while (iii) for intermediate values of the frequency noise variance, the transmission rate over the phase modulation channel has to be reduced due to the presence of phase noise.
pp. 411-415
15:00 Capacity Sensitivity in Additive Non-Gaussian Noise Channels
Malcolm Egan and Samir M. Perlaza (INRIA, France); Vyacheslav Kungurtsev (Czech Technical University in Prague, Czech Republic)
In this paper, a new framework based on the notion of \textit{capacity sensitivity} is introduced to study the capacity of continuous memoryless point-to-point channels. The capacity sensitivity reflects how the capacity changes with small perturbations in any of the parameters describing the channel, even when the capacity is not available in closed-form. This includes perturbations of the cost constraints on the input distribution as well as on the channel distribution. The framework is based on continuity of the capacity, which is shown for a class of perturbations in the cost constraint and the channel distribution. The continuity then forms the foundation for obtaining bounds on the capacity sensitivity. As an illustration, the capacity sensitivity bound is applied to obtain scaling laws when the support of additive $\alpha$-stable noise is truncated.
pp. 416-420
15:20 Communicating under Temperature and Energy Harvesting Constraints
Omur Ozel (Carnegie Mellon University, USA); Sennur Ulukus (University of Maryland, USA); Pulkit Grover (Carnegie Mellon University, USA)
Temperature constraints arise naturally in communication scenarios where the act of data transmission causes heat dissipation in a temperature sensitive situation due to radiation. We address this problem in point to point communications over an additive white Gaussian noise channel in an information theoretic setting. In the specific scenario, transmitted code symbols cause heat dissipation as an input to a first order discrete time heat circuit and the output of this dynamical system, being the temperature, has to remain below a critical level $T_c$. Additionally, we allow the transmitter to use an energy harvesting device to power its transmission. We investigate channel capacity for various combinations of peak and average temperature, average power, and energy harvesting constraints on the transmitted code symbols.
pp. 421-425
15:40 On Additive Channels with Generalized Gaussian Noise
Alex Dytso (Princeton University, USA); Ronit Bustin (Tel Aviv University, Israel); H. Vincent Poor (Princeton University, USA); Shlomo (Shitz) Shamai (The Technion, Israel)
The paper considers a problem of communication over an additive noise channel where the noise is distributed according to a Generalized Gaussian (GG) distribution. In the first part of the paper, a number of properties of the family of GG distributions are derived which are of independent interest. For example, considerable attention is given to the properties of the characteristic function of the GG distribution. In the second part of the paper, the capacity of an additive noise channel with GG noise is considered under p-th absolute moment constraints. It is shown that, even though Shannon's upper bound is achievable in some instances, in general such achievability is not possible. Moreover, it is shown that discrete inputs can achieve capacity within a constant gap or full degree of freedom for any p-th absolute moment constraint. Following the seminal work of Smith, the paper also gives a condition under which discrete inputs are exactly optimal.
pp. 426-430
16:00 The Capacity of Injective Semi-Deterministic Two-Way Channels
Anas Chaaban (King Abdullah University of Science and Technology, Saudi Arabia); Lav R. Varshney (University of Illinois at Urbana-Champaign, USA); Mohamed-Slim Alouini (King Abdullah University of Science and Technology (KAUST), Saudi Arabia)
The capacity region of the class of injective semi-deterministic two-way channels (TWCs) is investigated in this paper. To characterize this capacity, two conditions under which Shannon's bounds on the capacity region of TWCs are tight are first given. Using those conditions, it is shown that the capacity of this class of TWCs is characterized by the rectangle formed by the one-way capacities. This proves that adaptation is not needed for this class. This class encompasses, among others, all memoryless additive channels with input-independent noise, and hence, adaptation is useless for all such channels. This also shows that there exist continuous additive TWCs not of the exponential family type for which adaptation is not necessary. An example of a Cauchy TWC is given, and its capacity is characterized in closed form under a logarithmic constraint. Finally, the impact of the dependence of the noise on the inputs is discussed, and it is shown that adaptation may still be useless in such cases.
pp. 431-435

#### Mo3-5: Detection and Estimation 1

Room: K4
Chair: Venugopal Veeravalli (University of Illinois at Urbana-Champaign, USA)
14:40 Sequential Estimation based on Conditional Cost
George V. Moustakides (University of Patras, Greece); Tony Yaacoub and Yajun Mei (Georgia Institute of Technology, USA)
We consider the problem of parameter estimation under a sequential framework. Specifically we assume that an i.i.d. random process is observed sequentially with its common pdf having a random parameter that must be estimated. We are interested in designing a stopping time that will decide when is the best moment to stop sampling the process and an estimator that will use the acquired samples in order to provide the desired estimate. We follow a semi-Bayesian approach where we assign a cost which is a function of the estimate and the true parameter value and our goal is to minimize the average sample size guaranteeing at the same time that the average cost stays below some prescribed level. For our analysis we adopt a conditional average cost which leads to a considerable simplification in the sequential estimation problem, otherwise known to be analytically intractable. We apply our results to a number of examples and compare our method with the optimum fixed sample size but also with existing sequential schemes.
pp. 436-440
15:00 Fundamental limit of resolving two point sources limited by an arbitrary point spread function
Ronan Kerviche (University of Arizona, USA); Saikat Guha (Raytheon BBN Technologies, USA); Amit Ashok (University of Arizona, USA)
Estimating the angular separation between two incoherently radiating monochromatic point sources is a canonical toy problem to quantify spatial resolution in imaging. In recent work, Tsang et al. showed, using a Fisher Information analysis, that Rayleigh's resolution limit is just an artifact of the conventional wisdom of intensity measurement in the image plane. They showed that the optimal sensitivity of estimating the angle is only a function of the total photons collected during the camera's integration time but entirely independent of the angular separation itself no matter how small it is, and found the information-optimal mode basis, intensity detection in which achieves the aforesaid performance. We extend the above analysis, which was done for a Gaussian point spread function (PSF) to a hard-aperture pupil proving the information optimality of image-plane sinc-Bessel modes, and generalize the result further to an arbitrary PSF. We obtain new counterintuitive insights on energy vs. information content in spatial modes, and extend the Fisher Information analysis to exact calculations of minimum mean squared error, both for Gaussian and hard aperture pupils.
pp. 441-445
15:20 Denoising Linear Models with Permuted Data
Ashwin Pananjady, Martin J. Wainwright and Thomas Courtade (University of California, Berkeley, USA)
We consider the multivariate linear regression model with shuffled data and additive Gaussian noise, which arises in various correspondence estimation and matching problems. We focus on the denoising problem and characterize the minimax error rate up to logarithmic factors. We also analyze the performance of two versions of a computationally efficient estimator that are consistent for a large range of input parameters. Finally, we provide an exact algorithm for the noiseless problem and demonstrate its performance on an image point-cloud matching task. Our analysis also extends to datasets with outliers.
pp. 446-450
15:40 Signal Recovery from Unlabeled Samples
Saeid Haghighatshoar and Giuseppe Caire (Technische Universität Berlin, Germany)
In this paper, we study the recovery of a signal from a collection of unlabeled and possibly noisy measurements via a measurement matrix with random i.i.d. Gaussian components. We call the measurements unlabeled since their order is missing, namely, it is not known a priori which elements of the resulting measurements correspond to which row of the measurement matrix. We focus on the special case of ordered measurements, where only a subset of the measurements is kept and the order of the taken measurements is preserved. We identify a natural duality between this problem and the traditional Compressed Sensing, where we show that the unknown support (location of nonzero elements) of a sparse signal in Compressed Sensing corresponds in a natural way to the unknown location of the measurements kept in unlabeled sensing. While in Compressed Sensing it is possible to recover a sparse signal from an under-determined set of linear equations (less equations than the dimension of the signal), successful recovery in unlabeled sensing requires taking more samples than the dimension of the signal. We develop a low-complexity alternating minimization algorithm to recover the initial signal from the set of its unlabeled samples. We also study the behavior of the proposed algorithm for different signal dimensions and number of measurements empirically via numerical simulations. The results are a reminiscent of the phase-transition similar to that occurring in Compressed Sensing.
pp. 451-455
16:00 Estimation of Sparsity via Simple Measurements
Abhishek Agarwal (University of Minnesota-Twin Cities, USA); Larkin Flodin and Arya Mazumdar (University of Massachusetts Amherst, USA)
We consider several related problems of estimating the sparsity' or number of nonzero elements $d$ in a length $n$ vector $\boldsymbol{\mathbf{x}}$ by observing only $\boldsymbol{\mathbf{b}} = M \odot \boldsymbol{\mathbf{x}}$, where $M$ is a predesigned test matrix independent of $\boldsymbol{\mathbf{x}}$, and the operation $\odot$ varies between problems. We aim to provide a $\Delta$-approximation of sparsity for some constant $\Delta$ with a minimal number of measurements (rows of $M$). This framework generalizes multiple problems, such as estimation of sparsity in group testing and compressed sensing. We use techniques from coding theory as well as probabilistic methods to show that $O(D \log D \log n)$ rows are sufficient when the operation $\odot$ is logical OR (i.e., group testing), and nearly this many are necessary, where $D$ is a known upper bound on $d$. When instead the operation $\odot$ is multiplication over $\mathbb{R}$ or a finite field, we show that respectively $\Theta(D)$ and $\Theta(D \log \frac{n}{D})$ measurements are necessary and sufficient.
pp. 456-460

#### Mo3-6: Wireless Networks 1

Room: K5
Chair: Andrea Goldsmith (Stanford University, USA)
14:40 On Optimal Link Scheduling with Deadlines for Emptying a Wireless Network
Qing He and Di Yuan (Linköping University, Sweden); Anthony Ephremides (University of Maryland, USA)
We consider link scheduling in wireless networks for emptying the queues at the transmitters in minimum time, with time constraints, or deadlines, for one or multiple individual links. We formulate the minimum-time scheduling problem with deadlines (MTSD) mathematically and derive the optimal activation order of the link sets in a schedule solution. Theoretical results are obtained, showing that the MTSD can be treated as the conventional minimum-time scheduling problem by "absorbing" the deadline constraints into the rate region where the scheduling problem is defined. By this approach, optimality characterization and geometric interpretation for the MTSD are provided. Furthermore, we extend the results to the MTSD in a general form that accommodates an arbitrary rate region.
pp. 461-465
15:00 On the Coverage Probability of a Spatially Correlated Network
Chang-sik Choi, Jae Oh Woo and Jeffrey Andrews (The University of Texas at Austin, USA)
We propose a new cellular network model that captures both strong repulsion and randomness between base stations. The base station are modeled by superposition of a random shifted grid with intensity λg for the grid base stations and an independent Poisson point process with intensity λp for the random base stations. Assuming that the typical user is associated with the base station that provides the strongest average receive signal power, we derive the association probability of the typical user. In Rayleigh fading channels, the coverage probability of the typical user at the origin is derived.
pp. 466-470
15:20 Efficiently Finding Simple Schedules in Gaussian Half-Duplex Relay Line Networks
Yahya H. Ezzeldin (University of California, Los Angeles, USA); Martina Cardone (University of Califonia, Los Angeles, USA); Christina Fragouli (UCLA, USA); Daniela Tuninetti (University of Illinois at Chicago, USA)
The problem of operating a Gaussian Half-Duplex (HD) relay network optimally is challenging due to the exponential number of listen/transmit network states that need to be considered. Recent results have shown that, for the class of Gaussian HD networks with N relays, there always exists a simple schedule, i.e., with at most N +1 active states, that is sufficient for approximate (i.e., up to a constant gap) capacity characterization. This paper investigates how to efficiently find such a simple schedule over line networks. Towards this end, a polynomial-time algorithm is designed and proved to output a simple schedule that achieves the approximate capacity. The key ingredient of the algorithm is to leverage similarities between network states in HD and edge coloring in a graph. It is also shown that the algorithm allows to derive a closed-form expression for the approximate capacity of the Gaussian line network that can be evaluated distributively and in linear time.
pp. 471-475
15:40 Exact Speed and Transmission Cost in a Simple One-Dimensional Wireless Delay-Tolerant Network
Dimitrios Cheliotis (University of Athens, Greece); Ioannis Kontoyiannis (Athens UniversityEcon & Business, Greece); Michail Loulakis (National Technical University of Athens, Greece); Stavros Toumpis (Research Center - Athens University of Economics and Business, Greece)
We study a simple one-dimensional, discrete-time network model that consists of two nodes moving on a discrete circle, changing their direction of movement randomly, and a single packet traveling in the clockwise direction, using combinations of transmissions between the two nodes (when they are co-located) and physical transports on their buffers. In this setting, we provide exact, explicit expressions for the long-term averages of the packet speed and the wireless transmission cost. Our work is a first step towards providing simple and exact results for more realistic wireless delay-tolerant network models.
pp. 476-480
16:00 Analysis of Breakdown Probability of Wireless Sensor Networks with Unreliable Relay Nodes
Takayuki Nozaki (Yamaguchi University, Japan); Takafumi Nakano and Tadashi Wadayama (Nagoya Institute of Technology, Japan)
In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A survivor graph is the induced subgraph obtained by removing the broken relay nodes and their connecting edges from the original graph. If the survivor network is disconnected, we consider a network breakdown happens. The primal contribution of the paper is to derive an upper bound of the average network breakdown probability, where the expectation is taken over a regular graph ensemble. The proof of the bound is based on a natural one-to-one correspondence between a regular graph and a regular bipartite graph, and also on enumeration of bipartite graphs satisfying certain conditions. This proof argument is inspired by the analysis of weight distribution for low-density parity-check codes. Compared with estimates of the average network breakdown probability obtained by computer experiments, it is observed that the upper bound provides the values which are not only upper bounds but also precise estimates of the network breakdown probability when the node breakdown probability is small.
pp. 481-485

#### Mo3-7: Communications 1

Room: K6
Chair: Nan Liu (Southeast University, P.R. China)
14:40 Optimal Frame Synchronization Over a Finite State Markov Channel
M Sundaram R, Arup Kumar Das, Devendra Jalihal and Venkatesh Ramaiyan (Indian Institute of Technology Madras, India)
We study a problem of sequential frame detection over a finite state Markov channel (FSMC). We consider an asynchronous framework, where a sync frame of length $N$ symbols is transmitted uniformly over a large interval of known size $A$ slots. In this setup, we study the scaling needed of the sync frame length $N$ with the asynchronism interval length $A$ for error-free frame synchronization. We study the problem when channel state information (CSI) is known at the transmitter and the receiver, and compute a synchronization threshold, $\bar{\alpha}$, that relates the average sync frame length $\bar{N}$ and $A$ as $\bar{N} > \frac{\log_2(A)}{\bar{\alpha}}$ for asymptotic frame synchronization. Our discussion includes the description of a variable length and adaptive code word for FSMC that achieves the optimal delay performance.
pp. 486-490
15:00 Two-way Interference Channels with Jammers
Sidharth Jaggi (Chinese University of Hong Kong, Hong Kong); Michael Langberg (State University of New York at Buffalo, USA)
Alice and Bob want to exchange information over an additive interference channel that also contains a malicious eavesdropper-jammer James who aims to disrupt this two-way communication. In the baseline model (motivated by wireless jamming scenarios), Alice and Bob transmit length-$n$ $q$-ary encodings $x_A$ and $x_B$ respectively of their own messages. James observes the interference pattern $z = x_A + x_B$, and as a non-causal function of $z$ and his knowledge of Alice and Bob's codebooks, chooses a jamming pattern s of power (Hamming weight) at most $pn$. Alice and Bob then both observe the interfered-jammed signal $x_A + x_B + s$, and aim to decode each others' messages despite the jamming pattern $s$. We demonstrate that in such a model, the fact of interference actually aids communication by allowing for communication to occur in each direction at a rate of $1-H_q(p)$, i.e., the jammer can do no worse than act like random noise''. Interestingly, neither linear codes nor random codes (as usually'' defined) achieve this performance --- we thus define and analyze a new class of linearish'' codes that do. We then extend our results to general $q$-ary additive-error channels with asymmetric jamming patterns (with potentially different powers) to Alice and Bob, and also demonstrate how to simultaneously ensure information-theoretic secrecy of both Alice and Bob's messages from James.
pp. 491-495
15:20 Bit-Interleaved Coded Modulation for Phase Shift Keying on the Hypersphere
Christoph Rachinger (University of Erlangen-Nuremberg, Germany); Ralf R. Müller (Friedrich-Alexander Universität Erlangen-Nürnberg, Germany); Johannes Huber (University of Erlangen-Nuremberg, Germany)
We analyze the performance of Bit-Interleaved Coded Modulation (BICM) for Multiple-Input Multiple-Output (MIMO) systems employing Phase Shift Keying on the Hypersphere (PSKH), an extension of Phase Shift Keying (PSK) to higher dimensions. Because the quality of BICM relies on the bit-mapping between coded bits and signal points, PSKH constellations with superior distance properties and capacities might have poor power efficiency. In this paper, we analyze these losses in power efficiency and propose a new method to generate PSKH constellations, i.e., spherical codes, together with a BICM optimized bit-mapping. It turns out that for one bit per real dimension, individual QPSK per antenna is optimal, whereas for other constellation sizes notable gains can be achieved.
pp. 496-500
15:40 Rigorous Dynamics of Expectation-Propagation-Based Signal Recovery from Unitarily Invariant Measurements
Keigo Takeuchi (Toyohashi University of Technology, Japan)
This paper investigates sparse signal recovery based on expectation propagation (EP) from unitarily invariant measurements. A rigorous analysis is presented for the state evolution (SE) of an EP-based message-passing algorithm in the large system limit, where both input and output dimensions tend to infinity at an identical speed. The main result is the justification of an SE formula conjectured by Ma and Ping.
pp. 501-505
16:00 Geometrically uniform differential vector signaling schemes
Ezio Biglieri (Universitat Pompeu Fabra, Barcelona, Spain); Emanuele Viterbo (Monash University, Australia)
Using a geometric approach, we examine the design and the performance of geometrically uniform line coding schemes transmitting $b$ bits over $w=b+1$ wires and obtained from a subset of a permutation modulation signal set.
pp. 506-510

#### Mo3-8: Compressed Sensing 1

Room: K7+8
Chair: Gerhard Wunder (FU Berlin, Heisenberg Communications and Information Theory Group, Germany)
14:40 Statistical and computational phase transitions in spiked tensor estimation
Thibault Lesieur (Institut de Physique Théorique CEA, France); Leo Miolane (INRIA, DI ENS, France); Marc Lelarge (INRIA and ENS, France); Florent Krzakala (Ecole Normale Superieure, France); Lenka Zdeborova (Institut de Physique Theorique IPhT, CEA Saclay and CNRS, France)
We consider tensor factorizations using a generative model and a Bayesian approach. We compute rigorously the mutual information, the Minimal Mean Square Error (MMSE), and unveil information-theoretic phase transitions. In addition, we study the performance of Approximate Message Passing (AMP) and show that it achieves the MMSE for a large set of parameters, and that factorization is algorithmically "easy" in a much wider region than previously believed. It exists, however, a "hard" region where AMP fails to reach the MMSE and we conjecture that no polynomial algorithm will improve on AMP.
pp. 511-515
15:00 Corrupted Sensing with Sub-gaussian Measurements
Jinchi Chen and Yulong Liu (Beijing Institute of Technology, P.R. China)
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions for stable signal recovery from structured corruption with added unstructured noise. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-gaussian matrices.
pp. 516-520
15:20 On the Phase Transition of Corrupted Sensing
Huan Zhang (Institute of Electronics, Chinese Academy of Sciences, P.R. China); Yulong Liu (Beijing Institute of Technology, P.R. China); Lei Hong (Institute of Electronics, Chinese Academy of Sciences, P.R. China)
A sharp phase transition has been numerically observed when a constrained convex procedure is used to solve the corrupted sensing problem. In this paper, we present a theoretical analysis for this phenomenon. Specifically, we establish the threshold below which this convex procedure fails to recover signals and there is corruption with high probability. We prove that a sharp phase transition occurs around the sum of the squares of spherical Gaussian widths of two tangent cones. Numerical experiments are provided to demonstrate the correctness and sharpness of our results.
pp. 521-525
15:40 On the Success Probability of the Box-Constrained Rounding and Babai Detectors
Jinming Wen (University of Alberta, Canada); Xiao-Wen Chang (McGill University, Canada); Chintha Tellambura (University of Alberta, Canada)
In communications, one frequently needs to detect a parameter vector $\hat{\boldsymbol{x}}$ in a box from a linear model. The box-constrained rounding detector $\boldsymbol{x}^\text{BR}$ and Babai detector $\boldsymbol{x}^\text{BB}$ are often used to detect $\hat{\boldsymbol{x}}$ due to their high probability of correct detection, which is referred to as success probability, and their high efficiency of implimentation. It is generally believed that the success probability $P^\text{BR}$ of $\boldsymbol{x}^\text{BR}$ is not larger than the success probability $P^\text{BB}$ of $\boldsymbol{x}^\text{BB}$. In this paper, we first present formulas for $P^\text{BR}$ and $P^\text{BB}$ for two different situations: $\hat{\boldsymbol{x}}$ is deterministic and $\hat{\boldsymbol{x}}$ is uniformly distributed over the constraint box. Then, we give a simple example to show that $P^\text{BR}$ may be strictly larger than $P^\text{BB}$ if $\hat{\boldsymbol{x}}$ is deterministic, while we rigorously show that $P^\text{BR}\leq P^\text{BB}$ always holds if $\hat{\boldsymbol{x}}$ is uniformly distributed over the constraint box.
pp. 526-530
16:00 A Characterization of Sampling Patterns for Low-Tucker-Rank Tensor Completion Problem
Morteza Ashraphijuo (Columbia University, USA); Vaneet Aggarwal (Purdue University, USA); Xiaodong Wang (Columbia University, USA)
In this paper, we characterize the deterministic conditions on the locations of the sampled entries, which are equivalent (necessary and sufficient) to finite completability of a low-rank tensor given some components of its Tucker rank. In order to derive this characterization, we propose an algebraic geometric analysis on the Tucker manifold, which allows us to incorporate multiple rank components in the proposed analysis in contrast with the conventional geometric approaches on the Grassmannian manifold. Then, using the developed tools for this analysis, we also derive a sufficient condition on the sampling pattern that ensures there exists only one completion for the sampled tensor (unique completability).
pp. 531-535

#### Mo3-9: MIMO 1

Room: K9
Chair: Christoph Studer (Cornell University, USA)
14:40 Asymptotic Capacity Results for MIMO Wireless Optical Communication
Stefan M. Moser (ETH Zurich, Switzerland & National Chiao Tung University (NCTU), Taiwan); Michail Mylonakis (ETH Zürich, Switzerland); Ligong Wang (ETIS & CNRS, France); Michele A Wigger (Telecom ParisTech, France)
This paper provides several asymptotic capacity results for the multiple-input multiple-output free-space optical intensity channel in the regime of high signal-to-noise ratio (SNR). For the case where the channel matrix has full column rank, the asymptotic capacity is derived assuming a peak-power constraint on each transmit antenna, or an average-power constraint on the total power across all transmit antennas, or both. For multiple-input and single-output channels, the asymptotic high-SNR capacity is derived when either only the total average power is constrained, or only the per-antenna peak power is constrained, or both but with the average-power constraint being sufficiently loose.
pp. 536-540
15:00 On Capacity of Noncoherent MIMO with Asymmetric Link Strengths
Joyson Sebastian (University of California, Los Angeles, USA); Ayan Sengupta (Stanford University, USA); Suhas Diggavi (University of California Los Angeles, USA)
We study the generalized degrees of freedom (gDoF) of the block-fading noncoherent MIMO channel with asymmetric distributions of link strengths, and a coherence time of T symbol durations. We first derive the optimal signaling structure for communication over this channel, which is distinct from that for the i.i.d MIMO setting. We prove that for T=1, the gDoF is zero for MIMO channels with arbitrary link strength distributions, extending the result for MIMO with i.i.d links. We then show that selecting the statistically best antenna is gDoF-optimal for both Multiple Input Single Output (MISO) and Single Input Multiple Output (SIMO) channels. We also derive the gDoF for the 2x2 MIMO channel with different exponents in the direct and cross links. In this setting, we show that it is always necessary to use both antennas to achieve the optimal gDoF, in contrast to the results for 2x2 MIMO with identical link distributions.
pp. 541-545
15:20 On the Degrees-of-Freedom of the MIMO Three-Way Channel with Intermittent Connectivity
Anas Chaaban (King Abdullah University of Science and Technology, Saudi Arabia); Aydin Sezgin (RUB, Germany); Mohamed-Slim Alouini (King Abdullah University of Science and Technology (KAUST), Saudi Arabia)
The degrees-of-freedom (DoF) of the multi-antenna three-way channel (3WC) with an intermittent node is studied. Special attention is given to the impact of adaptation. A nonadaptive transmission scheme based on interference alignment, zero-forcing, and erasure-channel treatment is proposed, and its corresponding DoF region is derived. Then, it is shown that this scheme achieves the sum-DoF of the intermittent channel, in addition to the DoF region of the nonintermittent one. Thus, adaptation is not necessary from those perspectives. To the contrary, it is shown that adaptation is necessary for achieving the DoF region of the intermittent case. This is shown by deriving an outer bound for the intermittent channel with nonadaptive encoding, and giving a counterexample of an adaptive scheme which achieves DoF tuples outside this bound. This highlights the importance of cooperation in this intermittent network.
pp. 546-550
15:40 Outage Information Rate of Spatially Correlated Multi-Cluster Scattering MIMO Channels
Giorgio Taricco and Giuseppa Alfano (Politecnico di Torino, Italy)
A one-sided spatially-correlated multi-cluster scattering Rayleigh MIMO channel is considered in this work and its outage probability is derived in an analytic form based on Meijer function determinants. First, the spatially-uncorrelated case is addressed and the Moment Generating Function (MGF) of the information rate is expressed in an analytic closed-form. The MGF is then used to obtain the outage probability. A few special cases are addressed to provide a confirmation of the analytic results. Next, the MGF in the one-sided spatially correlated case is derived with the constraint of distinct positive spatial eigenvalues. Numerical results are included to provide confirming evidence of the analytic results. These results are then used to assess the outage probability degradation due to spatial correlation in a selected example.
pp. 551-555
16:00 A Generalized Zero-Forcing Precoder for Multiple Antenna Gaussian Broadcast Channels
Sha Hu and Fredrik Rusek (Lund University, Sweden)
In this paper, we consider precoder design for multiuser multiple-input-multiple-output (MIMO) Gaussian broadcast (BC) channels and propose a generalized zero-forcing (GZF) precoder based on successive dirty-paper coding (DPC), i.e., the GZF-DP precoder. The GZF-DP precoder is an extension of the GZF-DP precoder designed earlier for multi-input-single-output broadcast (MISO-BC) channels, and also a generalization of both the linear block-diagonalization ZF (BD-ZF) and the successive ZF with DPC (SZF-DPC) precoders. With the GZF-DP precoder, the depth of the inter-user interference after precoding (and before the DPC) can be specified at will by a parameter v, which provides a trade-off between the optimal rates and the DPC implementation-complexity. Utilizing DPC, the known noncausal inter-user interferences from the other (up to) v users are canceled through successive encoding. Within the class of GZF-DP, we analyze the optimal precoder designs both for sum-rate and minimum user-rate maximizations, which are solved in closed-forms in conjunction with water-filling algorithms depending on v. We show through numerical results that, the proposed GZF-DP precoder with a small v renders significant rate increments compared to the linear BD-ZF precoder, and is close to the SZF-DP preocder with a much less DPC complexity.
pp. 556-560

#### Mo3-A: Age of Information 3

Room: Berlin 3
Chair: Elif Uysal-Biyikoglu (METU & Currently on leave at The Ohio State University, Turkey)
14:40 Age of Information: Design and Analysis of Optimal Scheduling Algorithms
Yu-Pin Hsu (National Taipei University, Taiwan); Eytan Modiano (MIT, USA); Lingjie Duan (Singapore University of Technology and Design (SUTD), Singapore)
Age of information is a newly proposed metric that captures delay from an application layer perspective. The age measures the amount of time that elapsed from the moment the mostly recently received update was generated until the present time. In this paper, we study an age minimization problem over a wireless broadcast network with many users, where only one user can be served at a time. We formulate a Markov decision process (MDP) to find dynamic transmission scheduling schemes, with the purpose of minimizing the long-run average age. While showing that an optimal scheduling algorithm for the MDP is a simple stationary switch-type, we propose a sequence of finite- state approximations for our infinite-state MDP and prove its convergence. We then propose both optimal off-line and on-line scheduling algorithms for the finite-approximate MDPs, depending on knowledge of time-varying arrivals.
pp. 561-565
15:00 Backlog-Adaptive Compression: Age of Information
Jing Zhong, Roy Yates and Emina Soljanin (Rutgers University, USA)
The end-to-end delay of streaming source coding is characterized by an age of information (AoI) metric that measures the number of symbol periods the decoder output lags behind the encoder input. The source encoder receives input source symbols one per unit time and sequentially outputs binary codewords to a constant rate channel that transmits bits to the decoder. We examine a system in which knowledge of the busy/idle state at the channel interface enables the encoder to switch among codebooks with different source blocklengths based on the backlog of symbols at the encoder. We start by introducing two source sequence parsing policies and show that in each of them the blocklength process can be modeled by a Markov chain. We show by experiments that blocklength adjustment based on the channel interface state provides lower average age than codes with fixed blocklength. Aiming to avoid unnecessary frequent blocklength changes by the encoder backlog, we propose maximum blocklength control scheme at the encoder to further reduce the average age.
pp. 566-570
15:20 The Stationary Distribution of the Age of Information in FCFS Single-Server Queues
Yoshiaki Inoue (Osaka University, Japan); Hiroyuki Masuyama (Kyoto University, Japan); Tetsuya Takine (Osaka University, Japan); Toshiyuki Tanaka (Kyoto University, Japan)
We consider the stationary distributions of the age of information (AoI) and the peak AoI in information update systems. We first derive an invariant relation among the distributions of the AoI, the peak AoI, and the system delay, which holds for a wide class of information update systems. Next, based on it, we obtain general formulas for the stationary distributions of the AoI and the peak AoI in the first-come first-served (FCFS) GI/GI/1 queue, as a general model of information update systems. Finally, we derive explicit formulas for the Laplace-Stieltjes transforms of the stationary distributions of the AoI and the peak AoI in FCFS M/GI/1 and GI/M/1 queues.
pp. 571-575
15:40 Age-optimal Information Updates in Multihop Networks
Ahmed M Bedewy (The Ohio State University, USA); Yin Sun (the Ohio State University, USA); Ness B. Shroff (The Ohio State University, USA)
The problem of reducing the age-of-information has been extensively studied in the single-hop networks. In this paper, we minimize the age-of-information in general multihop networks. If the packet transmission times over the network links are exponentially distributed, we prove that a preemptive Last Generated First Served (LGFS) policy results in smaller age processes at all nodes of the network (in a stochastic ordering sense) than any other causal policy. In addition, for arbitrary general distributions of packet transmission times, the non-preemptive LGFS policy is shown to minimize the age processes at all nodes of the network among all non-preemptive work-conserving policies (again in a stochastic ordering sense). It is surprising that such simple policies can achieve optimality of the joint distribution of the age processes at all nodes even under arbitrary network topologies, as well as arbitrary packet generation and arrival times. These optimality results not only hold for the age processes, but also for any non-decreasing functional of the age processes.
pp. 576-580
16:00 Communication over a Channel that Wears Out
Ting-Yi Wu (University of Illinois at Champaign-Urbana, USA); Lav R. Varshney (University of Illinois at Urbana-Champaign, USA); Vincent Y. F. Tan (National University of Singapore, Singapore)
This work investigates the limits of communication over a noisy channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless binary-input channel and when the number of transmitted ones causes a sufficient amount of damage, the channel ceases to convey signals. We restrict attention to constant composition codes. Since infinite blocklength codes will always wear out the channel for any finite threshold of failure and therefore convey no information, we analyze the performance of finite blocklength codes to determine the maximum expected transmission volume at a given level of average error probability. We show that this maximization problem has a recursive form and can be solved by dynamic programming. A discussion of damage state feedback in channels that wear out is also provided. Numerical results show that a sequence of block codes is preferred to a single block code for streaming sources.
pp. 581-585

### Monday, June 26, 16:40 - 18:20

#### Mo4-1: Coding Theory 1

Room: Europa
Chair: Juergen Freudenberger (University of Applied Sciences, Konstanz & Institute for System Dynamics (ISD), Germany)
16:40 Non-linear Cyclic Codes that Attain the Gilbert-Varshamov Bound
Ishay Haviv (The Academic College of Tel Aviv-Yaffo, Israel); Michael Langberg (State University of New York at Buffalo, USA); Moshe Schwartz (Ben-Gurion University of the Negev, Israel); Eitan Yaakobi (Technion, Israel)
We prove that there exist non-linear binary cyclic codes that attain the Gilbert-Varshamov bound.
pp. 586-588
17:00 Strong Functional Representation Lemma and Applications to Coding Theorems
Cheuk Ting Li and Abbas El Gamal (Stanford University, USA)
This paper shows that for any random variables $X$ and $Y$, it is possible to represent $Y$ as a function of $(X,Z)$ such that $Z$ is independent of $X$ and $I(X;Z|Y)\le\log(I(X;Y)+1)+4$. We use this strong functional representation lemma (SFRL) to establish a tighter bound on the rate needed for one-shot exact channel simulation than was previously established by Harsha et. al., and to establish achievability results for one-shot variable-length lossy source coding and multiple description coding. We also show that the SFRL can be used to reduce the channel with state noncausally known at the encoder to a point-to-point channel, which provides a simple achievability proof of the Gelfand-Pinsker theorem. Finally we present an example in which the SFRL inequality is tight to within 5 bits.
pp. 589-593
17:20 On the VC-Dimension of Binary Codes
Sihuang Hu (Tel Aviv University, Israel); Nir Weinberger (Technion, Israel); Ofer Shayevitz (Tel Aviv University, Israel)
We investigate the asymptotic rates of length-$n$ binary codes with VC-dimension at most $dn$ and minimum distance at least $\delta n$. Two upper bounds are obtained, one as a simple corollary of a result by Haussler and the other via a shortening approach combining Sauer--Shelah lemma and the linear programming bound. Two lower bounds are given using Gilbert--Varshamov type arguments over constant-weight and Markov-type sets.
pp. 594-598
17:40 Duality of channels and codes
Joseph M. Renes (ETH Zurich, Switzerland)
For any given channel with classical inputs and possibly quantum outputs, a dual classical-input channel can be defined by embedding the original into a channel with quantum inputs and outputs. Here we give new uncertainty relations for a general class of entropies that lead to very close relationships between the original channel and its dual. Moreover, we show that channel duality can be combined with duality of linear codes, whereupon the uncertainty relations imply that the performance of a given code over a given channel is entirely characterized by the performance of the dual code on the dual channel. This has several applications. In the context of polar codes, it implies that the rates of polarization to ideal and useless channels must be identical. Duality also relates the tasks of channel coding and privacy amplification, implying that the finite blocklength performance of extractors and codes is precisely linked, and that optimal rate extractors can be transformed into capacity-achieving codes, and vice versa. Finally, duality also extends to the EXIT function of any channel and code. Here it implies that for any channel family, if the EXIT function for a fixed code has a sharp transition, then it must be such that the rate of the code equals the capacity at the transition. This may give a different route to proving a code family achieves capacity by establishing EXIT function transitions.
pp. 599-603
18:00 Polynomial Ring Transforms for Efficient XOR-based Erasure Coding
Jonathan Detchart (University of Toulouse & ISAE, France); Jerome Lacan (University of Toulouse, France)
The complexity of software implementations of MDS erasure codes mainly depends on the efficiency of the finite field operations implementation. In this paper, we propose a method to reduce the complexity of the finite field multiplication by using simple transforms between a field and a ring to perform the multiplication in a ring. We show that moving to a ring reduces the complexity of the operations. Then, we show that this construction allows the use of simple scheduling to reduce the number of operations.
pp. 604-608

#### Mo4-2: Coding for Storage

Room: Brussels
Chair: Camilla Hollanti (Aalto University, Finland)
16:40 Secure RAID Schemes from EVENODD and STAR Codes
Wentao Huang and Jehoshua Bruck (California Institute of Technology, USA)
We study secure RAID, i.e., low-complexity schemes to store information in a distributed manner that is resilient to node failures and resistant to node eavesdropping. We describe a technique to shorten a previously developed secure EVENODD scheme, which can optimally tolerate 2 node failures and 2 eavesdropping nodes. The shortening technique allows us to obtain secure EVENODD schemes of arbitrary lengths, which is important for practical application. We also construct a new secure RAID scheme from the STAR code. The scheme can tolerate 3 node failures and 3 eavesdropping nodes with optimal encoding/decoding and random access complexity.
pp. 609-613
17:00 Sector-disk codes with three global parities
Xiao Li and Iwan Duursma (University of Illinois at Urbana-Champaign, USA)
Codewords in array format find applications in disk storage where columns are stored on different disks in combination with parity checks across disks that protect data against disk failures. The addition of global parities protects against sector failures on any of the disks while keeping storage overhead low. We construct sector-disk array codes that tolerate any combination of two disk failures and three sector failures with minimal overhead. The construction is the first for codes of this type that does not rely on exhaustive search.
pp. 614-618
17:20 Coding for Racetrack Memories
Yeow Meng Chee and Han Mao Kiah (Nanyang Technological University, Singapore); Alexander Vardy (University of California San Diego, USA); Van Khu Vu (Nanyang Technological University, Singapore); Eitan Yaakobi (Technion, Israel)
pp. 619-623
17:40 On the Tradeoff Region of Secure Exact-Repair Regenerating Codes
Shuo Shao and Tie Liu (Texas A&M University, USA); Chao Tian (University of Tennessee Knoxville, USA); Cong Shen (University of Science and Technology of China, P.R. China)
We consider the $(n,k,d,\ell)$ secure exact-repair regenerating code problem, which generalizes the $(n,k,d)$ exact-repair regenerating code problem with the additional constraint that the stored file needs to be kept information-theoretically secure against an eavesdropper, who can access the data transmitted to regenerate a total of $\ell$ different failed nodes. For all known results on this problem, the achievable tradeoff regions between the normalized storage capacity and repair bandwidth have a single corner point, achieved by a scheme proposed by Shah, Rashmi and Kumar (the SRK point). Since the achievable tradeoff regions of the exact-repair regenerating code problem without any secrecy constraints are known to have multiple corner points in general, these existing results suggest a phase-change-like behavior, i.e., enforcing a secrecy constraint ($\ell\geq 1$) immediately reduces the tradeoff region to one with a single corner point. In this work, we first show that when the secrecy parameter $\ell$ is sufficiently large, the SRK point is indeed the only corner point of the tradeoff region. However, when $\ell$ is small, we show that the tradeoff region can in fact have multiple corner points. In particular, we establish a precise characterization of the tradeoff region for the $(7,6,6,1)$ problem, which has exactly two corner points. Thus, a smooth transition, instead of a phase-change-type of transition, should be expected as the secrecy constraint is gradually strengthened.
pp. 624-628
18:00 Construction of Unrestricted-Rate Parallel Random Input-Output Code
Shan Lu and Hiroshi Kamabe (Gifu University, Japan); Jun Cheng (Doshisha University, Japan); Akira Yamawaki (Gifu University, Japan)
A coding scheme for two-page unrestricted-rate P-RIO code that each page may have different code rates is proposed. In the second page, the code for each messages consists of two complementary codewords. There are total of $2^{n-1}$ codes which are disjoint to guarantees uniquely-decodable for $2^{n-1}$ messages. In the first page, the code for each message consists of all weight-$u$ vectors with their non-zero elements restricted to $(2u-1)$ same positions, where non-negative integer $u$ is less than or equal to half of code length. Finding disjoint codes in the first page is equivalent to construction of constant-weight codes, and the number of codes in the first page is the best-known number of codewords in constant-weight codes. Our coding scheme is constructive, and the code length is arbitrary. The sum rate of our proposed code are higher than that of previous work.
pp. 629-633

#### Mo4-3: Interference Channels 1

Room: K2
Chair: Daniela Tuninetti (University of Illinois at Chicago, USA)
16:40 Two-way interference channel capacity: How to have the cake and eat it too
Changho Suh and Jaewoong Cho (KAIST, Korea); David Tse (Stanford University, USA)
Two-way communication is prevalent and its fundamental limits are first studied in the point-to-point setting by Shannon [1]. One natural extension is a two-way interference channel (IC) with four independent messages: two associated with each direction of communication. In this work, we explore a deterministic two-way IC which captures key properties of the wireless Gaussian channel. Our main contribution lies in the complete capacity region characterization of the two-way IC via a new achievable scheme. One surprising consequence of this result is that not only we can get an interaction gain over the one-way non-feedback capacities, we can sometimes get all the way to perfect feedback capacities in both directions simultaneously.
pp. 634-638
17:00 Capacity Region of the Symmetric Injective K-User Deterministic Interference Channel
Mehrdad Kiamari and Salman Avestimehr (University of Southern California, USA)
We characterize the capacity region of the symmetric $K$-user Deterministic Interference Channel (DIC) for all channel parameters. The achievable rate region is derived by first projecting the achievable rate region of Han-Kobayashi (HK) scheme, which is in terms of common and private rates for each user, along the direction of aggregate rates for each user (i.e., the sum of common and private rates). We then show that the projected region is characterized by only the projection of those facets in the HK region for which the coefficient of common rate and private rate are the same for all users, hence simplifying the region. Furthermore, we derive a tight converse for each facet of the simplified achievable rate region.
pp. 639-643
17:20 State-Dependent Z-Interference Channel with Correlated States
Yunhao Sun and Yingbin Liang (Syracuse University, USA); Ruchen Duan (Samsung Semiconductor Inc., USA); Shlomo (Shitz) Shamai (The Technion, Israel)
This paper investigates the Gaussian state-dependent Z-interference channel (Z-IC), in which two receivers are respectively corrupted by correlated states that are noncausally known to transmitters and unknown to receivers. Three interference regimes are studied, and the capacity region or sum capacity boundary is characterized either fully or partially under various channel parameters. The impact of correlation between states on state and interference cancelation as well as capacity achievability is demonstrated via numerical analysis.
pp. 644-648
17:40 Novel Outer Bounds and Capacity Results for the Interference Channel with Conferencing Receivers
Reza K. Farsani and Amir K. Khandani (University of Waterloo, Canada)
Capacity bounds for the two-user interference channels with cooperative receivers via conferencing links of finite capacities are investigated. Capacity results known for these communication scenarios are limited to a very few special cases of the one-sided channels. One of the major challenges in analyzing such cooperative networks is how to establish efficient capacity outer bounds for them. In this paper, by applying new techniques, novel capacity outer bounds are established for the interference channels with conferencing receivers. Using the outer bounds, several new capacity results are proved for interesting channels with unidirectional cooperation in strong and mixed interference regimes. A fact is that a conferencing link (between receivers) may be utilized to provide one receiver with information about its corresponding signal or its non-corresponding signal (interference signal). As an interesting consequence, it is demonstrated that both strategies can be helpful to achieve capacity. Lastly, for the case of Gaussian interference channel with conferencing receivers, it is argued that our outer bound is strictly tighter than the previous one derived by Wang and Tse.
pp. 649-653
18:00 Approximate Capacity of a Class of Partially Connected Interference Channels
Muryong Kim and Yitao Chen (University of Texas at Austin, USA); Sriram Vishwanath (University of Texas Austin, USA)
We derive inner and outer bounds on the capacity region for a class of three-user partially connected interference channels. We focus on the impact of topology, interference alignment, and interplay between interference and noise. The representative channels we consider are the ones that have clear interference alignment gain. For these channels, Z-channel type outer bounds are tight to within a constant gap from capacity. We present near-optimal achievable schemes based on rate-splitting, lattice alignment, and successive decoding.
pp. 654-658

#### Mo4-4: Shannon Inequalities

Room: K3
Chair: Haim H Permuter (Ben-Gurion University, Israel)
16:40 Wasserstein Stability of the Entropy Power Inequality for Log-Concave Random Vectors
Thomas Courtade (University of California, Berkeley, USA); Max Fathi (CNRS & Université Paul Sabatier, Institut de Mathématiques de Toulouse, France); Ashwin Pananjady (University of California, Berkeley, USA)
We establish quantitative stability results for the entropy power inequality (EPI) in arbitrary dimension. Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the densities is log-concave and the other is Gaussian, then the deficit in the EPI can be controlled in terms of the $L^1$-Wasserstein distance. As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Wasserstein distance even if densities are uniformly log-concave on sets of measure arbitrarily close to one. The proofs are based on optimal transportation.
pp. 659-663
17:00 Two-Moment Inequalities for Renyi Entropy and Mutual Information
Galen Reeves (Duke University, USA)
This paper explores some applications of a two-moment inequality for the integral of the r-th power of a function, where 0<r<1. The first contribution is an upper bound on the Renyi entropy of a random vector in terms of the two different moments. When one of the moments is equal to zero, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. More generally, evaluation of the bound with two carefully chosen nonzero moments can lead to significant improvements with a modest increase in complexity. The second contribution is a method for upper bounding mutual information in terms of certain integrals with respect to the variance of the conditional density. The bounds have a number of useful properties arising from the connection with variance decompositions.
pp. 664-668
17:20 One-shot Multivariate Covering Lemmas via Weighted Sum and Concentration Inequalities
Mohammad Hossein Yassaee, Jingbo Liu and Sergio Verdú (Princeton University, USA)
New one-shot bounds for multivariate covering are derived via a weighted sum technique and a one-sided concentration inequality which is stronger than the McDiarmid inequality.The new bounds are more compact and sharper than known bounds in the literature. In particular, the covering error can be shown to decay doubly exponential in the blocklength. Implications for the error exponent in broadcast channels are discussed.
pp. 669-673
17:40 A min-entropy power inequality for groups
Peng Xu, James Melbourne and Mokshay Madiman (University of Delaware, USA)
We will develop a general notion of rearrangement for certain metric groups, and prove a Hardy-Littlewood type inequality. Combining this with a characterization of the extreme points of the set of probability measures with bounded densities with respect to a reference measure we will establish a general min-entropy inequality for convolutions. Special attention will be paid to the integers where a min-entropy power inequality will be conjectured and a partial result proved.
pp. 674-678
18:00 A Minimal Set of Shannon-type Inequalities for Functional Dependence Structures
Satyajit Thakor (Indian Institute of Technology Mandi, India); Terence H. Chan (University of South Australia, Australia); Alex Grant (Myriota Pty Ltd, Australia)
The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given inequality is a constrained Shannon-type inequality. Another important application of elemental inequalities is to formulate and compute the Shannon outer bound for multi-source multi-sink network coding capacity. Under this formulation, it is the region of feasible source rates subject to the elemental inequalities and network coding constraints that is of interest. Hence it is of fundamental interest to identify the redundancies induced amongst elemental inequalities when given a set of functional dependence constraints. In this paper, we characterize a minimal set of Shannon-type inequalities when functional dependence constraints are present.
pp. 679-683

#### Mo4-5: Bounds 1

Room: K4
Chair: Martina Cardone (University of Califonia, Los Angeles, USA)
16:40 Sum-set Inequalities from Aligned Image Sets: Instruments for Robust GDoF Bounds
Arash Gholami Davoodi (University of California, Irvine, USA); Syed Ali Jafar (University of California Irvine, USA)
We present sum-set inequalities specialized to the generalized degrees of freedom (GDoF) framework. These are information theoretic lower bounds on the entropy of bounded density linear combinations of discrete, power-limited dependent random variables in terms of the joint entropies of arbitrary linear combinations of new random variables that are obtained by power level partitioning of the original random variables. The bounds are useful instruments to obtain GDoF characterizations for wireless interference networks, especially with multiple antenna nodes, subject to arbitrary channel strength and channel uncertainty levels.
pp. 684-688
17:00 Scaling Exponent of Sparse Random Linear Codes over Binary Erasure Channels
Hessam Mahdavifar (University of Michigan, USA)
The problem of analyzing the finite-length scaling behavior of sparse random linear codes is considered. Random linear codes with random generator matrices whose entries are picked according to i.i.d. Bernoulli distribution with parameter $q = o(1)$ are called sparse. The parameter $q$ is referred to as the sparsity of the random linear code. We develop a methodology to show the optimality of the scaling exponent of uniform random linear codes, i.e., $q = 1/2$, with high probability. The results are then extended to sparse random linear codes with sparsity $q = \Theta(n^{-1/2})$, where $n$ is the code block length. The encoding complexity of such sparse random linear codes is reduced from $O(n^2)$, in uniform random linear codes, to $O(n^{1/2})$. It is also conjectured that $q = \log n / n$ is the lowest sparsity of random linear codes with optimal scaling exponent. The connection of these results to an open problem regarding finding binary polar codes with optimal scaling exponent are also discussed. In particular, we point out that as the size of the polarization kernel increases it can be used as the generator matrix for a code with optimal scaling exponent, without the need to do further polarization.
pp. 689-693
17:20 A Frequency-Domain Approach to Tightening the Generalized Levenshtein Bound
Zilong Liu and Yong Liang Guan (Nanyang Technological University, Singapore); Wai Ho Mow (Hong Kong University of Science and Technology & HKUST, Hong Kong)
Generalized Levenshtein bound (GLB) is a lower bound on the maximum aperiodic correlation sum of quasi-complementary sequence set (QCSS) which refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross- correlation sums. GLB is an indefinite fractional quadratic function of a simplex" weight vector $\mathbf{w}$ and three additional parameters associated with QCSS. We present a novel approach to analytically conduct fractional quadratic programming for the tightening of the GLB. Our key idea is to apply the frequency domain decomposition of the relevant circulant matrix (i.e., the numerator term of GLB) to convert the non-convex problem into a convex one. We derive a new weight vector which asymptotically leads to a tighter GLB (over the Welch bound) for all possible $(K,M)$ cases, where $K,M$ denote the set size, the number of channels, of QCSS, respectively.
pp. 694-698
17:40 Bounds for Cooperative Locality Using Generalized Hamming Weights
Khaled Abdel-Ghaffar (University of California, USA); Jos H. Weber (Delft University of Technology, The Netherlands)
The Cadambe-Mazumdar bound gives a necessary condition for a code to have a certain locality in case of a single erasure in terms of length, dimension, and Hamming distance of the code and of certain shortened codes. The bound has been generalized by Rawat, Mazumdar, and Vishwanath to recover multiple erasures in a cooperative repair scenario. In this paper, the generalized Hamming weights of the code and its shortened codes, which include the Hamming distance as one component, are incorporated to obtain bounds on locality to recover a single erasure or multiple erasures cooperatively. The new bounds give sharper necessary conditions than existing bounds.
pp. 699-703
18:00 Bounds on the Asymptotic Rate of Binary Constant Subblock-Composition Codes
Anshoo Tandon (National University of Singapore, Singapore); Han Mao Kiah (Nanyang Technological University, Singapore); Mehul Motani (National University of Singapore, Singapore)
The study of binary constant subblock-composition codes (CSCCs) has recently gained attention due to their application in diverse fields. These codes are a class of constrained codes where each codeword is partitioned into equal sized subblocks, and every subblock has the same fixed weight. We present novel upper and lower bounds on the asymptotic rate for binary CSCCs, using the sphere-packing and Gilbert-Varshamov (GV) type bounds, respectively. For a fixed subblock length and small code distance, we show that the asymptotic rate for CSCCs is strictly lower than the corresponding rate for constant weight codes (CWCs). We also provide a correction to an earlier result by Chee et al. (2014) on the asymptotic CSCC rate.
pp. 704-708

#### Mo4-6: Multiterminal Source Coding

Room: K5
Chair: Michelle Effros (California Institute of Technology, USA)
16:40 Distributed Cooperative Information Bottleneck
Matias Vera (Universidad de Buenos Aires - Facultad de Ingeniería, Argentina); Leonardo Rey Vega (University of Buenos Aires, Facultad de Ingeniería & CONICET, Argentina); Pablo Piantanida (CentraleSupélec-CNRS-Université Paris-Sud, France)
This paper investigates a scenario where two distant nodes separately observe memoryless process, namely $X_1$ and $X_2$, and can cooperate through multiple exchanges of messages with the goal of enabling a third node to learn "relevant information" (measured in terms of a multi-letter mutual information) about some hidden memoryless process $Y$, which is arbitrarily dependent on $(X_1,X_2)$. These interactive exchanges yield an explicit cooperation that helps the third node to identify, from the distributed observations $X_1$ and $X_2$, useful features for the inference of $Y$. An inner and an outer bound to the rate-relevance region of this problem is derived. Optimal characterization of the rate-relevance region under two different conditions on the dependence structures of the involved variables is showed. Also two examples for Gaussian sources are studied.
pp. 709-713
17:00 A Unified Approach to Error Exponents for Multiterminal Source Coding Systems
Shigeaki Kuzuoka (Wakayama University, Japan)
Two kinds of problems, (i) hypothesis testing with many-to-one compression and (ii) one-to-many lossy source coding with side-information at decoders, are investigated in a unified way. It is demonstrated that a simple key idea, which is developed by Iriyama for one-to-one source coding systems, can be applied to multiterminal source coding systems. In particular, general bounds on the error exponents of multiterminal hypothesis testing and one-to-many lossy source coding are given.
pp. 714-718
17:20 Generalized Gaussian Multiterminal Source Coding and Probabilistic Graphical Models
The sum-rate-distortion function of generalized Gaussian multiterminal source coding is shown to coincide with that of joint encoding in the high-resolution regime if and only if the source-encoder bipartite graph and the undirected graphical model (also known as Gaussian Markov network or Gaussian Markov random field) of the source distribution satisfy a certain condition.
pp. 719-723
17:40 Two-Encoder Multiterminal Source Coding With Side Information Under Logarithmic Loss
Abdellatif Zaidi (Université Paris-Est Marne La Vallée, France)
In this work, we study the problem of two-encoder multiterminal source coding with side information under logarithmic loss distortion measure. We establish a single-letter characterization of the rate-distortion region of this model in the discrete memoryless case. The proof of the converse relies heavily on that of Courtade-Weissman rate-distortion region of the classic two-encoder multiterminal distributed source coding without side information; and extends it to the case in which the decoder has access to a side information stream that is statistically dependent on the sources that need to be compressed. We also apply our result to the so-called Information Bottleneck Method and establish the optimal tradeoff between complexity and accuracy of the prediction in this setting.
pp. 724-728
18:00 Coding for Arbitrarily Varying Remote Sources
Amitalok J Budkuley (The Chinese University of Hong Kong, Hong Kong); Bikash K Dey (Indian Institute of Technology Bombay, India); Vinod M Prabhakaran (Tata Institute of Fundamental Research, India)
We study a lossy source coding problem for a memoryless remote source. The source data is broadcast over an arbitrarily varying channel (AVC) controlled by an adversary. One output of the AVC is received as input at the encoder, and another output is received as side information at the decoder. The adversary is assumed to know the source data non-causally, and can employ randomized jamming strategies arbitrarily correlated to the source data. The decoder reconstructs the source data from the encoded message and the side information. We determine the adversarial rate distortion function for the source under randomized coding. Interestingly, even with vector jamming strategies allowed, it is seen that the adversary cannot affect the rate any worse than when restricted to memoryless strategies.
pp. 729-733

#### Mo4-7: Security 1

Room: K6
Chair: Wei Kang (Southeast University, P.R. China)
16:40 On The Compound MIMO Wiretap Channel with Mean Feedback
Amr Abdelaziz (The Ohio State University & Military Technical College, USA); Ashraf Elbayoumy (Military Technical College, Egypt); Can Emre Koksal (The Ohio State University, USA); Hesham El Gamal (Ohio State University, USA)
Compound MIMO wiretap channel with double sided uncertainty is considered under channel mean information model. In mean information model, channel variations are centered around its mean value which is fed back to the transmitter. We show that the worst case main channel is anti-parallel to the channel mean information resulting in an overall unit rank channel. Further, the worst eavesdropper channel is shown to be isotropic around its mean information. Accordingly, we provide the capacity achieving beamforming direction. We show that the saddle point property holds under mean information model and, thus, compound secrecy capacity equals to the worst case capacity over the class of uncertainty. Moreover, capacity achieving beamforming direction is found to require matrix inversion, thus, we derive null steering (NS) beamforming as an alternative sub-optimal solution that precludes the necessity of matrix inversion. NS beamformer is the beamforming direction orthogonal to the eavesdropper mean channel that maintains the maximum possible gain in the direction mean main channel. Extensive computer simulation reveals that NS beamforming performs very close to the optimal solution. It also verifies that, NS beamforming outperforms both maximum ratio transmission (MRT) and zero forcing (ZF) beamforming approaches over the entire SNR range. Finally, an equivalence relation with MIMO wiretap channel in Rician fading environment is established.
pp. 734-738
17:00 Multiple Access Wiretap Channel with Cribbing
Noha Helal (University of Texas at Dallas, USA); Aria Nosratinia (University of Texas, Dallas, USA)
This paper introduces the discrete memoryless multiple access wiretap channel with noiseless cribbing, where the cribbing may be either causal or strictly causal. We derive lower bounds for secrecy rates for both causal and strictly causal cribbing under either a decode-forward or partial-decode-forward strategy. Our results recover the achievable rate regions of the MAC wiretap and MAC with cribbing, and demonstrate improvement of secrecy rate due to cribbing. An outer bound is presented for this channel under causal cribbing, which also serves as an outer bound for strictly causal case.
pp. 739-743
17:20 Wiretap channel capacity: Secrecy criteria, strong converse, and phase change
Eric Graves (Army Research Lab, USA); Tan Wong (University of Florida, USA)
This paper employs equal-image-size source partitioning techniques to derive the capacities of the general discrete memoryless wiretap channel (DM-WTC) under four different secrecy criteria. These criteria respectively specify requirements on the expected values and tail probabilities of the differences, in absolute value and in exponent, between the joint probability of the secret message and the eavesdropper's observation and the corresponding probability if they were independent. Some of these criteria reduce back to the standard leakage and variation distance constraints that have been previously considered in the literature. The capacities under these secrecy criteria are found to be different when non-vanishing error and secrecy tolerances are allowed. Based on these new results, we are able to conclude that the strong converse property generally holds for the DM-WTC only under the two secrecy criteria based on constraining the tail probabilities. Under the secrecy criteria based on the expected values, an interesting phase change phenomenon is observed as the tolerance values vary.
pp. 744-748
17:40 The Shannon Cipher System with a Guessing Eavesdropper
Lanqing Yu and Paul Cuff (Princeton University, USA)
We consider a Shannon cipher system in which distortion is allowed at the legitimate receiver. The secrecy metric used is the exponent of the probability that the reconstruction of the source sequence by the eavesdropper is within a distortion level. A single-letter characterization is provided when the message rate is large enough. Under the optimal code, the eavesdropper can do no better than either making a reconstruction blindly or guessing the key first and then reconstructing based on the sequence reconstructed by the legitimate receiver.
pp. 749-753
18:00 Privacy-Aware Guessing Efficiency
Shahab Asoodeh, Mario Diaz, Fady Alajaji and Tamas Linder (Queen's University, Canada)
We investigate the problem of guessing a discrete random variable $Y$ under a privacy constraint dictated by another correlated discrete random variable $X$, where both guessing efficiency and privacy are assessed in terms of the probability of correct guessing. We define $\tilde{h}(P_{XY}, \varepsilon)$ as the maximum probability of correctly guessing $Y$ given an auxiliary random variable $Z$, where the maximization is taken over all $P_{Z|Y}$ ensuring that the probability of correctly guessing $X$ given $Z$ does not exceed $\varepsilon$. We show that the map $\varepsilon\mapsto \tilde{h}(P_{XY}, \varepsilon)$ is strictly increasing, concave, and piecewise linear, which allows us to derive a closed form expression for $\tilde{h}(P_{XY}, \varepsilon)$ when $X$ and $Y$ are connected via a binary-input binary-output channel. For $\{(X_i, Y_i)\}_{i=1}^n$ being pairs of independent and identically distributed binary random vectors, we similarly define $\underline{h}_n(P_{X^nY^n}, \varepsilon)$ under the assumption that $Z^n$ is also a binary vector. Then we obtain a closed form expression for $\underline{\textit{h}}_n(P_{X^nY^n}, \varepsilon)$ for sufficiently large, but nontrivial values of $\varepsilon$.
pp. 754-758

#### Mo4-8: Privacy 1

Room: K7+8
Chair: Frans MJ Willems (Technical University Eindhoven, The Netherlands)
16:40 Optimal Schemes for Discrete Distribution Estimation under Local Differential Privacy
Min Ye (UMD, USA); Alexander Barg (University of Maryland, USA)
We consider the minimax estimation problem of a discrete distribution with support size $k$ under privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the distribution of the raw samples from the privatized samples. A positive number $\epsilon$ measures the privacy level of a privatization scheme. For a given $\epsilon,$ we want to find the optimal privatization scheme which minimizes the expected estimation loss for the worst-case distribution. Two schemes in the literature provide order optimal performance in the high-privacy regime when $\epsilon$ is very close to $0,$ and in the low-privacy regime when $e^{\epsilon}\approx k,$ respectively. In this paper, we propose a new family of schemes which substantially improve the performance of the existing schemes in the medium privacy regime when $1\ll e^{\epsilon} \ll k.$ More concretely, we prove that when $3.8 < \epsilon <\ln(k/9) ,$ our schemes reduce the expected estimation loss by $50\%$ under $\ell_2^2$ metric and $30\%$ under $\ell_1$ metric over the existing schemes. We also prove a tight lower bound for the whole region $e^{\epsilon} \ll k,$ which implies that our schemes are order optimal in this regime.
pp. 759-763
17:00 Limits of Location Privacy under Anonymization and Obfuscation
Nazanin Takbiri and Amir Houmansadr (University of Massachusetts Amherst, USA); Dennis Goeckel (University of Massachusetts, USA); Hossein Pishro-Nik (University of Massachusetts, Amherst, USA)
The prevalence of mobile devices and location-based services (LBS) has generated great concerns regarding the LBS users' privacy, which can be compromised by statistical analysis of their movement patterns. A number of algorithms have been proposed to protect the privacy of users in such systems, but the fundamental underpinnings of such remain unexplored. Recently, the concept of perfect location privacy was introduced and its achievability was studied for anonymization-based LBS systems, where user identifiers are permuted at regular intervals to prevent identification based on statistical analysis of long time sequences. In this paper, we significantly extend that investigation by incorporating the other major tool commonly employed to obtain location privacy: obfuscation, where user locations are purposely obscured to protect their privacy. Since anonymization and obfuscation reduce user utility in LBS systems, we investigate how location privacy varies with the degree to which each of these two methods is employed. We provide: (1) achievability results for the case where the location of each user is governed by an i.i.d. process; (2) converse results for the i.i.d. case as well as the more general Markov Chain model. We show that, as the number of users in the network grows, the obfuscation-anonymization plane can be divided into two regions: in the first region, all users have perfect location privacy; and, in the second region, no user has location privacy.
pp. 764-768
17:20 Operational Definitions for Some Common Information Leakage Metrics
Ibrahim Issa and Aaron Wagner (Cornell University, USA)
Maximal leakage from a random variable $X$ to a random variable $Y$ is defined as the multiplicative increase, upon observing $Y$, of the probability of correctly guessing a randomized function of $X$, maximized over all such functions [1]. Herein, this guessing framework is used to give operational definitions to common information leakage metrics, including Shannon capacity, maximal correlation, and local differential privacy. Shannon capacity is shown to capture the multiplicative increase of the probability of correct guessing over the restricted set of functions of $X$ that can be reliably reconstructed from $Y$, hence underestimating leakage. Maximal correlation is shown to capture the multiplicative change in the variance of functions of $X$, rather than the guessing probability. Local differential privacy is shown to capture the multiplicative increase of the guessing probability of functions of $X$, maximized over realizations of $Y$ and over distributions $P_X$. Moreover, maximizing over realizations of $Y$ for a fixed $P_X$ is shown to yield a valid leakage measure, which is equal to the maximum information rate.
pp. 769-773
17:40 Smart Meter Privacy Based on Adversarial Hypothesis Testing
Zuxing Li (KTH Royal Institute of Technology & Communication Theory Lab., Sweden); Tobias J. Oechtering (KTH Royal Institute of Technology & School of Electrical Engineering, EE, Sweden); Deniz Gündüz (Imperial College London, United Kingdom (Great Britain))
Privacy-preserving energy management is studied in the presence of a renewable energy source. It is assumed that the energy demand/supply from the energy provider is tracked by a smart meter. The resulting privacy leakage is measured through the probabilities of error in a binary hypothesis test, which tries to detect the consumer behavior based on the meter readings. An optimal privacy-preserving energy management policy maximizes the minimal Type II probability of error subject to a constraint on the Type I probability of error. When the privacy-preserving energy management policy is based on all the available information of energy demands, energy supplies, and hypothesis, the asymptotic exponential decay rate of the maximum minimal Type II probability of error is characterized by a divergence rate expression. Two special privacy-preserving energy management policies, the memoryless hypothesis-aware policy and the hypothesis-unaware policy with memory, are then considered and their performances are compared. Further, it is shown that the energy supply alphabet can be constrained to the energy demand alphabet without loss of optimality for the evaluation of a single-letter-divergence privacy-preserving guarantee.
pp. 774-778
18:00 Hypothesis Testing under Maximal Leakage Privacy Constraints
Jiachun Liao and Lalitha Sankar (Arizona State University, USA); Flavio P. Calmon (IBM, USA); Vincent Y. F. Tan (National University of Singapore, Singapore)
The problem of publishing privacy-guaranteed data for hypothesis testing is studied using the maximal leakage (ML) as a metric for privacy and the type-II error exponent as the utility metric. The optimal mechanism (random mapping) that maximizes utility for a bounded leakage guarantee is determined for the entire leakage range for binary datasets. For non-binary datasets, approximations in the high privacy and high utility regimes are developed. The results show that, for any desired leakage level, maximizing utility forces the ML privacy mechanism to reveal partial to complete knowledge about a subset of the source alphabet. The results developed on maximizing a convex function over a polytope may also of an independent interest.
pp. 779-783

#### Mo4-9: Subspace and LDPC Codes

Room: K9
Chair: Shu Lin (UC Davis, USA)
16:40 Cyclic Subspace Codes and Sidon Spaces
Netanel Raviv (Technion & Tel-Aviv University, Israel); Itzhak Tamo (Tel Aviv University, Israel)
The interest in subspace codes has increased in recent years due to their application in error correction for random network coding. In order to study their properties and find good constructions, the notion of cyclic subspace codes was introduced by using the extension field structure of the ambient space. However, to this date there exists no general construction with a polynomial relation between $k$, the dimension of the codewords, and $n$, the dimension of the entire space. Independently of the study of cyclic subspace codes, Sidon spaces were recently introduced by Bachoc et al. as a tool for the study of certain multiplicative properties of subspaces over finite fields. In this paper it is shown that Sidon spaces are necessary and sufficient for obtaining a full-orbit cyclic subspace code with minimum distance $2k-2$. By presenting several constructions of Sidon spaces, full-orbit cyclic subspace codes are obtained, in which $n$ is quadratic in $k$. The constructions are based on a variety of tools; namely, Sidon sets, that are sets of integers in which all pairwise sums are distinct, irreducible polynomials, and linearized polynomials. Further, the existence of a Sidon space in which $n$ is linear in $k$ is shown, alongside the fact that any Sidon space induces a Sidon set.
pp. 784-788
17:00 Grassmannian Codes from Multiple Families of Mutually Unbiased Bases
Olav Tirkkonen, Christopher Boyd and Roope Vehkalahti (Aalto University, Finland)
We explore the underlying algebraic structure of Mutually Unbiased Bases (MUBs), and their application to code design. Columns in MUBs have inner products with absolute values less or equal to $1/\sqrt{N}$. MUBs provide a systematic way of generating optimal codebooks for various coding and precoding applications. A maximal set of MUBs (MaxMUBs) in $N = 2^m$ dimensions, with $m \in \mathbb{Z}$, can produce codebooks of QPSK lines with good distance properties and alphabets which limit processing complexity. We expand the construction by identifying that in $N=2^m$ dimensions there exists $N^(m-1)/2$ families of MUB, each with $N$ matrices. Inner products of columns of these matrices are less or equal to $1/\sqrt{2}$. Considering Grassmannian line codebooks that can be generated from these matrices, we conjecture that Grassmannian codebooks of maximum cardinality for minimum chordal distance $1/\sqrt{2}$ can be constructed when entries are constrained to be normalized fourth roots of unity. Then decoding or encoding these codebooks can be performed without multiplications, and with a number of additions that scales linearly with the number of codewords, irrespective of the dimension.
pp. 789-793
17:20 Performance of ML Decoding for Ensembles of Binary and Nonbinary Regular LDPC Codes of Finite Lengths
Irina Bocharova and Boris D. Kudryashov (St. Petersburg University of Information Technologies, Mechanics and Optics, Russia); Vitaly Skachek (University of Tartu, Estonia)
The Gallager ensembles of binary regular LDPC codes and binary images of nonbinary regular LDPC codes are studied. Recurrent procedure for computing average spectra for these two ensembles is presented. By using the existing bounding techniques, estimates on the error probability of the maximum-likelihood (ML) decoding over an AWGN channel with BPSK signaling for short codes from different ensembles of LDPC codes are obtained. The numerical results show performance of the ML decoding for different code ensembles. Conclusions drawn based on the average code spectra are then verified by near-ML decoding simulations for both randomly selected and the best known short codes. The asymptotic ML decoding thresholds for AWGN and BS channels are calculated. As expected, codes with the ML decoding performance superior to that of the average code in the ensemble, are easy to find. However, it follows from the presented results that the ML decoding performance should not be used as a target for searching for good iteratively decodable codes.
pp. 794-798
17:40 Interleaved Subspace Codes in Fountain Mode
Vladimir Sidorenko and Hannes Bartz (Technical University of Munich, Germany); Antonia Wachter-Zeh (Technical University of Munich (TUM), Germany)
We consider subspace codes obtained by lifting L-interleaved [n,k] Gabidulin codes. When used in networks with random linear coding, these codes are able to correct with high probability gamma packet insertions and delta packet deletions if gamma/L + delta < n-k. We propose to use these subspace codes in the so called fountain mode. In this case we do not need to correct deletions and are able to correct with high probability a large number L(n-k) of packet insertions. We present a simplified decoder correcting insertions only.
pp. 799-803
18:00 LT codes on Partial Erasure Channels
Carolyn Mayer (University of Nebraska-Lincoln, USA); Christine A. Kelley (University of Nebraska - Lincoln, USA)
LT codes are a class of rateless codes designed for data dissemination on erasure channels. In this paper, we present a decoder for LT codes on partial erasure channels, which were recently introduced for multi-level read storage channel applications. We compare the efficiency of LT codes on these channels to those on the QEC.
pp. 804-808

#### Mo4-A: Energy Harvesting 1

Room: Berlin 3
Chair: Yu-Pin Hsu (National Taipei University, Taiwan)
16:40 Energy Harvesting Networks with General Utility Functions: Near Optimal Online Policies
Ahmed Arafa (University of Maryland College Park, USA); Abdulrahman Baknina and Sennur Ulukus (University of Maryland, USA)
We consider online scheduling policies for single-user energy harvesting communication systems, where the goal is to characterize online policies that maximize the long term average utility, for some general concave and monotonically increasing utility function. In our setting, the transmitter relies on energy harvested from nature to send its messages to the receiver, and is equipped with a finite-sized battery to store its energy. Energy packets are independent and identically distributed (i.i.d.) over time slots, and are revealed causally to the transmitter. Only the average arrival rate is known a priori. We first characterize the optimal solution for the case of Bernoulli arrivals. Then, for general i.i.d. arrivals, we first show that fixed fraction policies [Shaviv-Ozgur] are within a constant multiplicative gap from the optimal solution for all energy arrivals and battery sizes. We then derive a set of sufficient conditions on the utility function to guarantee that fixed fraction policies are within a constant additive gap as well from the optimal solution.
pp. 809-813
17:00 On Achievable Rates of AWGN Energy-Harvesting Channels with Block Energy Arrival and Non-Vanishing Error Probabilities
Silas L. Fong and Vincent Y. F. Tan (National University of Singapore, Singapore); Ayfer Özgür (Stanford University, USA)
This paper investigates the achievable rates of an additive white Gaussian noise (AWGN) energy-harvesting (EH) channel with an infinite battery under the assumption that the error probabilities do not vanish as the blocklength increases. The EH process is characterized by a sequence of blocks of harvested energy. The harvested energy remains constant within a block while the harvested energy across different blocks is characterized by a sequence of independent and identically distributed (i.i.d.) random variables. The blocks have length $L$, which can be interpreted as the coherence time of the energy arrival process. If L is a constant or grows sublinearly in the blocklength n, we fully characterize the first-order coding rate. In addition, we obtain lower and upper bounds on the second-order coding rate, which are proportional to $-\sqrt{\frac{L}{n}}$ for any fixed error probability <1/2. If L grows linearly in n, we obtain lower and upper bounds on the first-order coding rate, which coincide whenever the EH random variable is continuous. Our results suggest that correlation in the energy-arrival process decreases the effective blocklength by a factor of L.
pp. 814-818
17:20 Optimal Transmission for Energy Harvesting Nodes under Battery Size and Usage Constraints
Jing Yang (The Pennsylvania State University, USA); Jingxian Wu (University of Arkansas, USA)
In this paper, we study the optimal energy management policy of an energy harvesting transmitter by taking both battery degradation and finite battery constraints into consideration. We consider a scenario where the sensor is able to harvest energy from the ambient environment and use it to power its transmission. The harvested energy can be used for transmission immediately without entering the equipped battery, or charged into the battery and discharged later for transmission. When the battery is charged or discharged, a cost will be incurred to account for its impact on battery degradation. We impose a long-term average cost constraint on the battery, which is translated to the average number of charge/discharge operations per unit time. At the same time, we assume the capacity of the battery is finite, and the total amount of energy stored in the battery cannot exceed its capacity. Our objective is to develop an online energy management policy to maximize the long-term average throughput of the transmitter under both the battery usage constraint and finite battery constraint. We propose an energy-aware adaptive transmission policy, which is a modified version of the optimal policy for the infinite battery case. Our analysis indicates that the energy-aware adaptive transmission policy is asymptotically optimal when the battery size is sufficiently large. Simulation results corroborate the theoretical analysis.
pp. 819-823
17:40 Single-User Channel with Data and Energy Arrivals: Online Policies
Abdulrahman Baknina and Sennur Ulukus (University of Maryland, USA)
We consider a single-user channel in which the transmitter is equipped with finite-sized data and energy buffers. The transmitter receives energy and data packets randomly and intermittently over time and stores them in the finite-sized buffers. The arrival amounts are known only causally as they happen. We study the online power allocation problem, in which the transmitter relies only on the causal arrival (energy and data) information. We focus on the special case when the energy and data arrivals are fully-correlated. We first study the case when the arrivals are Bernoulli. For this case, we determine the optimal policy. Inspired by this policy and in order to study the case of general fully-correlated arrivals, we propose a structured policy and bound its performance by a multiplicative gap from the optimal. We then show that this policy is optimal when the energy arrivals dominate the data arrivals, and is within a constant additive gap from the optimal policy when the data arrivals dominate the energy arrivals.
pp. 824-828

Room: Foyer

## Tuesday, June 27

### Tuesday, June 27, 08:30 - 09:30

#### TuP: Plenary Talk: Biological Systems as Communication Networks - Urbashi Mitra

Urbashi Mitra
Room: Europa
Chair: Stephen Hanly (Macquarie University, Australia)

### Tuesday, June 27, 09:50 - 11:10

#### Tu1-1: Array Codes

Room: Europa
Chair: Joachim Rosenthal (University of Zurich, Switzerland)
09:50 Locality and Availability of Array Codes Constructed from Subspaces
Natalia Silberstein (Yahoo! Labs, Israel); Tuvi Etzion (Technion-Israel Institute of Technology, Israel); Moshe Schwartz (Ben-Gurion University of the Negev, Israel)
Ever-increasing amounts of data are created and processed in internet-scale companies such as Google, Facebook, and Amazon. The efficient storage of such copious amounts of data has thus become a fundamental and acute problem in modern computing. No single machine can possibly satisfy such immense storage demands. Therefore, distributed storage systems (DSS), which rely on tens of thousands of storage nodes, are the only viable solution. Such systems are broadly used in all modern internet-scale systems. However, the design of a DSS poses a number of crucial challenges, markedly different from single-user storage systems. Such systems must be able to reconstruct the data efficiently, to overcome failure of servers, to correct errors, etc. Lots of research was done in the last few years to answer these challenges and the research is increasing in parallel to the increasing amount of stored data. The main goal of this paper is to consider codes which have two of the most important features of distributed storage systems, namely, locality and availability. Our codes are array codes which are based on subspaces of a linear space over a finite field. We present several constructions of such codes which are $q$-analog to some of the known block codes. Some of these codes possess independent intellectual merit. We examine the locality and availability of the constructed codes. In particular we distinguish between two types of locality and availability, node vs. symbol, locality and availability. To our knowledge this is the first time that such a distinction is given in the literature.
pp. 829-833
10:10 Efficient Lowest Density MDS Array Codes of Column Distance 4
Zhijie Huang (Sun Yat-Sen University, P.R. China); Hong Jiang (University of Texas at Arlington, USA); Nong Xiao (Sun Yat-Sen University, P.R. China)
The extremely strict code length constraint is the main drawback of lowest density, maximum-distance separable (MDS) array codes of distance greater than 3. To break away from the status quo, we proposed in [6] a family of lowest density MDS array codes of (column) distance 4, called XI-Code. Compared with the previous alternatives, XI-Code has lower encoding and decoding complexities, and much looser constraint on the code length, thus is much more practical. In this paper, we present a new family of lowest density MDS array codes of (column) distance 4, called R$\Lambda$-Code, which is derived from XI-Code, and outperforms the latter substantially in terms of encoding complexity, decoding complexity, and memory consumption during encoding/decoding. The inherent connection between R$\Lambda$-Code and XI-Code and how the former is derived from the latter may provide inspiration for the readers to derive new codes from other existing codes in a similar way.
pp. 834-838
10:30 Triple-Fault-Tolerant Binary MDS Array Codes with Asymptotically Optimal Repair
Hanxu Hou (Dongguan University of Technology, P.R. China); Patrick Pak-Ching Lee (The Chinese University of Hong Kong, Hong Kong); Yunghsiang Sam Han (Dongguan University of Technology, P.R. China); Yuchong Hu (Huazhong University of Science and Technology, P.R. China)
Binary maximum distance separable (MDS) array codes are a special class of erasure codes for distributed storage that not only provide fault tolerance with minimum storage redundancy, but also achieve low computational complexity. They are constructed by encoding $k$ information columns into $r$ parity columns, in which each element in a column is a bit, such that any $k$ out of the $k+r$ columns suffice to recover all information bits. In addition to providing fault tolerance, it is critical to improve repair performance. Specifically, if a single column fails, our goal is to minimize the repair bandwidth by downloading the least amount of bits from $d$ non-failed columns, where $k\le d\le k+r-1$. However, existing binary MDS codes that achieve high data rates (i.e., $k/(k+r) > 1/2$) and minimum repair bandwidth only support double fault tolerance (i.e., $r=2$), which is insufficient for failure-prone distributed storage environments in practice. This paper fills the void by proposing an explicit construction of triple-fault-tolerant (i.e., $r=3$) binary MDS array codes that achieve asymptotically minimum repair bandwidth for $d=k+1$.
pp. 839-843
10:50 Codes for Graph Erasures
Lev Yohananov (Technion - Israel Institute of Technology, Israel); Eitan Yaakobi (Technion, Israel)
Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the information is stored on the edges of an undirected graph, and a code over graphs is a set of graphs. A node failure is the event where all edges in the neighborhood of the failed node have been erased. We say that a code over graphs can tolerate $\rho$ node failures if it can correct the erased edges of any $\rho$ failed nodes in the graph. While the construction of such codes can be easily accomplished by MDS codes, their field size has to be at least $\mathcal{O}(n^2)$, when $n$ is the number of nodes in the graph. In this work we present several constructions of codes over graphs with smaller field size. In particular, we present optimal codes over graphs correcting two node failures over the binary field, when the number of nodes in the graph is a prime number. We also present a construction of codes over graphs correcting $\rho$ node failures for all $\rho$ over a field of size at least $(n+1)/2-1$, and show how to improve this construction for optimal codes when $\rho=2,3$.
pp. 844-848

#### Tu1-2: Polar Codes 1

Room: Brussels
Chair: Ilya Dumer (University of California at Riverside, USA)
09:50 Fast Polarization for Non-Stationary Channels
Hessam Mahdavifar (University of Michigan, USA)
We consider the problem of polar coding for transmission over a non-stationary sequence of independent binary-input memoryless symmetric (BMS) channels $\left\{W_i\right\}_{i=1}^{\infty}$, where the $i$-th encoded bit is transmitted over $W_i$. We show, for the first time, a polar coding scheme that achieves the average symmetric capacity $$\overline{I}(\left\{W_i\right\}_{i=1}^{\infty}) = \lim_{N\rightarrow \infty} \frac{1}{N}\sum_{i=1}^N I(W_i),$$ assuming that the limit exists. The polar coding scheme is constructed using Ar{\i}kan's channel polarization transformation in combination with certain permutations at each polarization level and certain skipped operations. This guarantees a fast polarization process that results in polar coding schemes with block lengths upper bounded by a polynomial of $1/\epsilon$, where $\epsilon$ is the gap to the average capacity. More specifically, given an arbitrary sequence of BMS channels $\left\{W_i\right\}_{i=1}^{N}$ and $P_e$, where $0 < P_e <1$, we construct a polar code of length $N$ and rate $R$ guaranteeing a block error probability of at most $P_e$ for transmission over $\left\{W_i\right\}_{i=1}^{N}$ such that $$N \leq \frac{\kappa}{(\overline{I}_N - R)^{\mu}}$$ where $\mu$ is a constant, $\kappa$ is a constant depending on $P_e$ and $\mu$, and $\overline{I}_N$ is the average of the symmetric capacities $I(W_i)$, for $i=1,2,,\dots,N$. We further show a numerical upper bound on $\mu$ that is: $\mu \leq 10.78$. The encoding and decoding complexities of the constructed polar code preserves $O(N \log N)$ complexity of Ar{\i}kan's polar codes.
pp. 849-853
10:10 A Lower Bound on the Probability of Error of Polar Codes over BMS Channels
Boaz Shuval and Ido Tal (Technion, Israel)
Consider a polar code designed for some binary memoryless symmetric channel. We develop a lower bound on the probability of error of this polar code under successive-cancellation decoding. The bound exploits the correlation between the various codeword bits and improves upon existing lower bounds.
pp. 854-858
10:30 On the Pointwise Threshold Behavior of the Binary Erasure Polarization Subchannels
Erik Ordentlich (Yahoo, Inc., USA); Ron M. Roth (Technion, Israel)
It is shown that when Arikan's $n$-level polarization transformation is applied to the binary erasure channel, each of the resulting individual $2^n$ subchannels has a sharp threshold, for sufficiently large $n$.
pp. 859-863
10:50 Exploiting Source Redundancy to Improve the Rate of Polar Codes
Ying Wang, Krishna Narayanan and Anxiao Andrew Jiang (Texas A&M University, USA)
We consider a joint source-channel decoding (JSCD) problem where the source encoder leaves residual redundancy in the source. We first model the redundancy in the source encoder output as the output of a side information channel at the channel decoder, and show that this improves random error exponent. Then, we consider the use of polar codes in this framework when the source redundancy is modeled using a sequence of t-erasure correcting block codes. For this model, the rate of polar codes can be improved by unfreezing some of originally frozen bits and that the improvement in rate depends on the distribution of frozen bits within a codeword. We present a proof for the convergence of that distribution, as well as the convergence of the maximum rate improvement. The significant performance improvement and improved rate provide strong evidences that polar code is a good candidate to exploit the benefit of source redundancy in the JSCD scheme.
pp. 864-868

#### Tu1-3: Multiple Access 2

Room: K2
Chair: Abbas El Gamal (Stanford University, USA)
09:50 Outer Bounds for Gaussian Multiple Access Channels with State Known at One Encoder
Wei Yang (Princeton University, USA); Yingbin Liang (Syracuse University, USA); Shlomo (Shitz) Shamai (The Technion, Israel); H. Vincent Poor (Princeton University, USA)
This paper studies a two-user state-dependent Gaussian multiple-access channel with state noncausally known at one encoder. Two new outer bounds on the capacity region are derived, which improve uniformly over the best known (genie-aided) outer bound. The two corner points of the capacity region as well as the sum rate capacity are established, and it is shown that a single-letter solution is adequate to achieve both the corner points and the sum rate capacity. Furthermore, the full capacity region is characterized in situations in which the sum rate capacity is equal to the capacity of the helper problem. The proof relies on the optimal-transportation idea of Polyanskiy and Wu (which was used previously to establish an outer bound on the capacity region of the interference channel) and on a generalization of the worst-case Gaussian noise result to the case in which the input and the noise are dependent.
pp. 869-873
10:10 Homologous Codes for Multiple Access Channels
Pinar Sen (UCSD); Young-Han Kim (UCSD, USA)
Building on recent development by Padakandla and Pradhan, and by Lim, Feng, Pastore, Nazer, and Gastpar, this paper studies structured coding as a complete replacement for random coding in network information theory. The roles of two techniques used in nested coset coding to generate nonuniform codewords, namely, shaping and channel transformation, are clarified and illustrated via the simple example of the two-sender multiple access channel. While individually deficient, the optimal combination of shaping and channel transformation is shown to achieve the same performance as traditional random codes for this channel model, which opens up new possibilities of utilizing nested coset codes with the same generator matrix for a broader class of applications.
pp. 874-878
10:30 An Achievable Error Exponent for the Multiple Access Channel with Correlated Sources
Arezou Rezazadeh, Josep Font-Segura and Alfonso Martinez (Universitat Pompeu Fabra, Spain); Albert Guillén i Fàbregas (ICREA and Universitat Pompeu Fabra & University of Cambridge, Spain)
This paper derives an achievable random-coding error exponent for joint source-channel coding over a multiple access channel with correlated sources. The codebooks are generated by drawing codewords from a multi-letter distribution that depends on the composition of the source message.
pp. 879-882
10:50 A Broadcast Approach to Multiple Access Adapted to the Multiuser Channel
Samia Kazemi and Ali Tajer (Rensselaer Polytechnic Institute, USA)
pp. 883-887

#### Tu1-4: Information Measures

Room: K3
Chair: Thomas Courtade (University of California, Berkeley, USA)
09:50 On the Information Dimension Rate of Stochastic Processes
Bernhard C. Geiger (Technical University of Munich, Germany); Tobias Koch (Universidad Carlos III de Madrid & Gregorio Marañón Health Research Institute, Spain)
Jalali and Poor (Universal compressed sensing," arXiv:1406.7807v3, Jan. 2016) have recently proposed a generalization of R\'enyi's information dimension to stationary stochastic processes by defining the information dimension of the stochastic process as the information dimension of $k$ samples divided by $k$ in the limit as $k\to\infty$. This paper proposes an alternative definition of information dimension as the entropy rate of the uniformly-quantized stochastic process divided by minus the logarithm of the quantizer step size $1/m$ in the limit as $m\to\infty$. It is demonstrated that both definitions are equivalent for stochastic processes that are $\psi^*$-mixing, but that they may differ in general. In particular, it is shown that for Gaussian processes with essentially-bounded power spectral density (PSD), the proposed information dimension equals the Lebesgue measure of the PSD's support. This is in stark contrast to the information dimension proposed by Jalali and Poor, which is $1$ if the process's PSD is positive on a set of positive Lebesgue measure, irrespective of its support size.
pp. 888-892
10:10 A Variational Characterization of Rényi Divergences
Venkat Anantharam (University of California at Berkeley, USA)
We present a variational characterization of the Rényi divergences between any two probability distributions on an arbitrary measurable space, in terms of relative entropies. This yields as a corollary a recently developed variational formula, due to Atar, Chowdhary and Dupuis, for exponential integrals of bounded measurable functions in terms of Rényi divergences. We also develop a similar variational characterization of the Rényi divergence rates between two stationary finite state Markov chains in terms of relative entropy rates. This leads to an analog of the variational formula of Atar, Chowdary and Dupuis in the framework of stationary finite state Markov chains.
pp. 893-897
10:30 A de Bruijn identity for discrete random variables
Oliver Johnson (University of Bristol, United Kingdom (Great Britain)); Saikat Guha (Raytheon BBN Technologies, USA)
We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.
pp. 898-902
10:50 Direct Estimation of Information Divergence Using Nearest Neighbor Ratios
Morteza Noshad (University of Michigan, USA); Kevin Moon (Yale University, USA); Salimeh Yasaei Sekeh (University of Michigan, Ann Arbor, USA); Alfred Hero III (University of Michigan, USA)
We propose a direct estimation method for Renyi and $f$-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets $X$ and $Y$, respectively with $N$ and $M$ samples, where $\eta:=M/N$ is a constant value. Considering the $k$-nearest neighbor ($k$-NN) graph of $Y$ in the joint data set $(X,Y)$, we show that the average powered ratio of the number of $X$ points to the number of $Y$ points among all $k$-NN points is proportional to Renyi divergence of $X$ and $Y$ densities. A similar method can also be used to estimate $f$-divergence measures. We derive bias and variance rates, and show that for the class of $\gamma$-Holder smooth functions, the estimator achieves the MSE rate of $N^{-2\gamma/(\gamma+d)}$. Furthermore, by using a weighted ensemble estimation technique, for density functions with continuous and bounded derivatives of up to the order $d$, and some extra conditions at the support set boundary, we derive an ensemble estimator that achieves the parametric MSE rate of $O(1/N)$. Our estimators are more computationally tractable than other competing estimators, which makes them appealing in many practical applications.
pp. 903-907

#### Tu1-5: Joint Source-Channel Coding 1

Room: K4
Chair: Aaron Wagner (Cornell University, USA)
09:50 Expurgated Joint Source-Channel Coding Bounds and Error Exponents
Jonathan Scarlett (EPFL, Switzerland); Alfonso Martinez (Universitat Pompeu Fabra, Spain); Albert Guillén i Fàbregas (ICREA and Universitat Pompeu Fabra & University of Cambridge, Spain)
This paper studies expurgated random-coding bounds and exponents for joint source-channel coding (JSCC). We extend Gallager's expurgation techniques for channel coding to the JSCC setting, and derive a non-asymptotic bound that recovers two exponents derived by Csisz\'{a}r using the method of types. Our approach has the notable advantage of being directly applicable to channels with continuous alphabets.
pp. 908-912
10:10 Graph Information Ratio
Lele Wang (Stanford University & Tel Aviv University, USA); Ofer Shayevitz (Tel Aviv University, Israel)
We introduce the notion of information ratio $\text{Ir}(H/G)$ between two (simple, undirected) graphs $G$ and $H$, which characterizes the maximal number of source symbols per channel use that can be reliably sent over a channel with confusion graph $H$, where reliability is measured w.r.t. a source confusion graph $G$. Many different results are provided, including in particular lower and upper bounds on $\text{Ir}(H/G)$ in terms of various graph properties, inequalities and identities for behavior under strong product and disjoint union, relations to graph cores, and notions of graph criticality. Informally speaking, $\text{Ir}(H/G)$ can be interpreted as a measure of similarity between $G$ and $H$. We make this notion precise by introducing the concept of information equivalence between graphs, a more quantitative version of homomorphic equivalence. We then describe a natural partial ordering over the space of information equivalence classes, and endow it with a suitable metric structure that is contractive under the strong product. Various examples and intuitions are discussed.
pp. 913-917
10:30 Second Order Analysis for Joint Source-Channel Coding with Markovian Source
Ryo Yaguchi and Masahito Hayashi (Nagoya University, Japan)
We derive the second order rates of joint source-channel coding, whose source obeys the ergodic Markov process by introducing new distribution family, switched Gaussian convolution distribution, when the channel is a discrete memoryless. We also compare the joint source-channel scheme with the separation scheme.
pp. 918-922
10:50 On the Necessary Conditions for Transmitting Correlated Sources over a Multiple Access Channel
Basak Guler (The Pennsylvania State University, USA); Deniz Gündüz (Imperial College London, United Kingdom (Great Britain)); Aylin Yener (Pennsylvania State University, USA)
We study the lossy communication of correlated sources over a multiple access channel (MAC). In particular, we provide a new set of necessary conditions for the achievability of a distortion pair over a given channel. The necessary conditions are then specialized to the case of bivariate Gaussian sources and doubly symmetric binary sources over a Gaussian multiple access channel. Our results indicate that the new necessary conditions provide the tightest conditions to date in certain cases.
pp. 923-927

#### Tu1-6: Strong Converses

Room: K5
Chair: Shun Watanabe (Tokyo University of Agriculture and Technology, Japan)
09:50 Strong Converse for Content Identification with Lossy Recovery
Lin Zhou, Vincent Y. F. Tan and Mehul Motani (National University of Singapore, Singapore)
In this paper, we revisit the content identification problem with lossy recovery (Tuncel and G\"und\"uz, 2014) and establish the exponential strong converse theorem for the problem. Further, we derive an upper bound on the joint excess-distortion and error exponent for the problem.
pp. 928-932
10:10 Strong Converse Theorems for Discrete Memoryless Networks with Tight Cut-Set Bound
Silas L. Fong and Vincent Y. F. Tan (National University of Singapore, Singapore)
This paper considers a multimessage network where each node may send a message to any other node in the network. Under the discrete memoryless model, we prove the strong converse theorem for any network with tight cut-set bound, i.e., whose cut-set bound is achievable. Our result implies that for any network with tight cut-set bound and any fixed rate vector that resides outside the capacity region, the average error probabilities of any sequence of length-n codes operated at the rate vector must tend to 1 as n grows. The proof is based on the method of types. The proof techniques are inspired by the work of Csiszar and Korner in 1982 which fully characterized the reliability function of any discrete memoryless channel (DMC) with feedback for rates above capacity. Our proof techniques can be extended to the Gaussian case.
pp. 933-937
10:30 Reverse hypercontractivity region for the binary erasure channel
Chandra Nair (Chinese University of Hong Kong, Hong Kong); Yan Nan Wang (The Chinese University of Hong Kong, Hong Kong)
In this paper, we obtain the reverse hypercontractive region for the pair of variables $(X,Y)$ where $X$ is a uniformly distributed binary random variable and $Y$ (a ternary random variable) is obtained by passing $X$ through a symmetric binary erasure channel (BEC), for a non-trivial range of parameters. The technique used builds on two result results: $a)$ characterization of reverse hypercontractivity using information measures, and $b)$ computation of the forward hypercontractive region for the BEC.
pp. 938-942
10:50 Beyond the Blowing-Up Lemma: Sharp Converses via Reverse Hypercontractivity
Jingbo Liu, Ramon van Handel and Sergio Verdú (Princeton University, USA)
This paper proposes a general method for establishing non-asymptotic converses in network information theory via reverse hypercontractivity of Markov semigroups. In contrast to the blowing-up lemma, the proposed approach is applicable to non-discrete settings, and yields the optimal order of the second-order term in the rate expansion (square root of the blocklength) in the regime of non-vanishing error probability.
pp. 943-947

#### Tu1-7: Crypto 1

Room: K6
Chair: Matthieu Bloch (Georgia Institute of Technology, USA)
09:50 An Information-theoretic Approach to Hardness Amplification
Ueli Maurer (ETH Zurich, Switzerland)
Consider two independent games of chance, $G$ and $H$, which can be won with probability at most $\beta$ and $\gamma$, respectively. Then it can be shown that the game consisting of winning both $G$ and $H$ can be won with probability at most $\beta\gamma$. If the bounds on the winning probability are only due to the computational hardness of the problems and the computational complexity constraints of the game solver algorithm, then the analogous statement is not trivial but indeed holds in an approximate sense under certain conditions. This paper provides a general information-theoretic treatment of this result, showing that it is an abstract statement that is independent of complexity-theoretic considerations and exhibiting explicitly the requirement that a given game instance must be clonable. The core of the proof is a lemma on multi-argument conditional probability distributions. The amplification statement can be generalized to an arbitrary number of independent games, making the winning probability exponentially small in the number of such games.
pp. 948-952
10:10 Witness-Hiding Proofs of Knowledge for Cable Locks
Chen-Da Liu Zhang, Ueli Maurer, Martin Raszyk and Daniel Tschudi (ETH Zurich, Switzerland)
We consider the general setting where users need to provide a secret code c to a verifying entity V in order to obtain access to a resource. More generally, the right to access the resource could, for example, be granted if one knows one of two codes c1 and c2. For privacy reasons, a party P may want to hide which of the two codes it knows and only prove that it knows at least one of them. For example, if the knowledge of a code corresponds to membership in a certain society, one may want to hide which society one belongs to. In cryptography, such a proof is called a witness-hiding proof of knowledge. How can P prove such a statement to V? This paper is concerned with witness-hiding proofs of knowledge using simple mechanical tools. Specifically, we consider cable (or bicycle) locks, where the codes of the locks correspond to the secret codes. The above example of proving knowledge of either c1 or c2 in a witness-hiding fashion can be achieved simply as follows. When given the two locks closed and unlinked (by V), P presents the configuration of the two locks interlocked, which can be generated if and only if P knows at least one of the codes. In the most general case with n codes c1,...,cn, the access right is characterized by a so-called knowledge structure G, a subset of the power set of {1,...,n}. Access is granted if a user knows the codes corresponding to any of the subsets of G. We present lock-based protocols for witness-hiding proofs of knowledge for any such monotone knowledge structure, and investigate the efficiency (i.e., in particular, the number of lock configurations that P must present) in several settings such as the availability of solid rings or the availability of multiple locks for a given code. The topic of this paper is similar in spirit to other works, such as the picture hanging puzzles by Demaine et al., which explore connections between topology and real-world applications, where the motivation arises also, or even primarily, from mathematical curiosity.
pp. 953-957
10:30 Privacy Amplification of Distributed Encrypted Sources with Correlated Keys
Bagus Santoso (University of Electro-Communications); Yasutada Oohama (University of Electro-Communications, Japan)
In this paper, we consider a system where multiple sources are encrypted in separated nodes and sent through their respective public communication channels into a joint sink node. We are interested at the problem on protecting the security of an already existing system such above, which is found out to have correlated encryption keys. Specifically, we focus on finding a solution which does not require the modification of either the source data or the keys, since physically modifying terminals or key generators of an existing system in real world is not always feasible. We propose a solution under a security model where an eavesdropper obtains all ciphertexts, i.e., encrypted sources, by accessing available public communication channels. Our main technique is to use encoders of certain linear codes to encode the ciphertexts before sending them to public communication channels. We show that if the rates of linear codes are within a certain rate region: (1) the success probability of any eavesdropper to extract the original sources from the encoded ciphertexts without the keys is negligible, while (2) one who has legitimate keys is able to retrieve the original source data with negligible error probability.
pp. 958-962

#### Tu1-8: Wireless Communication

Room: K7+8
Chair: Yingbin Liang (Syracuse University, USA)
09:50 Can Full-Duplex More than Double the Capacity of Wireless Networks?
Serj Haddad (EPFL, Switzerland); Ayfer Özgür (Stanford University, USA); Emre Telatar (EPFL, Switzerland)
Usually, wireless radios are half-duplex, i.e. they can not transmit and receive at the same time over the same frequency band. However, building on self-interference cancellation techniques, full-duplex radios have emerged as a viable paradigm over the recent years. In this paper, we ask the following question: how much can full-duplex increase the capacity of wireless networks? Intuitively, one may expect that full-duplex radios can at most double the capacity of wireless networks, since they enable nodes to transmit and receive at the same time. In this paper, we show that the capacity gain can indeed be larger than a factor of 2; in particular, we construct a specific instance of a wireless relay network where the capacity with full-duplex radios is triple the capacity of the network when the relays are half-duplex. We also propose a universal schedule for half-duplex networks composed of independent, memoryless, point-to-point channels which achieves at least a fraction of 1/4 of the corresponding full-duplex capacity. This means that for wireless networks composed of point-to-point channels full-duplex capability at the relays cannot more than quadruple the capacity of network.
pp. 963-967
10:10 Short-Message Communication and FIR System Identification using Huffman Sequences
Philipp Walk (California Institute of Technology, USA); Peter Jung (TU-Berlin, Communications and Information Theory Group & Fraunhofer HHI - Heinrich Hertz Institute, Germany); Babak Hassibi (California Institute of Technology, USA)
Providing short-message communication and simultaneous channel estimation for sporadic and fast fading scenarios is a challenge for future wireless networks. In this work we propose a novel blind communication and deconvolution scheme by using Huffman sequences, which allows to solve three important tasks at once: (i) determination of the transmit power (ii) identification of the instantaneous discrete-time FIR channel if the channel delay is less than $L/2$ and (iii) simultaneously communicating $L-1$ bits of information. Our signal reconstruction uses a recent semi-definite program that can recover two unknown signals from their auto-correlations and cross-correlations. This convex algorithm shows numerical stability and operates fully deterministic without any further channel assumptions.
pp. 968-972
10:30 Novel Construction Methods of Quaternion Orthogonal Designs based on Complex Orthogonal Designs
Erum Mushtaq (National University of Sciences and Technology (NUST), Pakistan); Sajid Ali and Syed Ali Hassan (National University of Sciences and Technology, Pakistan)
Quaternion orthogonal designs (QODs) are considered the foundation of orthogonal space time polarization block codes (OSTPBCs). OSTPBCs benefit from orthogonal polarizations and orthogonal space and time block coding simultaneously to enhance the capacity of wireless communication systems. To exploit these advantages of OSTPBCs, this paper explores two generalized construction techniques of QODs, where the first one is based on symmetric-paired designs while the second technique maps the complex orthogonal designs (CODs) to QODs directly. With these schemes, QODs for any number of transmit antennas can be constructed. Moreover, a low-complexity maximum-likelihood (ML) decoder for the proposed construction techniques has been presented that provides optimal decoupled decoding with phenomenal complexity reduction. Simulation results show that the diversity order of the first QOD construction is higher than the second design given the number of transmit antennas are same.
pp. 973-977

#### Tu1-9: Hypothesis Testing 2

Room: K9
Chair: Yanina Shkel (UIUC and Princeton University, USA)
09:50 Hypothesis Test for Upper Bound on the Size of Random Defective Set
Arkadii Dyachkov and Ilya Vorobyev (Moscow State University, Russia); Nikita Polyanskii (Huawei Technologies Co. & Institute for Information Transmission Problems, Russia); Vladislav Shchukin (Institute for Information Transmission Problems, Russia)
Let $1 \leq s < t$, $N \geq 1$ be fixed integers and a complex electronic circuit of size $t$ is said to be an $s$-active, $s \ll t$, and can work as a system block if not more than $s$ elements of the circuit are defective. Otherwise, the circuit is said to be an $s$-defective and should be replaced by a similar $s$-active circuit. Suppose that there exists a possibility to run $N$ non-adaptive group tests to check the $s$-activity of the circuit. As usual, we say that a (disjunctive) group test yields the positive response if the group contains at least one defective element. In this paper, we will interpret the unknown set of defective elements as a random set and discuss upper bounds on the error probability of the hypothesis test for the null hypothesis $\{H_0: \text{the circuit is s-active}\}$ verse the alternative hypothesis $\{H_1: \text{the circuit is s-defective}\}$. Along with the conventional decoding algorithm based on the known random set of positive responses and disjunctive $s$-codes, we consider a $T$-weight decision rule, which is based on the simple comparison of a fixed threshold $T$, $1 \leq T < N$, with the known random number of positive responses $p$, $0 \leq p \leq N$.
pp. 978-982
10:10 Distributed Hypothesis Testing Over Noisy Channels
Sreejith Sreekumar and Deniz Gündüz (Imperial College London, United Kingdom (Great Britain))
A distributed binary hypothesis testing problem, in which multiple observers transmit their observations to a detector over noisy channels, is studied. Given its own side information, the goal of the detector is to decide between two hypotheses for the joint distribution of the data. Single-letter upper and lower bounds on the optimal type 2 error exponent (T2-EE), when the type 1 error probability vanishes with the block-length are obtained. These bounds coincide and characterize the optimal T2-EE when only a single helper is involved. Our result shows that the optimal T2-EE depends on the marginal distributions of the data and the channels rather than their joint distribution. However, an operational separation between HT and channel coding does not hold, and the optimal T2-EE is achieved by generating channel inputs correlated with observed data.
pp. 983-987
10:30 Linear-Complexity Exponentially-Consistent Tests for Universal Outlying Sequence Detection
Yuheng Bu and Shaofeng Zou (University of Illinois at Urbana Champaign, USA); Venugopal Veeravalli (University of Illinois at Urbana-Champaign, USA)
We study a universal outlying sequence detection problem, in which there are $M$ sequences of samples out of which a small subset of outliers need to be detected. A sequence is considered as an outlier if the observations therein are generated by a distribution different from those generating the observations in the majority of the sequences. In the universal setting, the goal is to identify all the outliers without any knowledge about the underlying generating distributions. In prior work, this problem was studied as a universal hypothesis testing problem, and a generalized likelihood (GL) test was constructed and its asymptotic performance characterized. In this paper, we propose a different class of tests for this problem based on distribution clustering. Such tests are shown to be exponentially consistent and their time complexity is linear in the total number of sequences, in contrast with the GL test, which has time complexity that is exponential in the number of outliers. Furthermore, our tests based on clustering are applicable to more general scenarios. For example, when both the typical and outlier distributions form clusters, the clustering based test is exponentially consistent, but the GL test is not even applicable.
pp. 988-992
10:50 Active Hypothesis Testing on A Tree: Anomaly Detection under Hierarchical Observations
Chao Wang (Cornell University, USA); Kobi Cohen (Ben-Gurion University of the Negev, Israel); Qing Zhao (Cornell University, USA)
The problem of detecting a few anomalous processes among a large number of M processes is considered. At each time, aggregated observations can be taken from a chosen subset of processes, where the chosen subset conforms to a given binary tree structure. The random observations are i.i.d. over time with a general distribution that may depend on the size of the chosen subset and the number of anomalous processes in the subset. The objective is a sequential search strategy that minimizes the sample complexity (i.e., the expected number of observations which represents detection delay) subject to a reliability constraint. A sequential test that results in a biased random walk on the tree is developed and is shown to be asymptotically optimal in terms of detection accuracy. Furthermore, it achieves the optimal logarithmic-order sample complexity in M provided that the Kullback-Liebler divergence between aggregated observations in the presence and the absence of anomalous processes are bounded away from zero at all levels of the tree structure as M approaches infinity. Sufficient conditions on the decaying rate of the aggregated observations to pure noise under which a sublinear scaling in M is preserved are also identified for the Bernoulli case.
pp. 993-997

### Tuesday, June 27, 11:30 - 12:50

#### Tu2-1: Coding Techniques 2

Room: Europa
Chair: Alexander Barg (University of Maryland, USA)
11:30 Fractional decoding: Error correction from partial information
Itzhak Tamo (Tel Aviv University, Israel); Min Ye (UMD, USA); Alexander Barg (University of Maryland, USA)
We consider error correction by maximum distance separable (MDS) codes based on a part of the received codeword. Our problem is motivated by applications in distributed storage. While efficiently correcting erasures by MDS storage codes (the repair problem'') has been widely studied in recent literature, the problem of correcting errors in a similar setting seems to represent a new question in coding theory. Suppose that $k$ data symbols are encoded using an $(n,k)$ MDS code, and some of the codeword coordinates are located on faulty storage nodes that introduce errors. We want to recover the original data from the corrupted codeword under the constraint that the decoder can download only an $\alpha$ proportion of the codeword (fractional decoding). For any $(n,k)$ code we show that the number of correctable errors under this constraint is bounded above by $\lfloor (n-k/\alpha)/2 \rfloor.$ Moreover, we present two families of MDS array codes which achieves this bound with equality under a simple decoding procedure. The decoder downloads an $\alpha$ proportion of each of the codeword's coordinates, and provides a much larger decoding radius compared to the naive approach of reading some $\alpha n$ coordinates of the codeword. One of the code families is formed of Reed-Solomon (RS) codes with well-chosen evaluation points, while the other is based on folded RS codes. Finally, we show that folded RS codes also have the optimal list decoding radius under the fractional decoding constraint.
pp. 998-1002
11:50 Performance of Optimal Data Shaping Codes
Yi Liu, Pengfei Huang and Paul H. Siegel (University of California, San Diego, USA)
Data shaping is a coding technique that has been proposed to increase the lifetime of flash memory devices. Several data shaping codes have been described in recent work, including endurance codes and direct shaping codes for structured data. In this paper, we study information-theoretic properties of a general class of data shaping codes and prove a separation theorem stating that optimal data shaping can be achieved by the concatenation of optimal lossless compression with optimal endurance coding. We also determine the expansion factor that minimizes the total wear cost. Finally, we analyze the performance of direct shaping codes and establish a condition for their optimality.
pp. 1003-1007
12:10 Multilevel Code Construction for Compound Fading Channels
Antonio Campello (Imperial College London, United Kingdom (Great Britain)); Ling Liu (Department of Electrical and Electronic Engineering Imperial College London, United Kingdom (Great Britain)); Cong Ling (Imperial College London, United Kingdom (Great Britain))
We consider explicit constructions of multi-level lattice codes that universally approach the capacity of the compound block-fading channel. Specifically, building on algebraic partitions of lattices, we show how to construct codes with negligible probability of error for any channel realization and normalized log-density approaching the Poltyrev limit. Capacity analyses and numerical results on the achievable rates for each partition level are provided. The proposed codes have several enjoyable properties such as constructiveness and good decoding complexity, as compared to random one-level codes. Numerical results for finite-dimensional multi-level lattices based on polar codes are exhibited.
pp. 1008-1012
12:30 Dense Gray Codes in Mixed Radices
Jessica Fan and Thomas H. Cormen (Dartmouth College, USA)
The standard binary reflected Gray code produces a permutation of the sequence of integers <0,1,...,n-1>, where n is a power of 2, such that the binary representation of each integer in the permuted sequence differs from the binary representation of the preceding integer in exactly one bit. In an earlier paper, we presented two methods to compute binary dense Gray codes, which extend the possible values of n to the set of all positive integers while preserving both the Gray code property---only one bit changes between each pair of consecutive integers---and the denseness property---the sequence contains exactly the n integers 0 to n-1. This paper generalizes our method for binary dense Gray codes to arbitrary radices that may be either a single fixed radix for all digits or mixed radices, so that each digit may have a different radix. That is, we show how to produce a permutation of <0,1,...,n-1> represented in any set of radices, such that the representation of each number differs from the representation of the preceding number in exactly one digit, and the values of these digits differ by exactly 1. We provide a simple formula for this permutation, which we can use to quickly compute a Hamiltonian path for a dynamic array of n nodes, where the nodes are added and deleted in order along the k dimensions of a grid network.
pp. 1013-1017

#### Tu2-2: Locally Repairable Codes 2

Room: Brussels
Chair: Antonia Tulino (Bell Labs, USA & Università Federico II, Italy)
11:30 Balanced and Sparse Tamo-Barg Codes
Wael Halbawi (California Institute of Technology, USA); Iwan Duursma and Hoang Dau (University of Illinois at Urbana-Champaign, USA); Babak Hassibi (California Institute of Technology, USA)
We construct balanced and sparse generator matrices for Tamo and Barg's Locally Recoverable Codes (LRCs). More specifically, for length $n$, dimension $k$ and locality $r$ cyclic Tamo--Barg code, we show how to deterministically construct a generator matrix where the number of nonzeros in any two columns differs by at most one, and where the weight of every row is $d + r - 1$, where $d$ is the minimum distance of the code. Since LRCs are designed mainly for distributed storage systems, the results presented here provide a computationally balanced and efficient encoding scheme for these codes. The balanced property ensures the computational effort exerted is the essentially the same for any server, whilst the sparse property ensures that this effort is minimal. The work presented in this paper extends a similar result for Reed--Solomon (RS) codes, where it is now known that any cyclic RS code possesses a generator matrix that is balanced as described, but is sparsest, meaning that each row has $d$ nonzeros.
pp. 1018-1022
11:50 Bounds and Constructions of Codes with All-Symbol Locality and Availability
Stanislav Kruglik (Moscow Institute of Physics and Technology & Skolkovo Institute of Science and Technology, Russia); Alexey A. Frolov (Skolkovo Institute of Science and Technology & IITP RAS, Russia)
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the shortening method and improves existing shortening bounds. To reduce the gap in between upper and lower bounds we do not restrict the alphabet size and propose explicit constructions of codes with locality and availability via rank-metric codes. The first construction relies on expander graphs and is better in low rate region, the second construction utilizes LRC codes developed by Wang et al. as inner codes and better in high rate region.
pp. 1023-1027
12:10 Security for Minimum Storage Regenerating Codes and Locally Repairable Codes
Swanand Kadhe and Alex Sprintson (Texas A&M University, USA)
We consider the problem of designing 'repair efficient' distributed storage systems, which are information-theoretically secure against a passive eavesdropper that can gain access to a limited number of storage nodes. We present a framework that enables design of a broad range of secure storage codes through a joint construction of inner and outer codes. As case studies, we focus on two specific families of storage codes: (i) minimum storage regenerating (MSR) codes, and (ii) maximally recoverable (MR) codes, which are a class of locally repairable codes (LRCs). The main idea of this framework is to utilize the existing constructions of storage codes to jointly design an outer coset code and inner storage code. Finally, we present a construction of an outer coset code over small field size to secure locally repairable codes presented by Tamo and Barg for the special case of an eavesdropper that can observe any subset of nodes of maximum possible size.
pp. 1028-1032

Room: K2
Chair: Vincent Y. F. Tan (National University of Singapore, Singapore)
11:30 The Arbitrarily Varying Degraded Broadcast Channel with Causal Side Information at the Encoder
Uzi Pereg (Technion); Yossef Steinberg (Technion, Israel)
In this work, we study the arbitrarily varying degraded broadcast channel (AVDBC), when state information is available at the transmitter in a causal manner. We establish inner and outer bounds on both the random code capacity region and the deterministic code capacity region. The capacity region is then determined for a class of channels satisfying a condition on the mutual informations between the strategy variables and the channel outputs. As an example, we show that the condition holds for the arbitrarily varying binary symmetric broadcast channel, and we find the corresponding capacity region.
pp. 1033-1037
Mehdi Yazdanpanah (The Chinese University of Hong Kong, Hong Kong); Chandra Nair (Chinese University of Hong Kong, Hong Kong)
In this article, we resolve open problem 8.2 in Network Information Theory Book by El Gamal and Kim. We show that superposition coding is sub-optimal for a three receiver broadcast channel with two message sets $(M_0,M_1)$ where two of the three receivers need to decode messages $(M_0,M_1)$ while the remaining one just needs to decode the message $M_0$.
pp. 1038-1042
Dor Itzhak and Yossef Steinberg (Technion, Israel)
As demonstrated in many recent studies, cooperation between users can greatly improve the performance of communication systems. Most of the works in the literature present models where all the users are aware of the resources available for cooperation. However, the scenario where cooperation links are sometimes unavailable or that some users cannot be updated whether the cooperation links are present or not, is more realistic in today's dynamic ad-hoc communication systems. In such a case we need coding schemes that exploit the cooperation links if they are present, and can still operate if cooperation is not possible. In this work we study the general broadcast channel model with degraded message sets and cooperation links that may be absent, and derive it's capacity region under such uncertainty conditions.
pp. 1043-1047
12:30 On the Capacity Region of the K-User Discrete Memoryless Broadcast Channel with Two Degraded Messages
Mahesh K Varanasi (University of Colorado, USA); Mohamed Salman (University of Colorado Boulder, USA)
The K-user discrete memoryless (DM) broadcast channel (BC) with two degraded messages, with one common message to be decoded by all receivers and a private message by a subset of receivers, is studied. The receivers that must decode both messages are referred to as private receivers and the remaining ones that must decode only the common message as common receivers. We obtain two main results. The first main result establishes the capacity region of two classes of DM BCs characterized by the associated sets of pair-wise relationships between and among the common and private receivers, each described by the well-known more capable and less noisy conditions. For both these classes, the capacity region is achieved by superposition coding and joint decoding so that the main contribution herein lies in the proofs of the converses. When specialized to the two previously well-studied cases of a single private receiver and a single common receiver, the two aforementioned classes are respectively as large as or larger than those for which capacity was previously obtained. The second main result is a new inner bound in closed form for arbitrary $K$ and a general subset of private receivers that involves rate splitting, superposition coding, and indirect decoding and we state its capacity optimality for a new class of four-receiver DM BCs.
pp. 1048-1052

#### Tu2-4: Channel Capacity 2

Room: K3
Chair: Amos Lapidoth (ETHZ, Switzerland)
11:30 The Optimal Exponent Function for the Additive White Gaussian Noise Channel at Rates above the Capacity
Yasutada Oohama (University of Electro-Communications, Japan)
We consider the additive white Gaussian noise channels. We prove that the error probability of decoding tends to one exponentially for rates above the capacity and derive the optimal exponent function. We shall demonstrate that the information spectrum approach is quite useful for investigating this problem.
pp. 1053-1057
11:50 A Generalized Ozarow-Wyner Capacity Bound with Applications
Alex Dytso, Mario Goldenbaum and H. Vincent Poor (Princeton University, USA); Shlomo (Shitz) Shamai (The Technion, Israel)
In this paper, a generalized Ozarow-Wyner capacity bound is presented that holds for arbitrary noise channels. The bound is then used to approximate the capacity of a large class of additive noise channels that are subject to a $p$-th moment input constraint, where $p$ is some positive real number, as well as to the Cauchy noise channel with a logarithmic moment constraint. For both channel models the gap to the capacity is precisely specified.
pp. 1058-1062
12:10 A Bound on the Shannon Capacity via a Linear Programming Variation
Sihuang Hu, Itzhak Tamo and Ofer Shayevitz (Tel Aviv University, Israel)
We prove an upper bound on the Shannon capacity of a graph via a linear programming variation. We also show that our bound can be better than Lovasz theta number and Haemers minimum rank bound.
pp. 1063-1066
12:30 On the Discreteness of Capacity-Achieving Distributions for the Censored Channel
Arash Behboodi, Gholamreza Alirezaei and Rudolf Mathar (RWTH Aachen University, Germany)
The censored channel is one of the fundamental channels in information theory, which belongs to the class of non-linear channels. It is modeled by cascading an additive noise channel with a clipping operator. This paper is concerned with the information theoretic capacity of this channel. A necessary and sufficient condition for optimality of the input distribution is derived and it is shown that the capacity-achieving input distribution for the amplitude-limited censored channel has only a finite number of mass points. This result holds for a large class of noise distributions including additive Gaussian noise.
pp. 1067-1071

#### Tu2-5: Massive MIMO

Room: K4
Chair: Christoph Studer (Cornell University, USA)
11:30 Massive Device Connectivity with Massive MIMO
Liang Liu and Wei Yu (University of Toronto, Canada)
This paper studies a single-cell uplink massive device communication scenario in which a large number of single antenna devices are connected to the base station (BS), but user traffic is sporadic so that at a given coherence interval, only a subset of users are active. For such a system, active user detection and channel estimation are key issues. To accommodate such a large number of active users, this paper studies the asymptotic regime where the BS is equipped with a large number of antennas. A grant-free two-phase access scheme is adopted where user activity detection and channel estimation are performed in the first phase, and data is transmitted in the second phase. Our main contributions are as follows. First, this paper shows that despite the non-orthogonality of pilot sequences (which is necessary for accommodating a large number of potential devices), in the asymptotic massive multiple-input multiple-output (MIMO) regime, both the missed detection and false alarm probabilities can be made to go to zero by utilizing compressed sensing techniques that exploit sparsity in user activities. Further, this paper shows that despite the guaranteed success in user activity detection, the non-orthogonality of pilot sequences nevertheless can cause significant channel estimation error, thus the overall achievable transmission rate in the massive MIMO regime is mostly limited by channel estimation rather than device activity detection performance. This paper quantifies the cost due to non-orthogonal pilots for massive connectivity and further identifies the optimal pilot length in this setting.
pp. 1072-1076
11:50 On the MISO Channel with Feedback: Can Infinitely Massive Antennas Achieve Infinite Capacity?
Jinyuan Chen (Louisiana Tech University, USA)
We consider communication over a multiple-input single-output (MISO) block fading channel in the presence of an independent noiseless feedback link. We assume that the transmitter and receiver have no prior knowledge of the channel state realizations, but the transmitter and receiver can acquire the channel state information (CSIT/CSIR) via downlink training and feedback. For this channel, we show that increasing the number of transmit antennas to infinity will not achieve an infinite capacity, for a finite channel coherence and a finite input constraint on the second or fourth moment. This insight follows from our new capacity bounds that hold for any linear and nonlinear coding strategies, and any channel training schemes. In addition to the channel capacity bounds, we also provide a characterization on the beamforming gain that is also known as array gain or power gain, at the regime with large number of antennas.
pp. 1077-1081
12:10 The BOX-LASSO with Application to GSSK Modulation in Massive MIMO Systems
Ismail Ben Atitallah (KAUST, Saudi Arabia); Christos Thrampoulidis (MIT, USA); Abla Kammoun (Kaust, Saudi Arabia); Tareq Y. Al-Naffouri (King Abdullah University of Science and Technology, USA); Mohamed-Slim Alouini (King Abdullah University of Science and Technology (KAUST), Saudi Arabia); Babak Hassibi (California Institute of Technology, USA)
The BOX-LASSO is a variant of the popular LASSO that includes an additional box-constraint. We propose its use as a decoder in modern Multiple Input Multiple Output (MIMO) communication systems with modulation methods such as the Generalized Space Shift Keying (GSSK) modulation, which produce constellation vectors that are inherently sparse and have elements that belong to finite alphabets. In that direction, we prove novel explicit asymptotic characterizations of the squared-error and of the per-element error rate of the BOX-LASSO, under iid Gaussian measurements. In particular, the theoretical predictions can be used to quantify the improved performance of the BOX-LASSO, when compared to the previously used standard LASSO. We include simulation results that validate both these premises and our theoretical predictions.
pp. 1082-1086
12:30 Multi-Users Space-Time Modulation with QAM Division for Massive Uplink Communications
Jian-Kang Zhang and Zheng Dong (McMaster University, Canada)
In this paper, we consider the design of multi-users space-time modulation (MUSTM) for an uplink MIMO system with one base station equipped with the massive number of antennas and $N$ single-antenna users, where it is assumed that only large scale channel coefficients are available at both the transmitter and the receiver. For such a system, a novel concept called uniquely factorable (UF) MUSTM is introduced. Then, using our recently developed framework on uniquely decomposable constellation group with energy-efficient quadrature amplitude modulation (QAM), and properly and timely assigning each sub-constellation to each user at each time slot, we develop a machinery method for systematically designing a family of invertible UF-MUSTM with flexible data rates in order to assure the reliable estimation of the transmitted signal as well as of the channel for the massive MIMO system. In addition, a simple cross-correlation receiver is proposed to efficiently and effectively detect such UF-MUSTM. Its pair-wise error probability (PEP) is derived, showing that our proposed invertible UF-MUSRM enables full receiver diversity. Furthermore, the optimal closed-form power allocation and the optimal user constellation assignment are found to maximize the worst-case coding gain under a peak power constraint on each user and each time slot.
pp. 1087-1091

#### Tu2-6: MIMO 2

Room: K5
Chair: Vasanthan Raghavan (Qualcomm, Inc., USA)
11:30 Generalized Degrees-of-Freedom of the 2-User Case MISO Broadcast Channel with Distributed CSIT
Antonio Bazco (EURECOM & Mitsubitshi Electric Research Centre Europe, France); Paul de Kerret (EURECOM, France); David Gesbert (Eurecom Institute, France); Nicolas Gresset (Mitsubishi Electric Research Centre Europe, France)
This work analyses the Generalized Degrees-of-Freedom (GDoF) of the 2-User Multiple-Input Single-Output (MISO) Broadcast Channel (BC) in the so-called Distributed CSIT regime, with application to decentralized wireless networks. This regime differs from the classical limited CSIT one in that the CSIT is not just noisy but also imperfectly shared across the transmitters (TXs). Hence, each TX precodes data on the basis of local CSIT and statistical quality information at other TXs. We derive the GDoF result and obtain the surprising outcome that by specific accounting of the pathloss information, it becomes possible for the decentralized precoded network to reach the same performance as a genie-aided centralized network where the central node has obtained the estimates of both TXs. The key idea allowing this surprising robustness is to let the TXs have asymmetrical roles such that the most informed TX is able to balance the lower CSIT quality at the other TX.
pp. 1092-1096
11:50 Spatially Correlated MIMO Broadcast Channel: Analysis of Overlapping Correlation Eigenspaces
Fan Zhang and Mohamed Fadel (University of Texas at Dallas, USA); Aria Nosratinia (University of Texas, Dallas, USA)
Antenna correlation is prevalent in higher frequencies as well as in massive MIMO, thus the study of {\em correlated} MIMO broadcast channels is becoming a subject of increasing interest. This paper explores the fundamental limits of such systems, focusing on cases where correlation eigenspaces are neither independent nor identical, so that known beam-space division techniques do not directly apply. We begin by introducing a simple but novel tight outer bound on the degrees of freedom (DoF) of noncoherent point-to-point MIMO channels under transmit antenna correlation. We then analyze the performance of a two-user MIMO broadcast channel when one correlation eigenspace is a subspace of the other. We extend the result to $K$-user MIMO broadcast channel. Our results show that it is possible to exploit the differences between the correlation structure of transmit antennas towards different receivers to extract DoF gains out of the system. The extent of these gains are highlighted via several examples.
pp. 1097-1101
12:10 On the Achievable Rates of Decentralized Equalization in Massive MU-MIMO Systems
Charles Jeon (Cornell University, USA); Kaipeng Li and Joseph R. Cavallaro (Rice University, USA); Christoph Studer (Cornell University, USA)
Massive multi-user (MU) multiple-input multiple-output (MIMO) promises significant gains in spectral efficiency compared to traditional, small-scale MIMO technology. Linear equalization algorithms, such as zero forcing (ZF) or minimum mean-square error (MMSE)-based methods, typically rely on centralized processing at the base station (BS), which results in (i) excessively high interconnect and chip input/output data rates, and (ii) high computational complexity. In this paper, we investigate the achievable rates of decentralized equalization that mitigates both of these issues. We consider two distinct BS architectures that partition the antenna array into clusters, each associated with independent radio-frequency chains and signal processing hardware, and the results of each cluster are fused in a feedforward network. For both architectures, we consider ZF, MMSE, and a novel, non-linear equalization algorithm that builds upon approximate message passing (AMP), and we theoretically analyze the achievable rates of these methods. Our results demonstrate that decentralized equalization with our AMP-based methods incurs no or only a negligible loss in terms of achievable rates compared to that of centralized solutions.
pp. 1102-1106
12:30 V-BLAST in Lattice Reduction and Integer Forcing
Sebastian Stern and Robert F.H. Fischer (Ulm University, Germany)
Lattice-reduction-aided decision-feedback equalization (LRA DFE) and successive integer forcing are MIMO detection schemes which combine the equalization in a suited basis with the principle of successive interference cancellation (SIC). To this end, the reduction algorithm not only has to find a suited basis, but it should also provide an optimized detection order for SIC: the V-BLAST ordering, known to be optimal for conventional DFE. How these two tasks can be solved jointly has so far remained unclear in the literature. In this paper, we describe how the Lenstra-Lenstra-Lovasz (LLL) reduction has to be adapted to achieve this aim. Moreover, we propose a weakened variant of the Hermite-Korkine-Zolotareff (HKZ) reduction that optimally solves both tasks jointly. Results obtained from numerical simulations complement the theoretical derivations.
pp. 1107-1111

#### Tu2-7: Energy Harvesting 2

Room: K6
Chair: Deniz Gündüz (Imperial College London, United Kingdom (Great Britain))
11:30 Energy-Based Adaptive Multiple Access in LPWAN IoT Systems with Energy Harvesting
Nicolò Michelusi (Purdue University, USA); Marco Levorato (University of California, Irvine, USA)
This paper develops a control framework for a network of energy harvesting nodes connected to a Base Station (BS) over a multiple access channel. The objective is to adapt their transmission strategy to the state of the network, including the energy available to the individual nodes. In order to reduce the complexity of control, an optimization framework is proposed where energy storage dynamics are replaced by dynamic average power constraints induced by the time correlated energy supply, thus enabling lightweight and flexible network control. Specifically, the BS adapts the packet transmission probability of the "active" nodes (those currently under a favorable energy harvesting state) so as to maximize the average long-term throughput, under these dynamic average power constraints. The resulting policy takes the form of the packet transmission probability as a function of the energy harvesting state and number of active nodes. The structure of the throughput-optimal genie-aided policy, in which the number of active nodes is known non-causally at the BS, is proved. Inspired by the genie-aided policy, a Bayesian estimation approach is presented to address the case where the BS estimates the number of active nodes based on the observed network transmission pattern. It is shown that the proposed scheme outperforms by 20% a scheme in which the nodes operate based on local state information only, and performs well even when energy storage dynamics are taken into account.
pp. 1112-1116
11:50 Near Optimal Online Distortion Minimization for Energy Harvesting Nodes
Ahmed Arafa (University of Maryland College Park, USA); Sennur Ulukus (University of Maryland, USA)
We consider online scheduling for an energy harvesting communication system where a sensor node collects samples from a Gaussian source and sends them to a destination node over a Gaussian channel. The sensor is equipped with a finite-sized battery that is recharged by an independent and identically distributed (i.i.d.) energy harvesting process over time. The goal is to minimize the long term average distortion of the source samples received at the destination. We study two problems: the first is when sampling is cost-free, and the second is when there is a sampling cost incurred whenever samples are collected. We show that fixed fraction policies [Shaviv-Ozgur], in which a fixed fraction of the battery state is consumed in each time slot, are near-optimal in the sense that they achieve a long term average distortion that lies within a constant additive gap from the optimal solution for all energy arrivals and battery sizes. For the problem with sampling costs, the transmission policy is bursty; the sensor can collect samples and transmit for only a portion of the time.
pp. 1117-1121
12:10 Scheduling Status Updates to Minimize Age of Information with an Energy Harvesting Sensor
Tan Bacinoglu (METU, Turkey); Elif Uysal-Biyikoglu (METU)
Age of Information is a measure of the freshness of status updates in monitoring applications and update-based systems. We study a real-time sensing scenario with a sensor which is restricted by time-varying energy constraints and battery limitations. The sensor sends updates over a packet erasure channel with no feedback. The problem of finding an age- optimal threshold policy, with the transmission threshold being a function of the energy state and the estimated current age, is formulated. The average age is analyzed for the unit battery scenario under a memoryless energy arrival process. Somewhat surprizingly, for any finite arrival rate of energy, there is a positive age threshold for transmission, which corresponding to transmitting lower than the rate of energy arrivals. A lower bound on the average age is obtained for general battery size.
pp. 1122-1126
12:30 Code Design for Binary Energy Harvesting Channel
Mehdi Dabirnia and Tolga M. Duman (Bilkent University, Turkey)
We consider a binary energy harvesting communication system with a finite battery transmitter over a noisy channel, and design explicit and implementable codes based on concatenation of a nonlinear trellis code (NLTC) with an outer low density parity check (LDPC) code. We propose two different decoding methods where the simplified one ignores the memory in the battery state while the more sophisticated one utilizes the memory. Numerical results demonstrate that the designed codes outperform other reference schemes. The results also show the superiority of the improved decoding approach over the naive solution.
pp. 1127-1131

#### Tu2-8: Compressed Sensing 2

Room: K7+8
Chair: Tara Javidi (UCSD, USA)
11:30 A Greedy Blind Calibration Method for Compressed Sensing with Unknown Sensor Gains
Valerio Cambareri and Amirafshar Moshtaghpour (Université Catholique de Louvain, Belgium); Laurent Jacques (University of Louvain, Belgium)
The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual physical implementation, which can amply differ from the assumed model. In this paper we tackle the bilinear inverse problem of recovering a sparse input signal and some unknown, unstructured multiplicative factors affecting the sensors that capture each compressive measurement. Our methodology relies on collecting a few snapshots under new draws of the sensing operator, and applying a greedy algorithm based on projected gradient descent and the principles of iterative hard thresholding. We explore empirically the sample complexity requirements of this algorithm by testing its phase transition, and show in a practically relevant instance of this problem for compressive imaging that the exact solution can be obtained with only a few snapshots.
pp. 1132-1136
11:50 Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization
Jess Banks (University of California-Berkeley, USA); Cristopher Moore (Santa Fe Institute); Roman Vershynin (University of Michigan, USA); Nicolas Verzelen (INRA, USA); Jiaming Xu (Purdue University, USA)
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is conjectured to exhibit a sharp information-theoretic threshold, below which the signal is too weak for any algorithm to detect. We derive upper and lower bounds on these thresholds by applying the first and second moment methods to the likelihood ratio between these planted models'' and null models where the signal matrix is zero. For sparse PCA and submatrix localization, we determine this threshold exactly in the limit where the number of blocks is large or the signal matrix is very sparse; for the clustering problem, our bounds differ by a factor of $\sqrt{2}$ when the number of clusters is large. Moreover, our upper bounds show that for each of these problems there is a significant regime where reliable detection is information-theoretically possible but where known algorithms such as PCA fail completely, since the spectrum of the observed matrix is uninformative. This regime is analogous to the conjectured hard but detectable' regime for community detection in sparse graphs.
pp. 1137-1141
12:10 Almost Optimal Phaseless Compressed Sensing with Sublinear Decoding Time
Vasileios Nakos (Harvard University, USA)
In the problem of compressive phase retrieval, one wants to recover an approximately $k$-sparse signal $x \in \mathbb{C}^n$, given the magnitudes of the entries of $\Phi x$, where $\Phi \in \mathbb{C}^{m \times n}$. This problem has received a fair amount of attention, with sublinear time algorithms appearing in several publications. In this paper we further investigate the direction of sublinear decoding for real signals by giving a recovery scheme under the $\ell_2 / \ell_2$ guarantee, with almost optimal, $\mathcal{O}(k \log n)$, number of measurements. Our result outperforms all previous work in the number of measurements, while it also achieves a stronger error guarantee and a smaller failure probability. Moreover, we give a very simple deterministic scheme that recovers all $k$-sparse vectors in $\mathcal{O}(k^3)$ time, using $4k-1$ measurements.
pp. 1142-1146
12:30 A Characterization of Sampling Patterns for Low-Rank Multi-View Data Completion Problem
Morteza Ashraphijuo and Xiaodong Wang (Columbia University, USA); Vaneet Aggarwal (Purdue University, USA)
In this paper, we consider the problem of completing a sampled matrix $\mathbf{U}=[\mathbf{U}_1|\mathbf{U}_2]$ given the ranks of $\mathbf{U}$, $\mathbf{U}_1$, and $\mathbf{U}_2$ which is known as the multi-view data completion problem. We characterize the deterministic conditions on the locations of the sampled entries that is equivalent (necessary and sufficient) to finite completability of the sampled matrix. To this end, in contrast with the existing analysis on Grassmannian manifold for a single-view matrix, i.e., conventional matrix completion, we propose a geometric analysis on the manifold structure for multi-view data to incorporate more than one rank constraint. Then, using the proposed geometric analysis, we propose sufficient conditions on the sampling pattern, under which there exists only one completion (unique completability) given the three rank constraints.
pp. 1147-1151

#### Tu2-9: Source Coding 2

Room: K9
Chair: Ertem Tuncel (UC Riverside, USA)
11:30 Coding of Binary AIFV Code Trees
Kentaro Sumigawa and Hirosuke Yamamoto (The University of Tokyo, Japan)
Binary AIFV codes, which can attain better compression rate than Huffman codes, uses two code trees that may have incomplete internal nodes, and source symbols are assigned to some internal nodes in addition to leaves. Although the code trees of Huffman codes, which are full binary trees, are well studied, the AIFV code trees have not yet studied in detail. In this paper, we show that there exists a bijection between binary AIFV code trees and Schr\"oder paths, and give two coding schemes to represent Schr\"oder paths. The first one is a fixed length coding scheme, which has O($n^2$) time-complexity. The second one is a variable length coding scheme using a simple AIFV code. The latter attains O($n$) time-complexity, but the coding rate has loss less than 4.1\% of the optimal coding rate.
pp. 1152-1156
11:50 Universal lossy compression under logarithmic loss
Yanina Shkel (UIUC and Princeton University, USA); Maxim Raginsky (University of Illinois at Urbana-Champaign, USA); Sergio Verdú (Princeton University, USA)
Universal lossy source coding with the logarithmic loss distortion criterion is studied. Bounds on the non-asymptotic fundamental limit of fixed-length universal coding with respect to a family of distributions are derived. These bounds generalize the well-known minimax bounds for universal lossless source coding. The asymptotic behavior of the resulting optimization problem is studied for a family of iid sources with a finite alphabet size, and is characterized up to a constant. The redundancy of memoryless sources behaves like $\frac{k}{2}\log n$, where $n$ is the blocklength and $k$ is the number of degrees of freedom in the parameter space. The impact of the coding rate is on the constant term: higher compression rate effectively reduces the volume of the parameter uncertainty set.
pp. 1157-1161
12:10 Towards Optimal Quantization of Neural Networks
Avhishek Chatterjee and Lav R. Varshney (University of Illinois at Urbana-Champaign, USA)
Due to the unprecedented success of deep neural networks in inference tasks like speech and image recognition, there has been increasing interest in using them in mobile and in-sensor applications.As most current deep neural networks are very large in size, a major challenge lies in storing the network in devices with limited memory. Consequently there is growing interest in compressing deep networks by quantizing synaptic weights, but most prior work is heuristic and lacking theoretical foundations. Here we develop an approach to quantizing deep networks using functional high-rate quantization theory. Under certain technical conditions, this approach leads to an optimal quantizer that is computed using the celebrated backpropagation algorithm. In all other cases, a heuristic quantizer with certain regularization guarantees can be computed.
pp. 1162-1166
12:30 Stochastic Stability of Non-Markovian Processes and Adaptive Quantizers
In many applications, the common assumption that a driving noise process affecting a system is independent or Markovian may not be realistic, but the noise process may be assumed to be stationary. To study such problems, this paper investigates stochastic stability properties of a class of non-Markovian processes, where the existence of a stationary measure, asymptotic mean stationarity and ergodicity conditions are studied. Applications in adaptive quantization and stochastic networked control are presented.
pp. 1167-1171

### Tuesday, June 27, 14:40 - 16:20

#### Tu3-1: Network Coding 1

Room: Europa
Chair: Tuvi Etzion (Technion-Israel Institute of Technology, Israel)
14:40 Secrecy and Robustness for Active Attack in Secure Network Coding
Masahito Hayashi (Nagoya University, Japan); Masaki Owari (Shizuoka University, Japan); Go Kato (NTT Corporation, Japan); Ning Cai (Xidian University, P.R. China)
In the network coding, we discuss the effect by sequential error injection to information leakage. We show that there is no improvement when the network is composed of linear operations. However, when the network contains non-linear operations, we find a counterexample to improve Eve's obtained information. Further, we discuss the asymptotic rate in the linear network under the secrecy and robustness conditions.
pp. 1172-1176
15:00 Linear Network Coding for Two-Unicast-Z Networks: A Commutative Algebraic Perspective and Fundamental Limits
Mohammad Fahim (The Pennsylvania State University, USA); Viveck Cadambe (Pennsylvania State University, USA)
We consider a two-unicast-Z network over a directed acyclic graph of unit capacitated edges; the two-unicast-Z network is a special case of two-unicast networks where one of the destinations has apriori side information of the unwanted (interfering) message. In this paper, we settle open questions on the limits of network coding for two-unicast- Z networks by showing that the generalized network sharing bound is not tight, vector linear codes outperform scalar linear codes, and non-linear codes outperform linear codes in general. We also develop a commutative algebraic approach to deriving linear network coding achievability results, and demonstrate our approach by providing an alternate proof to the previous result of Wang et. al. regarding feasibility of rate (1, 1) in the network.
pp. 1177-1181
15:20 Network-Coded Fronthaul Transmission for Cache-Aided C-RAN
Tian Ding (The Chinese University of Hong Kong, Hong Kong); Xiaojun Yuan (University of Electronic Science and Technology of China, P.R. China); Soung Chang Liew (The Chinese University of Hong Kong, Hong Kong)
In this paper, we study the cache-aided cloud radio access network (C-RAN) with wireless fronthaul, where multiple cache-enabled users are served by multiple cache-enabled transmitters that are connected to a cloud processor through a wireless fronthaul link. We put forth a caching-and-delivery scheme that combines network-coded fronthaul transmission with cache- aided interference management. By broadcasting network-coded messages, the cloud processor provides additional information of the requested files to the transmitters, so as to reduce the edge delivery time. Based on our scheme, an achievable normalized delivery time (NDT) is derived with respect to the cache sizes and the fronthaul capacity.
pp. 1182-1186
15:40 Optimal Secondary Access in Retransmission based Primary Networks via Chain Decoding
Nicolò Michelusi (Purdue University, USA)
This paper investigates the design of secondary access policies which exploit the temporal redundancy of the retransmission protocol employed by primary users (PU) to improve the spectral efficiency of wireless networks. Secondary users (SU) perform selective retransmissions in order to optimize the potential of interference cancellation by buffering the corrupted signals at the SU receiver, and then decoding them via the successive application of chain decoding [1]. The structure of the optimal SU access policy is investigated, so as to maximize the SU throughput under a constraint on the maximum interference caused to the PU. The optimal policy and its performance are found in closed form. It is shown that the optimal policy reflects an optimal randomization among three modes of operation of the SU: 1) The SU remains idle over the entire retransmission interval of the PU, to avoid interfering with the PU; 2) The SU transmits only after decoding the PU packet to leverage interference cancellation; 3) The SU always transmits over the entire retransmission interval of the PU, so as to leverage the chain decoding potential. It is shown numerically that chain decoding attains a throughput gain of 15% with respect to a state-of-the art scheme where the SU does not perform selective retransmissions.
pp. 1187-1191

#### Tu3-2: LDPC Codes 2

Room: Brussels
Chair: Khaled Abdel-Ghaffar (University of California, USA)
14:40 Characterization and Efficient Exhaustive Search Algorithm for Elementary Trapping Sets of Irregular LDPC Codes
Yoones Hashemi Toroghi and Amir Banihashemi (Carleton University, Canada)
In this paper, we propose a characterization of elementary trapping sets (ETSs) for irregular low-density parity-check (LDPC) codes. These sets are known to be the main culprits in the error floor region of such codes. The proposed characterization is based on a hierarchical graphical representation of ETSs, starting from simple cycles of the graph, or from single variable nodes, and involves three simple expansion techniques: degree-one tree ($dot$), $path$ and $lollipop$, thus, the terminology dpl characterization. The proposed $dpl$ characterization corresponds to an efficient search algorithm, that, for a given irregular LDPC code, can find all the instances of $(a,b)$ ETSs with size $a$ and with the number of unsatisfied check nodes $b$, within any range of interest $a \leq a_{max}$ and $b \leq b_{max}$, exhaustively. Simulation results are presented to show the versatility of the search algorithm, and to demonstrate that, compared to the literature, significant improvement in search speed can be obtained.
pp. 1192-1196
15:00 An Adaptive EMS Algorithm for Nonbinary LDPC Codes
Youngjun Hwang (Samsung Electronics Company, Ltd., Korea); Sunghye Cho and Kyeongcheol Yang (Pohang University of Science and Technology (POSTECH), Korea)
The extended min-sum (EMS) algorithm for decoding low-density parity-check codes over the finite field with $q$ elements significantly reduces decoding complexity by truncating each message of length $q$ into a message of effective length $n_m$. The number of effectively dominant components in each truncated message may gradually decrease with the number of decoding iterations. Based on this observation, we propose a novel adaptive EMS algorithm, called a two-length EMS (TL-EMS) algorithm. It chooses one of two candidate values as the effective message length $n_m$ for each message by reflecting the concept called message separation. Numerical results show that it can significantly reduce the computational complexity with little performance degradation.
pp. 1197-1201
15:20 A Two-Stage Decoding Algorithm for Short Nonbinary LDPC Codes with Near-ML Performance
Dixia Deng (Xidian University, P.R. China); Hengzhou Xu (Zhoukou Normal University, P.R. China); Baoming Bai and Ji Zhang (Xidian University, P.R. China)
This paper proposes a two-stage decoding algorithm (called BP-LED) for short nonbinary low-density parity-check (LDPC) codes. It consists of the classical belief propagation (BP) decoder and a list erasures decoder (LED). Simulation results show that, for the (16, 8) LDPC code over GF(256) in the CCSDS standard, our proposed BP-LED algorithm can achieve a coding gain of 0.6 dB with respect to the FFT-QSPA. By choosing the parameters suitable for the proposed algorithm, it has a negligible performance loss with low decoding complexity compared with the BP-MRB (most reliable basis) algorithm.
pp. 1202-1206
15:40 Design of Improved Quasi-Cyclic Protograph-Based Raptor-Like LDPC Codes for Short Block-Lengths
Sudarsan Vasista Srinivasan Ranganathan (University of California, Los Angeles, USA); Dariush Divsalar (Jet Propulsion Laboratory, USA); Richard Wesel (University of California, Los Angeles, USA)
Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a recently proposed family of easily encodable and decodable rate-compatible LDPC (RC-LDPC) codes. These codes have an excellent iterative decoding threshold and performance across all design rates. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the RC code family at various design rates. In this work, we propose a design method to obtain better quasi-cyclic (QC) RC-LDPC codes with PBRL structure for short block-lengths (of a few hundred bits). We achieve this by maximizing an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protograph of a PBRL ensemble. The obtained codes outperform the original PBRL codes at short block-lengths by significantly improving the error floor behavior at all design rates. Furthermore, we identify a reduction in complexity of the design procedure, facilitated by the general structure of a PBRL ensemble.
pp. 1207-1211
16:00 Finite-Length LDPC Codes on the q-ary Multi-Bit Channel
Rami Cohen (Technion - Israel Institute of Technology, Israel); Yuval Cassuto (Technion, Israel)
In this paper, we address the finite-length decoding performance of LDPC codes over the q-ary multi-bit channel (QMBC). The QMBC is defined over the full q-ary symbols, while addressing the differences in reliability between the bits composing the symbol. We show that unlike the binary erasure channel, the QMBC iterative decoder does not necessarily halt at stopping sets. Instead, its performance depends on the edge-label configuration of the LDPC code graph. We characterize good edge-label configurations, and propose an edge-labeling algorithm for improved iterative-decoding performance. We then provide finite-length maximum-likelihood decoding analysis for both the standard non-binary random ensemble and LDPC ensembles. Finally, simulations are presented to demonstrate the advantages of the proposed edge-labeling algorithm.
pp. 1212-1216

#### Tu3-3: Caching 2

Room: K2
Chair: Bobak Nazer (Boston University, USA)
14:40 Online Edge Caching in Fog-Aided Wireless Networks
Seyyed Mohammadreza Azimi (New Jersey Institute of Technology, USA); Osvaldo Simeone (King's College London, United Kingdom (Great Britain)); Avik Sengupta (Intel Corporation, USA); Ravi Tandon (University of Arizona, USA)
In a Fog Radio Access Network (F-RAN) architecture, edge nodes (ENs), such as base stations, are equipped with limited-capacity caches, as well as with fronthaul links that can support given transmission rates from a cloud processor. Existing information-theoretic analyses of content delivery in F-RANs have focused on offline caching with separate content placement and delivery phases. In contrast, this work considers an online caching set-up, in which the set of popular files is time-varying and both cache replenishment and content delivery can take place in each time slot. The analysis is centered on the characterization of the long-term Normalized Delivery Time (NDT), which captures the temporal dependence of the coding latencies accrued across multiple time slots in the high signal to noise ratio regime. Online caching and delivery schemes based on reactive and proactive caching are investigated, and their performance is compared to optimal offline caching schemes both analytically and via numerical results.
pp. 1217-1221
Shirin Saeedi Bidokhti (Stanford University, USA); Michele A Wigger (Telecom ParisTech, France); Aylin Yener (Pennsylvania State University, USA)
pp. 1222-1226
15:20 Rate-Memory Trade-off for the Two-User Broadcast Caching Network with Correlated Sources
Parisa Hassanzadeh (New York University, USA); Antonia Tulino (Bell Laboratories, USA & Università degli studi di Napoli, Italy); Jaime Llorca (Nokia Bell Labs, USA); Elza Erkip (New York University, USA)
This paper studies the fundamental limits of caching in a network with two receivers and two files generated by a two-component discrete memoryless source with arbitrary joint distribution. Each receiver is equipped with a cache of equal capacity, and the requested files are delivered over a shared error- free broadcast link. First, a lower bound on the optimal peak rate-memory trade-off is provided. Then, in order to leverage the correlation among the library files to alleviate the load over the shared link, a two-step correlation-aware cache-aided coded multicast (CACM) scheme is proposed. The first step uses Gray-Wyner source coding to represent the library via one common and two private descriptions, such that a second correlation- unaware multiple-request CACM step can exploit the additional coded multicast opportunities that arise. It is shown that the rate achieved by the proposed two-step scheme matches the lower bound for a significant memory regime and it is within half of the conditional entropy for all other memory values.
15:40 On the Optimality of Separation between Caching and Delivery in General Cache Networks
We consider a system, containing a library of multiple files and a general memoryless communication network through which a server is connected to multiple users, each equipped with a local isolated cache of certain size that can be used to store part of the library. Each user will ask for one of the files in the library, which needs to be delivered by the server through the intermediate communication network. The objective is to design the cache placement (without prior knowledge of users' future requests) and the delivery phase in order to minimize the (normalized) delivery delay. We assume that the delivery phase consists of two steps: (1) generation of a set of multicast messages at the server, one for each subset of users, and (2) delivery of the multicast messages to the users. In this setting, we show that there exists a universal scheme for cache placement and multicast message generation, which is independent of the underlying communication network between the server and the users, and achieves the optimal delivery delay to within a constant factor for all memoryless networks. We prove this result, even though the capacity region of the underlying communication network is not known, even approximately. This result shows that in the aforementioned setting, a separation between caching and multicast message generation on one hand, and delivering the multicast messages to the users on the other hand is approximately optimal. This result has the important practical implication that the prefetching can be done independent of network structure in the upcoming delivery phase.
pp. 1232-1236
16:00 Coded Caching with Linear Subpacketization is Possible using Ruzsa-Szeméredi Graphs
Karthikeyan Shanmugam (IBM Research, T. J Watson Center, USA); Antonia Tulino (Bell Laboratories, USA & Università degli studi di Napoli, Italy); Alexandros Dimakis (University of Texas at Austin, USA)
Coded caching is a problem where encoded broadcasts are used to satisfy users requesting popular files and having caching capabilities. Recent work by Maddah-Ali and Niesen showed that it is possible to satisfy a scaling number of users with only a constant number of broadcast transmissions by exploiting coding and caching. Unfortunately, all previous schemes required the splitting of files into an exponential number of packets before the significant coding gains of caching appeared. The question of what can be achieved with polynomial subpacketization (in the number of users) has been a central open problem in this area. We resolve this problem and present the first coded caching scheme with polynomial (in fact, linear) subpacketization. We obtain a number of transmissions that is not constant, but can be any polynomial in the number of users with an exponent arbitrarily close to zero. Our central technical tool is a novel connection between Ruzsa-Szem\'eredi graphs and coded caching.
pp. 2810-2814

#### Tu3-4: Second Order

Room: K3
Chair: Giuseppe Durisi (Chalmers University of Technology, Sweden)
14:40 Dispersion of the Discrete Arbitrarily-Varying Channel with Limited Shared Randomness
Oliver Kosut (Arizona State University, USA); Joerg Kliewer (New Jersey Institute of Technology, USA)
The second-order behavior of the discrete memoryless arbitrarily-varying channel is considered in the fixed error regime when the encoder and decoder share randomness that is independent from the adversarial choice of state. The dispersion (coefficient of the second-order term) is exactly characterized for most channels of interest when infinite shared randomness is allowed, and it is shown that precisely the same dispersion is achievable with only O(log n) bits of shared randomness. We also show that the dispersion is identical to that of the non-adversarial channel induced by the adversary simply choosing an i.i.d. state sequence according to the correct distribution. Further, we present some remarks on the connection to the compound channel, as well as on cost constraints for input and state sequences.
pp. 1237-1241
15:00 On the calculation of the minimax-converse of the channel coding problem
Nir Elkayam (Tel Aviv University, Israel); Meir Feder (Tel-Aviv University, Israel)
A minimax-converse has been suggested for the general channel coding problem. This converse comes in two flavors. The first flavor is generally used for the analysis of the coding problem with non-vanishing error probability and provides an upper bound on the rate given the error probability. The second flavor fixes the rate and provides a lower bound on the error probability. Both converses are given as a min-max optimization problem of an appropriate binary hypothesis testing problem. The minimax solution can also be used in conjunction with random coding to achieve optimal'' coding performance. In this paper we study the properties of the second form, i.e., when the rate is fixed. Necessary and sufficient conditions on the saddle point solution are proved. Moreover, an algorithm for the computation of the saddle point, and hence the bound, is developed. In the DMC case, the algorithm runs in a polynomial time.
pp. 1242-1246
15:20 Exact Moderate Deviation Asymptotics in Streaming Data Transmission
Si-Hyeon Lee (POSTECH, Korea); Vincent Y. F. Tan (National University of Singapore, Singapore); Ashish Khisti (University of Toronto, Canada)
In this paper, a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of $T$ blocks. In this streaming setup, the fundamental interplay between the coding rate, the error probability, and the blocklength in the moderate deviations regime is studied. For output symmetric channels, the moderate deviations constant is shown to improve over the block coding or non-streaming setup by exactly a factor of $T$ for a certain range of moderate deviations scalings. For the converse proof, a more powerful decoder to which some extra information is fedforward is assumed. The error probability is bounded first for an auxiliary channel and this result is translated back to the original channel by using a newly developed change-of-measure lemma, where the speed of decay of the remainder term in the exponent is carefully characterized.
pp. 1247-1251
15:40 Infinite Dispersion in Bursty Communication
Longguang Li and Aslan Tchamkerten (Telecom ParisTech, France)
This paper establishes finite-length tradeoffs between detection delay, output sampling rate, and communication rate for bursty communication. These tradeoffs imply regimes where the rate gap to capacity is captured by the inverse of the sampling rate rather than the usual dispersion.
pp. 1252-1256
16:00 Achievable Moderate Deviations Asymptotics for Streaming Slepian-Wolf Coding
Lin Zhou, Vincent Y. F. Tan and Mehul Motani (National University of Singapore, Singapore)
Motivated by streaming multi-view video coding, we consider the problem of blockwise streaming compression of a pair of correlated sources, which we term streaming Slepian-Wolf coding. We study the moderate deviations regime in which the rate pairs of a sequence of codes converges, along a straight line, to various points on the boundary of the Slepian-Wolf region at a speed slower than the inverse square root of the blocklength $n$, while the error probability decays subexponentially fast in $n$. Our main result focuses on directions of approaches to corner points of the Slepian-Wolf region. It states that for each correlated source and all corner points, there exists a non-empty subset of directions of approaches such that the moderate deviations constant (the constant of proportionality for the subexponential decay of the error probability) is enhanced (over the non-streaming case) by at least a factor of $T$, the block delay of decoding symbol pairs. Further, we specialize our main result to the setting of lossless streaming source coding.
pp. 1257-1261

#### Tu3-5: Detection and Estimation 2

Room: K4
Chair: Jing Yang (The Pennsylvania State University, USA)
14:40 Demystifying Fixed k-Nearest Neighbor Information Estimators
Weihao Gao (University Of Illinois at Urbana-Champaign, USA); Sewoong Oh (University of Illinois at Urbana-Champaign, USA); Pramod Viswanath (University of Illinois, Urbana-Champaign, USA)
Estimating mutual information from i.i.d. samples drawn from an unknown joint density function is a basic statistical problem of broad interest with multitudinous applications. The most popular estimator is one proposed by Kraskov and Stogbauer and Grassberger (KSG) in 2004, and is nonparametric and based on the distances of each sample to its $k$-th nearest neighboring sample, where $k$ is a fixed small integer. Despite its widespread use (part of scientific software packages), theoretical properties of this estimator have been largely unexplored. In this paper we demonstrate that the estimator is consistent and also identify an upper bound on the rate of convergence of the $\ell_2$ error as a function of number of samples. We argue that the performance benefits of the KSG estimator stems from a curious "correlation boosting" effect and build on this intuition to modify the KSG estimator in novel ways to construct a superior estimator. As a byproduct of our investigations, we obtain nearly tight rates of convergence of the $\ell_2$ error of the well known fixed $k$ nearest neighbor estimator of differential entropy by Kozachenko and Leonenko.
pp. 1262-1266
15:00 Structure of optimal strategies for remote estimation over Gilbert-Elliott channel with feedback
We investigate remote estimation over a Gilbert- Elliot channel with feedback. The channel is modelled as an ON/OFF channel, where the state of the channel evolves as a Markov chain. The channel state is observed by the receiver and fed back to the transmitter with one unit delay. In addition, the transmitter gets ACK/NACK feedback for successful/unsuccessful transmission. Using ideas from team theory, we establish the structure of optimal transmission and estimation strategies and identify a dynamic program to determine optimal strategies with that structure. We then consider first-order autoregressive sources where the noise process has unimodal and symmetric distribution. Using ideas from majorization theory, we show that the optimal transmission strategy has a threshold structure and the optimal estimation strategy is Kalman-filter like.
pp. 1267-1271
15:20 Sparse Gaussian Mixture Detection: Low Complexity, High Performance Tests via Quantization
Jonathan G Ligo (University of Illinois at Urbana-Champaign, USA); George V. Moustakides (University of Patras, Greece); Venugopal Veeravalli (University of Illinois at Urbana-Champaign, USA)
We study the problem of testing between a sparse signal in noise, modeled as a mixture distribution, versus pure noise, with a Gaussian signal and noise of same variance, but differing means as the mixture proportion tends to zero. We construct a simple new adaptive test based on quantizing data with sample size-dependent quantizers and prove its consistency. The proposed test has almost linear time complexity and sub-linear space complexity, which is better than existing tests, and in particular, the celebrated Higher Criticism test. Moreover, our numerical results show that the proposed test is competitive with commonly used tests even with a small number of quantizer levels.
pp. 1272-1276
15:40 Compressive Estimation of a Stochastic Process with Unknown Autocorrelation Function
Mahdi Barzegar Khalilsarai, Saeid Haghighatshoar and Giuseppe Caire (Technische Universität Berlin, Germany); Gerhard Wunder (FU Berlin, Heisenberg Communications and Information Theory Group, Germany)
In this paper, we study the prediction of a circularly symmetric zero-mean stationary Gaussian process from a window of observations consisting of finitely many samples. This is a prevalent problem in a wide range of applications in communication theory and signal processing. Due to the stationarity, when the autocorrelation function or equivalently the power spectral density (PSD) of the process is available, the Minimum Mean Squared Error (MMSE) predictor is readily obtained. In particular, it is given by a linear operator that depends on autocorrelation of the process as well as the noise power in the observed samples. The prediction becomes, however, quite challenging when the PSD of the process is unknown. In this paper, we propose a blind predictor that does not require the a priori knowledge of the PSD of the process and compare its performance with that of an MMSE predictor that has the full knowledge of the the PSD of the process. To design such a blind predictor, we use the random spectral representation of a stationary Gaussian process. We apply the well-known atomic-norm minimization technique to the observed samples to obtain a discrete quantization of the underlying random spectrum, which we use to predict the process. Our simulation results show that this estimator has a good performance comparable with that of the MMSE estimator.
pp. 1277-1281
16:00 Robust sequential change-point detection by convex optimization
Yang Cao and Yao Xie (Georgia Institute of Technology, USA)
We address the computational challenge of finding the robust sequential change-point detection procedures when the pre- and post-change distributions are not completely specified. Earlier works (Veeravalli, Basar, Poor 1994) and (Unnikrishnan, Veeravalli, Meyn 2011) establish the general conditions for robust procedures which include finding a pair of least favorable distributions (LFDs). However, in the multi-dimensional setting, it is hard to find such LFDs computationally. We present a method based on convex optimization to that address this issue when the distributions are Gaussian with unknown parameters from pre-specified uncertainty sets. We also establish theoretical properties of our robust procedures, and numerical examples demonstrate their good performance.
pp. 1282-1286

#### Tu3-6: Sequences 1

Room: K5
Chair: Prakash Narayan (University of Maryland, USA)
14:40 Perfect polyphase sequences from cubic polynomials
Min Kyu Song and Hong-Yeop Song (Yonsei University, Korea)
In this paper, we propose a new construction of perfect $p^k$-ary sequences of period $p^k$, where $p$ is an odd prime and $k\geq 2$ is a positive integer, based on cubic polynomials over the integers modulo $p^k$. We show that, for some appropriate parameters, it generates perfect polyphase sequences which are not the generalized chirp-like sequences constructed by Popovic in 1992.
pp. 1287-1290
15:00 Bayesian definition of random sequences with respect to conditional probabilities
Hayato Takahashi (Random Data Laboratory, Japan)
We review the recent progress on the definition of randomness with respect to conditional probabilities and a generalization of van Lambalgen theorem (Takahashi 2006, 2008, 2009, 2011). In addition we generalize Kjos Hanssen theorem (2010) when the consistency of the posterior distributions holds. Finally we propose a definition of random sequences with respect to conditional probabilities as the section of Martin-L\"of random set at the random parameters and argue the validity of the definition from the Bayesian statistical point of view.
pp. 1291-1295
15:20 On the Correlation between Boolean Functions of Sequences of Random Variables
In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a new upper-bound on the correlation between the outputs of these functions. The upper-bound is useful in various disciplines which deal with common-information. We build upon Witsenhausen's bound on maximum-correlation. The previous upper-bound did not take the effective length of the Boolean functions into account. One possible application of the new bound is to characterize the communication-cooperation tradeoff in multi-terminal communications. In this problem, there are lower-bounds on the effective length of the Boolean functions due to the rate-distortion constraints in the problem, as well as lower bounds on the output correlation at different nodes due to the multi-terminal nature of the problem.
pp. 1296-1300
15:40 The Hybrid k-Deck Problem: Reconstructing Sequences from Short and Long Traces
Ryan Gabrys (UIUC, USA); Olgica Milenkovic (University of Illinois at Urbana-Champaign (UIUC), USA)
We introduce a new variant of the k-deck problem, which in its traditional formulation asks for determining the smallest k that allows one to reconstruct any binary sequence of length n from the multiset of its k-length subsequences. In our version of the problem, termed the hybrid k-deck problem, one is given a certain number of special subsequences of the sequence of length n - t, t > 0, and the question of interest is to determine the smallest value of k such that the k-deck, along with the subsequences, allows for reconstructing the original sequence in an error-free manner. We first consider the case that one is given a single subsequence of the sequence of length n - t, obtained by deleting zeros only, and seek the value of k that allows for hybrid reconstruction. We prove that in this case, $k \in [\log t+2,\min\{{t+1,O( \sqrt{n \cdot (1+\log t)})\}}]$. We then proceed to extend the single-subsequence setup to the case where one is given M subsequences of length n-t obtained by deleting zeroes only. In this case, we first aggregate the asymmetric traces, and then invoke the single-trace results. The analysis and problem at hand are motivated by nanopore sequencing problems for DNA-based data storage.
pp. 1301-1305

#### Tu3-7: Communications 2

Room: K6
Chair: Tobias Koch (Universidad Carlos III de Madrid & Gregorio Marañón Health Research Institute, Spain)
14:40 Reliability of Universal Decoding Based on Vector--Quantized Codewords
Neri Merhav (Technion, Israel)
Motivated by applications of biometric identification and content identification systems, we consider the problem of random coding for channels, where each codeword undergoes vector quantization, and where the decoder bases its decision only on the compressed codewords and the channel output, which is in turn, the channel's response to the transmission of an original codeword, before compression. For memoryless sources and memoryless channels with finite alphabets, we propose a new universal decoder and analyze its error exponent, which improves on an earlier result by Dasarathy and Draper (2011), who used the classic maximum mutual information (MMI) universal decoder. We show that our universal decoder provides the same error exponent as that of the optimal, maximum likelihood (ML) decoder, at least as long as all single-letter transition probabilities of the channel are positive.
pp. 1306-1310
15:00 Sample Complexity of the Boolean Multireference Alignment Problem
Joao M Pereira, Amit Singer and Emmanuel Abbe (Princeton University, USA)
The Boolean multireference alignment problem consists in recovering a Boolean signal from multiple shifted and noisy observations. In this paper we obtain an expression for the error exponent of the maximum A posteriori decoder. This expression is used to characterize the number of measurements needed for signal recovery in the low SNR regime, in terms of higher order autocorrelations of the signal. The characterization is explicit for various signal dimensions, such as prime and even dimensions.
pp. 1311-1315
15:20 On the optimality of treating interference as noise in the 2 x M LD X-channel
Soheil Gherekhloo (RUB, Germany); Yasemin Karacora (Ruhr-Universität Bochum, Germany); Aydin Sezgin (RUB, Germany)
The optimality of the simple scheme of treating interference as noise (TIN) is studied in this paper for the 2 × M linear deterministic (LD) X-channel. A new capacity upper bound is derived. In the considered scheme (denoted as 2-IC-TIN), the setup is reduced to a 2-user interference channel while the receivers employ TIN. It is shown that as long as 2-IC-TIN is optimal in a M × 2 X-channel, it is also capacity-optimal in the 2 × M X-channel which is generated by changing the role of transmitters and receivers. The result of this paper expands the capacity optimal regime of TIN for the 2 × M LD X-channel compared to the state of the art.
pp. 1316-1320
15:40 Interaction Information for Causal Inference: The Case of Directed Triangle
AmirEmad Ghassami and Negar Kiyavash (University of Illinois at Urbana-Champaign, USA)
Interaction information is one of the multivariate generalizations of mutual information, which expresses the amount of information shared among a set of variables, beyond the information shared in any proper subset of those variables. Unlike (conditional) mutual information, which is always non-negative, interaction information can be negative. We utilize this property to find the direction of causal influences among variables in a triangle topology under some mild assumptions.
pp. 1321-1325
16:00 Completely blind sensing of multi-band signals
Taehyung Lim (UC San Diego, USA); Massimo Franceschetti (University of California at San Diego, USA)
A solution for the completely blind sensing problem of determining the minimum number of measurements sufficient to recover multi-band signals without any spectral information beside an upper bound on the measure of the whole support set in the frequency domain is presented. A scaling law for the number of measurements sufficient for reconstruction is provided, as well as a tight converse bound. Results show that a factor of two in the measurement rate is the price pay for blindness, compared to reconstruction with full spectral knowledge. The minimum number of measurements is also related to the fractal (Minkowski-Bouligand) dimension of a discrete approximating set, defined in terms of the Kolmogorov $\epsilon$-entropy. A comparison with analogous results in compressed sensing is illustrated, where the relevant dimensionality notion in a stochastic setting is the information (Rényi) dimension, defined in terms of the Shannon entropy.
pp. 1326-1330

#### Tu3-8: Information Theory and Statistics 1

Room: K7+8
Chair: Pierre Moulin (University of Illinois at Urbana-Champaign, USA)
14:40 An Information-Theoretic Approach to Universal Feature Selection in High-Dimensional Inference
Shao-Lun Huang (Tsinghua-Berkeley Shenzhen Institute, P.R. China); Anuran Makur and Lizhong Zheng (Massachusetts Institute of Technology, USA); Gregory Wornell (MIT, USA)
We develop an information theoretic framework for addressing feature selection in applications where the inference task is not specified in advance and the data is from a large alphabet. We introduce a natural notion of universality for such problems, and show that locally optimal solutions are straightforward to obtain, admit natural interpretations via information geometry, have computationally efficient implementations, and represent a practically useful learning methodology. Our development also reveals the key role of Hirschfeld-Gebelein-Renyi maximal correlation and the alternating conditional expectations (ACE) algorithm in such problems.
pp. 1331-1335
15:00 Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables
Saber Salehkaleybar, Jalal Etesami and Negar Kiyavash (University of Illinois at Urbana-Champaign, USA)
We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations.
pp. 1336-1340
15:20 Closed-Form Moments of Finite-Dimension Non-central Wishart Matrices via Concentration of Spectral Measure
Xinmin Li and Ling Qiu (University of Science and Technology of China, P.R. China)
In this paper, we derive a closed-form expression for the moments of finite-dimension non-central Wishart matrices. Such question has become an extensively researched topic in wireless communication and signal processing. The capacity analysis of massive MIMO system is established in the finite dimension regime via the concentration of spectral measure of random matrix. Two kinds of the significant probability measures are used to characterize the spectral distributions of random matrix. The closed-form expressions of capacity can provide a valuable insight instead of Mente-Carlo simulation. In addition, the exact convergence probabilities in these two measures are obtained
pp. 1341-1345
15:40 Information-geometrical characterization of statistical models which are statistically equivalent to probability simplexes
Hiroshi Nagaoka (University of Electro-Communications, Japan)
The probability simplex is the set of all probability distributions on a finite set and is the most fundamental object in the finite probability theory. In this paper we give a characterization of statistical models on finite sets which are statistically equivalent to probability simplexes in terms of $¥alpha$-families including exponential families and mixture families. The subject has a close relation to some fundamental aspects of information geometry such as $¥alpha$-connections and autoparallelity.
pp. 1346-1350
16:00 Density Functional Estimators with k-Nearest Neighbor Bandwidths
Weihao Gao (University Of Illinois at Urbana-Champaign, USA); Sewoong Oh (University of Illinois at Urbana-Champaign, USA); Pramod Viswanath (University of Illinois, Urbana-Champaign, USA)
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional estimation problems, practitioners are left on their own to choose an appropriate bandwidth for each application in hand. Further, kernel density estimators suffer from boundary biases, which are prevalent in real world data with lower dimensional structures. We propose using the fixed-k nearest neighbor distances for the bandwidth, which adaptively adjusts to local geometry. Further, we propose a novel estimator based on local likelihood density estimators, that mitigates the boundary biases. Although such a choice of fixed-k nearest neighbor distances to bandwidths results in inconsistent estimators, we provide a simple debiasing scheme that precomputes the asymptotic bias and divides off this term. With this novel correction, we show consistency of this debiased estimator. We provide numerical experiments suggesting that it improves upon competing state-of-the-art methods.
pp. 1351-1355

#### Tu3-9: Machine Learning 1

Room: K9
Chair: Toshiyuki Tanaka (Kyoto University, Japan)
14:40 Energy decay and conservation in deep convolutional neural networks
Philipp Grohs (University of Vienna, Austria); Thomas Wiatowski and Helmut Bölcskei (ETH Zurich, Switzerland)
Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how many layers are actually needed to have most of the input signal's features be contained in the feature vector generated by the network. This question can be formalized by asking how quickly the energy contained in the feature maps decays across layers. In addition, it is desirable that none of the input signal's features be lost'' in the feature extraction network or, more formally, we want energy conservation in the sense of the energy contained in the feature vector being proportional to that of the corresponding input signal. This paper establishes conditions for energy conservation for a wide class of deep convolutional neural networks and characterizes corresponding feature map energy decay rates. Specifically, we consider general scattering networks, and find that under mild analyticity and high-pass conditions on the filters (which encompass, inter alia, various constructions of Weyl-Heisenberg filters, wavelets, ridgelets, ($\alpha$)-curvelets, and shearlets) the feature map energy decays at least polynomially. For broad families of wavelets and Weyl-Heisenberg filters, the guaranteed decay rate is shown to be exponential. Our results yield handy estimates of the number of layers needed to have at least $((1-\varepsilon)\cdot 100)\%$ of the input signal energy be contained in the feature vector.
pp. 1356-1360
15:00 Neural Offset Min-Sum Decoding
Loren Lugosch and Warren Gross (McGill University, Canada)
Recently, it was shown that if multiplicative weights are assigned to the edges of a Tanner graph used in belief propagation decoding, it is possible to use deep learning techniques to find values for the weights which improve the error-correction performance of the decoder. Unfortunately, this approach requires many multiplications, which are generally expensive operations. In this paper, we suggest a more hardware-friendly approach in which offset min-sum decoding is augmented with learnable offset parameters. Our method uses no multiplications and has a parameter count less than half that of the multiplicative algorithm. This both speeds up training and provides a feasible path to hardware architectures. After describing our method, we compare the performance of the two neural decoding algorithms and show that our method achieves error-correction performance within 0.1 dB of the multiplicative approach and as much as 1 dB better than traditional belief propagation for the codes under consideration.
pp. 1361-1365
15:20 Learning-Based Epsilon Most Stringent Test for Gaussian Samples Classification
Lionel Fillatre (Université Côte d'Azur, France); Igor Nikiforov (Université de Technologie de Troyes, UTT/ICD/LM2S & UMR 6281, CNRS, France)
This paper studies the problem of classifying some Gaussian samples into one of two parametric probabilistic models, also called sources, when the parameter and the a priori probability of each source are unknown. Each source is governed by an univariate normal distribution whose mean is unknown. A training sequence is available for each source in order to compensate the lack of prior information. An almost optimal most stringent test is proposed to solve this classification problem subject to a constrained false alarm probability. This learning-based test minimizes its maximum shortcoming with respect to the most powerful test which knows exactly the parameters of the sources. It also guarantees a prescribed false alarm probability whatever the size of the training sequences. The threshold, the probability of false alarm and the probability of correct detection are calculated analytically.
pp. 1366-1370
15:40 Quickest Search and Learning over Multiple Sequences
Javad Heydari and Ali Tajer (Rensselaer Polytechnic Institute, USA)
Consider a set of random sequences, each consisting of independent and identically distributed random variables. Each sequence is generated according to one of the two possible distributions $F_0$ or $F_1$ with prior probabilities $(1-\epsilon)$ and $\epsilon$, respectively. The objective is to design a sequential decision-making procedure that identifies a sequence generated according to $F_1$ with the fewest number of measurements. Earlier analyses of this search problem have demonstrated that the optimal design of the sequential rules strongly hinge on the known value of $\epsilon$. Such information, however, might not be available in certain applications, especially in anomaly detection where the anomalous sequences occur with unpredicted patterns. Motivated by this premise, this paper designs a sequential inference mechanism that forms two coupled decisions for identifying a sequence of interest, and also learning the value of $\epsilon$. The paper devises three strategies that place different levels of emphasis on each of these inference goals.
pp. 1371-1375
16:00 Minimax Lower Bounds for Ridge Combinations Including Neural Nets
Jason Klusowski and Andrew R Barron (Yale University, USA)
Estimation of functions of $d$ variables is considered using ridge combinations of the form $\textstyle\sum_{k=1}^m c_{1,k} \phi(\textstyle\sum_{j=1}^d c_{0,j,k}x_j-b_k)$ where the activation function $\phi$ is a function with bounded value and derivative. These include single-hidden layer neural networks, polynomials, and sinusoidal models. From a sample of size $n$ of possibly noisy values at random sites $X \in B = [-1,1]^d$, the minimax mean square error is examined for functions in the closure of the $\ell_1$ hull of ridge functions with activation $\phi$. It is shown to be of order $d/n$ to a fractional power (when $d$ is of smaller order than $n$), and to be of order $(\log d)/n$ to a fractional power (when $d$ is of larger order than $n$). Dependence on constraints $v_0$ and $v_1$ on the $\ell_1$ norms of inner parameter $c_0$ and outer parameter $c_1$, respectively, is also examined. Also, lower and upper bounds on the fractional power are given. The heart of the analysis is development of information-theoretic packing numbers for these classes of functions.
pp. 1376-1380

### Tuesday, June 27, 16:40 - 18:20

#### Tu4-1: Coding Theory 2

Room: Europa
Chair: Emina Soljanin (Rutgers University, USA)
16:40 Pseudo-Wigner Matrices from Dual BCH Codes
Ilya Soloveychik, Yu Xiang and Vahid Tarokh (Harvard University, USA)
We consider the problem of generating pseudo-random matrices based on the similarity of their spectra to Wigner's semicircular law. We introduce r-independent pseudo-Wigner ensembles and prove closeness of their spectra to the semicircular density in Kolmogorov distance. We give an explicit construction of a family of N by N pseudo-Wigner ensembles using dual BCH codes and show that the Kolmogorov complexity of the constructed matrices is of the order of log(N). Finally, we provide numerical simulations verifying our theoretical results.
pp. 1381-1385
17:00 On codes achieving zero error capacities in limited magnitude error channels
Bella Bose (Oregon State University, USA); Noha Elarief (Hewlett Packard, Corvallis, OR., USA); Luca G. Tallini (Università di Teramo, Italy)
Shannon in his 1956 seminal paper introduced the concept of the zero error capacity, $C_0$, of a noisy channel. This is defined as the least upper bound of rates at which it is possible to transmit information with zero probability of error. At present not many codes are known to achieve the zero error capacity. In this paper, some codes which achieve zero error capacities in limited magnitude error channels are described. The code lengths of these zero error capacity achieving codes can be of any finite length $n=1,2,\ldots$, in contrast to the long lengths required for the known regular capacity achieving codes such as turbo codes, LDPC codes and polar codes. Both non-systematic and systematic codes are described.
pp. 1386-1390
17:20 On the Capacities of Balanced Codes with Run-Length Constraints
Akiko Manada and Hiroyoshi Morita (The University of Electro-Communications, Japan)
A balanced code is a set of words over $\{a, b\}$ such that the number of $a$'s and the number of $b$'s in a word are equal, and many applications using balanced codes have been proposed so far. Recently, not only the original balanced code, but also balanced codes with some other constraints have been studied mainly for an application of data storage media. However, contrary to other typical sets of words satisfying some constraints, the capacities of such balanced codes have not been well studied up to this moment. In this paper, we focus on balanced codes satisfying various run-length constraints and analyze their capacities. More precisely, we exhibit lower bounds on the capacities, or present the explicit capacities for certain cases.
pp. 1391-1395
17:40 Geometric Orthogonal Codes Better than Optical Orthogonal Codes
Yeow Meng Chee and Han Mao Kiah (Nanyang Technological University, Singapore); San Ling (NTU, Singapore); Hengjia Wei (Nanyang Technological University, Singapore)
The class of geometric orthogonal codes (GOCs) were introduced by Doty and Winslow (2016) for more robust macrobonding in DNA origami. They observed that GOCs are closely related to optical orthogonal codes (OOCs). It is possible for GOCs to have size greater than OOCs of corresponding parameters due to slightly more relaxed constraints on correlations. However, the existence of GOCs exceeding the size of optimal OOCs of corresponding parameters have never been demonstrated. This paper gives the first infinite family of GOCs of size greater than optimal OOCs.
pp. 1396-1400
18:00 The Augustin Center and The Sphere Packing Bound For Memoryless Channels
Baris Nakiboglu (None, Turkey)
For any channel with a convex constraint set and finite Augustin capacity, the existence of a unique Augustin center and the associated Erven-Harremoes bound are established. Augustin-Legendre capacity, center, and radius are introduced and proved to be equal to the corresponding Renyi-Gallager entities. Sphere packing bounds with polynomial prefactors are derived for codes on two families of channels: (possibly non-stationary) memoryless channels with multiple additive cost constraints and stationary memoryless channels with convex constraints on the empirical distribution of the input codewords.
pp. 1401-1405

#### Tu4-2: Coding for Distributed Storage 1

Room: Brussels
Chair: Vitaly Skachek (University of Tartu, Estonia)
16:40 Secrecy Capacity of Minimum Storage Regenerating Codes
Ankit Singh Rawat (Massachusetts Institute of Technology, USA)
This paper revisits the problem of designing secure minimum storage regenerating (MSR) codes for distributed storage systems (DSS). A secure MSR code ensures that a DSS does not reveal the stored information to a passive eavesdropper. The eavesdropper is assumed to have access to the content stored on $\ell_1$ number of storage nodes in the system and the data downloaded during the bandwidth efficient repair of an additional $\ell_2$ number of storage nodes. This paper combines the Gabidulin codes based precoding [Rawat et al.] and a new construction of MSR codes (without security requirements) by Ye and Barg in order to obtain secure MSR codes. Such optimal secure MSR codes were previously known only in the setting where the eavesdropper was allowed to observe the repair of $\ell_2$ nodes among a specific subset of $k$ nodes [Rawat et al., Goparaju et al.]. The secure coding scheme presented in this paper allows the eavesdropper to observe repair of any $\ell_2$ out of $n$ nodes in the system and characterizes the secrecy capacity of linear repairable MSR codes.
pp. 1406-1410
17:00 Cooperative Data Exchange based on MDS codes
Su Li (EPFL, Switzerland); Michael Gastpar (EPFL & University of California, Berkeley, Switzerland)
The coded cooperative data exchange problem is studied for the fully connected network. In this problem, each node initially only possesses a subset of the K packets making up the file. Nodes make broadcast transmissions that are received by all other nodes. The goal is for each node to recover the full file. In this paper, we present a polynomial-time deterministic algorithm to compute the optimal (i.e., minimal) number of required broadcast transmissions and to determine the precise transmissions to be made by the nodes. A particular feature of our approach is that each of the K-d transmissions is a linear combination of exactly d+1 packets, and we show how to optimally choose the value of d. We also show how the coefficients of these linear combinations can be chosen by leveraging a connection to Maximum Distance Separable (MDS) codes.
pp. 1411-1415
17:20 Asymptotically Optimal Regenerating Codes Over Any Field
Netanel Raviv (Technion & Tel-Aviv University, Israel)
The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. In this paper, by using notions from the theory of extension fields and matrix analysis, two explicit constructions of regenerating codes are obtained. These codes approach the cut-set bound as the reconstruction degree increases, and may be realized over any given field if the file size is large enough. Since distributed storage systems are the main purpose of regenerating codes, this file size restriction is trivially satisfied in most conceivable scenarios. The first construction attains the cut-set bound at the MBR point asymptotically for all parameters, whereas the second one attains the cut-set bound at the MSR point asymptotically for low-rate parameters.
pp. 1416-1420
17:40 Private Information Retrieval in Distributed Storage Systems Using an Arbitrary Linear Code
Siddhartha Kumar (University of Bergen & Simula Research Laboratory, Norway); Eirik Rosnes (University of Bergen, Norway); Alexandre Graell i Amat (Chalmers University of Technology, Sweden)
We propose an information-theoretic private information retrieval (PIR) scheme for distributed storage systems where data is stored using a linear systematic code of rate R > 1/2. The proposed scheme generalizes the PIR scheme for data stored using maximum distance separable codes recently proposed by Tajeddine and El Rouayheb for the scenario of a single spy node. We further propose an algorithm to optimize the communication price of privacy (cPoP) using the structure of the underlying linear code. As an example, we apply the proposed algorithm to several distributed storage codes, showing that the cPoP can be significantly reduced by exploiting the structure of the distributed storage code.
pp. 1421-1425

#### Tu4-3: Interference Channels 2

Room: K2
Chair: Changho Suh (KAIST, Korea)
16:40 Nash Region of the Linear Deterministic Interference Channel with Noisy Output Feedback
Victor Quintero and Samir M. Perlaza (INRIA, France); Jean-Marie Gorce (INSA-Lyon & CITI, Inria, France); H. Vincent Poor (Princeton University, USA)
In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference channel with noisy channel-output feedback is characterized for all $\eta > 0$ arbitrarily small. The $\eta$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $\eta$-NE. More specifically, given an $\eta$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $\eta$ bits per channel use. Existing results such as the $\eta$-NE region of the linear deterministic IC without feedback and with perfect output feedback are obtained as particular cases of the result presented in this paper.
pp. 1426-1430
17:00 Characterization of Degrees of Freedom versus Receivers Backhaul Load in K-User Interference Channel
Borna Kananian (Sharif University of Technology, Iran & Hong Kong University of Science and Technology, Hong Kong); Mohammad Ali Maddah-Ali (Bell Labs, Alcatel Lucent, USA); Seyed Pooya Shariatpanahi (Institute for Research in Fundamental Sciences (IPM), Iran); Babak Hossein Khalaj (Sharif University of Technology, Iran)
pp. 1431-1435
17:20 Discrete Modulation for Interference Mitigation
Mirza Uzair Baig and Anders Høst-Madsen (University of Hawaii, USA); Aria Nosratinia (University of Texas, Dallas, USA)
This paper analyzes the performance of discrete input distributions (coded modulation) in certain 3 user interference channels. This approach is motivated in part by the necessity of using coded modulation in practical systems, and in part by the potential of discrete distributions for interference alignment as well as the demonstrated importance of discrete input distributions for transmission over the $2\times2$ interference channel when treating interference as noise. The contribution of this work includes the establishment of achievable rates subject to discrete (PAM) modulations. In the process, new bounds involving the minimum distance of the sum of discrete modulations have been developed that are useful for facilitating further work in this area.
pp. 1436-1440
17:40 Communicating Correlated Sources Over an Interference Channel
A new coding technique, based on \textit{fixed block-length} codes, is proposed for the problem of communicating a pair of correlated sources over a $2-$user interference channel. Its performance is analyzed to derive a new set of sufficient conditions. The latter is proven to be strictly less binding than the current known best, which is due to Liu and Chen [Dec, 2011]. Our findings are inspired by Dueck's example [Mar, 1981].
pp. 1441-1445
18:00 Topological Interference Management: Linear Cooperation is not useful for Wyner's Networks
Aly El Gamal (Purdue University, USA)
In this work, we study the value of cooperative transmission in wireless networks if no channel state information is available at the transmitters (no CSIT). Our focus is on large locally connected networks, where each transmitter is connected to the receiver that has the same index as well as L succeeding receivers. The cases of L=1 and L=2 represent Wyner's asymmetric and symmetric network models, respectively. The considered rate criterion is the per user Degrees of Freedom (puDoF) as the number of transmitter-receiver pairs goes to infinity. For the case when L=1, it was shown in previous work that linear cooperation schemes do not increases the puDoF value, and that the optimal scheme relies on assigning each message to a single transmitter and using orthogonal access (TDMA). Here, we extend this conclusion to the case where L=2, by proving optimality of TDMA in this case as well. We conclude by discussing whether increasing the value of L can create a value for linear cooperation schemes from a DoF perspective.
pp. 1446-1450

#### Tu4-4: Entropy 2

Room: K3
Chair: Stefan M. Moser (ETH Zurich, Switzerland & National Chiao Tung University (NCTU), Taiwan)
16:40 Urns and entropies revisited
František Matúš (Academy of Sciences of the Czech Republic & Institute of Information Theory and Automation, Czech Republic)
An urn containing colored balls is sampled sequentially without replacement. New lower and upper bounds on the conditional and unconditional mutual information, and multiinformation are presented. They estimate dependence between drawings in terms of the colored ball configuration. Asymptotics are worked out when the number of balls increases and the proportion of the balls of each color stabilizes. Inequalities by Stam and by Diaconis and Freedman are compared and improved. Distances between the sampling with and without replacement, and between the multinomial and multivariate hypergeometric distributions are discussed.
pp. 1451-1454
17:00 Metric and topological entropy bounds on state estimation for stochastic non-linear systems
Christoph Kawan (University of Passau, Germany); Serdar Yüksel (Queen's University, Canada)
This paper studies state estimation over noisy channels for stochastic non-linear systems. We consider three estimation objectives, a strong and a weak form of almost sure stability of the estimation error as well as quadratic stability in expectation. For all three objectives, we derive lower bounds on the smallest channel capacity $C_0$ above which the objective can be achieved with an arbitrarily small error. Lower bounds are obtained via a dynamical systems (through a novel construction of a dynamical system), an information-theoretic and a random dynamical systems approach. The first two approaches show that for a large class of systems, such as additive noise systems, $C_0 = \infty$, i.e., the estimation objectives cannot be achieved via channels of finite capacity. The random dynamical systems approach is shown to be operationally non-adequate for the problem, since it yields finite lower bounds $C_0$ under mild assumptions. Finally, we prove that a memoryless noisy channel in general constitutes no obstruction to asymptotic almost sure state estimation with arbitrarily small errors, when there is no noise in the system.
pp. 1455-1459
17:20 Playing Games with Bounded Entropy
We study a two-player zero-sum game in which one of the players is restricted to mixed strategies with limited randomness. More precisely, we consider the maximum payoff that the maximizer (Alice) can secure with limited randomness h. This problem finds an operational interpretation in the context of repeated games with non-ideal sources of randomness. The computational aspects of this problem has not received much attention in the game theory literature. We begin by observing the equivalence of this problem with entropy minimization problems in other scientific contexts. Next, we provide two explicit lower bounds on the entropy-payoff tradeoff curve. To do this, we provide and utilize new results for the set of distribution that guarantee a certain payoff for Alice (mixed strategies corresponding to a security level for Alice). In particular, we study how this set of distribution shrinks as we increase the security level. While the use of total variation distance is common in game theory, our derivation indicates the suitability of utilizing the Renyi-divergence of order two.
pp. 1460-1464
17:40 Entropic Causality and Greedy Minimum Entropy Coupling
Murat Kocaoglu (The University of Texas at Austin, USA); Alexandros Dimakis (University of Texas at Austin, USA); Sriram Vishwanath (University of Texas Austin, USA); Babak Hassibi (California Institute of Technology, USA)
We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropic causality that works in a very general functional model but makes the assumption that the unobserved exogenous variable has small entropy in the true causal direction. This framework requires the solution of a minimum entropy coupling problem: Given marginal distributions of $m$ discrete random variables, each on n states, find the joint distribution with minimum entropy, that respects the given marginals. This corresponds to minimizing a concave function of $n^m$ variables over a convex polytope defined by $nm$ linear constraints, called a transportation polytope. Unfortunately, it was recently shown that this minimum entropy coupling problem is NP-hard, even for 2 variables with $n$ states. Even representing points (joint distributions) over this space can require exponential complexity (in $n,m$) if done naively. In our recent work we introduced an efficient greedy algorithm to find an approximate solution for this problem. In this paper we analyze this algorithm and establish two results: that our algorithm always finds a local minimum and also is within an additive approximation error from the unknown global optimum.
pp. 1465-1469
18:00 On Structural Entropy of Uniform Random Intersection Graphs
Marcin Kardas (Wrocław University of Technology, Poland); Zbigniew Golebiewski (Wroclaw University of Technology, Poland); Jakub Lemiesz (Wroclaw University of Science and Technology, Poland); Krzysztof Majcher (TU Wroclaw, Poland)
Recently, the need for efficient representations of data conveyed by graphical structures has emerged in many different contexts. While compressing such data one must consider two types of information. The first type is the information carried by the labels embedded in the structure. The second type is the information conveyed by the structure itself. In this extended abstract we address the latter type, namely we study the information carried by the structure of Uniform Random Intersection Graphs (URIGs). Random Intersection Graphs emerge in many scenarios, e.g., they correspond to the topology of many social networks and secure wireless networks, and they are induced in the clusterization process. We analyze algebraic properties of an automorphism group of the underlying structure of URIGs and derive a precise asymptotic formula for their structural entropy for various values of model parameters.
pp. 1470-1474

#### Tu4-5: Bounds 2

Room: K4
Chair: Viveck Cadambe (Pennsylvania State University, USA)
16:40 Dependence Measures Bounding the Exploration Bias for General Measurements
Jiantao Jiao, Yanjun Han and Tsachy Weissman (Stanford University, USA)
We propose a framework to analyze and quantify the bias in adaptive data analysis. It generalizes that proposed by Russo and Zou'15, applying to all measurements whose moment generating function exists, and to all measurements with a finite $p$-norm. We introduce a new class of dependence measures which retain key properties of mutual information while more effectively quantifying the exploration bias for heavy tailed distributions. We provide examples of cases where our bounds are nearly tight in situations where the original framework of Russo and Zou'15 does not apply.
pp. 1475-1479
17:00 Binary Subblock Energy-Constrained Codes: Bounds on Code Size and Asymptotic Rate
Anshoo Tandon (National University of Singapore, Singapore); Han Mao Kiah (Nanyang Technological University, Singapore); Mehul Motani (National University of Singapore, Singapore)
The subblock energy-constrained codes (SECCs) have recently been shown to be suitable candidates for simultaneous energy and information transfer, where bounds on SECC capacity were presented for communication over noisy channels. In this paper, we study binary SECCs with given error correction capability, by considering codes with a certain minimum distance. Binary SECCs are a class of constrained codes where each codeword is partitioned into equal sized subblocks, and every subblock has weight exceeding a given threshold. We present several upper and lower bounds on the optimal SECC code size, and also derive the asymptotic Gilbert-Varshamov (GV) and sphere-packing bounds for SECCs. A related class of codes are the heavy weight codes (HWCs) where the weight of each codeword exceeds a given threshold. We show that for a fixed subblock length, the asymptotic rate for SECCs is strictly lower than the corresponding rate for HWCs when the relative distance of the code is small. The rate gap between HWCs and SECCs denotes the penalty due to imposition of weight constraint per subblock, relative to the codeword based weight constraint.
pp. 1480-1484
17:20 Sampled Graph-Signals: Iterative Recovery with an Analytic Error Bound
Norbert Goertz (Vienna University of Technology (TU Wien), Austria)
Recovery of graph signals from a limited number of sampled components is investigated. An iterative graph-signal recovery algorithm is motivated and derived, including an analytic upper bound for the reconstruction error.
pp. 1485-1489
17:40 Multidimensional Semiconstrained Systems
Ohad Elishco, Tom Meyerovitch and Moshe Schwartz (Ben-Gurion University of the Negev, Israel)
We generalize the notion of independence entropy to the study of semiconstrained systems. Using it, we obtain a new lower bound on the capacity of multidimensional semiconstrained systems. We show the new bound improves upon the best-known bound in a case study of $(0, k, p)$- RLL semiconstrained systems.
pp. 1490-1494
18:00 Variable-length codes for channels with memory and feedback: error-exponent lower bounds
Achilleas Anastasopoulos and Jui Wu (University of Michigan, USA)
The reliability function of memoryless channels with noiseless feedback and variable-length coding has been found to be a linear function of the average rate in the classic work of Burnashev. In this work we consider unifilar channels with noiseless feedback and study specific transmission schemes, the performance of which provides lower bounds for the channel reliability function. In unifilar channels the channel state evolves in a deterministic fashion based on the previous state, input, and output, and is known to the transmitter but is unknown to the receiver. We consider a two-stage transmission scheme. In the first stage, both transmitter and receiver summarize their common information in an M-dimensional vector with elements in the state space of the unifilar channel and an M-dimensional probability mass function, with M being the number of messages. The second stage, which is entered when one of the messages is sufficiently reliable, is resolving a binary hypothesis testing problem. The analysis assumes the presence of some common randomness shared by the transmitter and receiver, and is based on the study of the log-likelihood ratio of the transmitted message posterior belief, and in particular on the study of its multi-step drift. Simulation results confirm that the bounds are tight compared to the upper bounds derived in a companion paper.
pp. 1495-1499

#### Tu4-6: Sequences 2

Room: K5
Chair: Yossef Steinberg (Technion, Israel)
16:40 On Empirical Cumulant Generating Functions of Code Lengths for Individual Sequences
Neri Merhav (Technion, Israel)
We consider the problem of lossless compression of individual sequences using finite-state (FS) machines, from the perspective of the best achievable empirical cumulant generating function (CGF) of the code length, i.e., the normalized logarithm of the empirical average of the exponentiated code length. Since the probabilistic CGF is minimized in terms of the Renyi entropy of the source, one of the motivations of this study is to derive an individual-sequence analogue of the R\'enyi entropy, in the same way that the FS compressibility is the individual-sequence counterpart of the Shannon entropy. We consider the CGF of the code-length both from the perspective of fixed-to-variable (F-V) length coding and the perspective of variable-to-variable (V-V) length coding, where the latter turns out to yield a better result, that coincides with the FS compressibility. We also extend our results to compression with side information, available at both the encoder and decoder. In this case, the V-V version no longer coincides with the FS compressibility, but results in a different complexity measure.
pp. 1500-1504
17:00 Degree-$(k + 1)$ Perfect Gaussian Integer Sequences of Period $p^k$
Ho-Hsuan Chang (I-Shou University, Taiwan)
This paper presents a method for constructing degree-$(k + 1)$ perfect Gaussian integer sequence (PGIS) of period $N = p^k$, where $p$ is a prime number. The study begins with the partitioning of set $Z_N$ into $k + 1$ subsets and exploration of their properties and theorems. The base sequences can be defined and the associated $k + 1$ degree PGIS is constructed based on the partitioning of $Z_N$. The $k$ constraint equations that govern the $k + 1$ different sequence coefficients to match the criteria for a sequence to be perfect are nonlinear equations, which makes the construction of higher degree PGISs especially challenging. A new method of transforming $k$ nonlinear constraint equations into $2k−2$ linear equations with $2k−2$ variables is presented. It is then easy to derive a unique solution, from which the construction of degree-$(k + 1)$ PGISs becomes straightforward. Both degree-5 and degree7 PGIS examples are provided for demonstration.
pp. 1505-1509
17:20 Reconstruction of Sequences over Non-Identical Channels
Michal Horovitz (Technion - Israel Institute of Technology, Israel); Eitan Yaakobi (Technion, Israel)
Motivated by the error behavior in DNA storage channels, in this work we extend the previously studied sequence reconstruction problem by Levenshtein. The reconstruction problem studies the model in which the information is read through multiple noisy channels, and the decoder, which receives all channel estimations, is required to decode the information. For the combinatorial setup, the assumption is that all the channels can cause at most some $t$ errors. However, since the channels do not necessarily have the same behavior, we generalize this model and assume that the channels are not identical and thus may cause a different maximum number of errors. For example, we assume that there are $N$ channels, that can cause at most $t_1$ or $t_2$ errors, where $t_1<t_2$, and the number of channels with at most $t_1$ errors is at most $\lceil pN\rceil$, for some fixed $0<p<1$. If the information codeword belongs to a code with minimum distance $d$, the problem is then to find the minimum number of channels $N$ that guarantees successful decoding in the worst case.
pp. 1510-1514
17:40 Classification of a Sequence Family Using Plateaued Functions
Serdar Boztas (RMIT University, Australia); Ferruh Ozbudak (Middle East Technical University, Turkey); Eda Tekin (Karabuk University, Turkey)
The design of CDMA sequence families using quadratic functions dates back to Gold sequences from the 1960s. Since then there have been a number of different such designs with good correlation properties, some optimal and some nearoptimal, and the term "Gold-like" is usually used to denote such sequences. In this paper we use the concept of plateaued functions in order to classify such sequence families and present some examples in this direction which depend on the characteristic p and degree n of the Galois field Fpn used to define the sequences.
pp. 1515-1518

#### Tu4-7: Security 2

Room: K6
Chair: Arya Mazumdar (University of Massachusetts Amherst, USA)
16:40 Secret Key Agreement under Discussion Rate Constraints
Chung Chan (The Chinese University of Hong Kong, Hong Kong); Manuj Mukherjee and Navin Kashyap (Indian Institute of Science, India); Qiaoqiao Zhou (The Chinese University of Hong Kong, Hong Kong)
For the multiterminal secret key agreement problem, new single-letter lower bounds are obtained regarding the public discussion rate required to achieve any given secret key rate below the capacity. The results apply to general source model without helpers or wiretapper's side information but can be strengthened for hypergraphical sources. In particular, for the pairwise independent network, the results give rise to a complete characterization of the maximum secret key rate under a constraint on the total discussion rate.
pp. 1519-1523
17:00 A Game Theoretic Treatment for Pair-wise Secret-Key Generation in Many-to-One Networks
Remi A Chou and Aylin Yener (Pennsylvania State University, USA)
We consider secret-key generation between several agents and a base station that observe independent and identically distributed (i.i.d.) realizations of correlated random variables. Each agent wishes to generate the longest possible individual key with the base station by means of public communication. All keys must be jointly kept secret from all external entities. We do not require them to be kept secret among the agents. In this many-to-one secret-key generation setting, it can be shown that the agents can take advantage of a collective protocol to increase the sum-rate of all the generated keys. However, when each agent is only interested in maximizing its own secret-key rate, agents may be unwilling to participate in a collective protocol. Furthermore, when such a collective protocol is employed, how to fairly allocate individual key rates arises as a valid issue. We study this tension between cooperation and self-interest with a game-theoretic treatment. We establish that cooperation is in the best interest of all agents and that there exists individual secret-key rate allocations that incentivize the agents to follow the protocol. Additionally, we propose an explicit and low-complexity coding scheme based on polar codes and hash functions that achieves such allocations.
pp. 1524-1528
17:20 Information-Theoretically Secure Key Generation and Management
Xin-Wen Wu (Griffith University, Australia); En-hui Yang (University of Waterloo, Canada)
In this paper, we address the problems of key generation and management for enabling one-key-for-one-file secure encryption, where every file is encrypted by using an independent random key, which is highly desired in long-term protection of data stored on public clouds and other applications. A new concept dubbed information-theoretical $\epsilon$-security is introduced to measure the security of a keystore (i.e., a set of random keys, $k_i$, $1\leq i\leq\Lambda$, each having length of l bits) which are generated from a random string of $L$ bits, called the keystore seed. An efficient keystore generation scheme is presented, and the resulting keystore $\Psi=\{k_i: 1\leq i \leq \Lambda\}$ is shown to be information-theoretically $\epsilon$-secure with small $\epsilon$. Specifically, they satisfy the following properties: (1) $\Lambda \gg L$ is sufficiently large to realize one-key-for-one-file encryption for applications with a large number of files; (2) for any key index $i$, the key $k_i$ is uniformly distributed over the key space $\{0,1\}^l$ and hence statistically independent of $i$ if $i$ is chosen randomly; (3) for any two independent $i, j, 1 \leq i,j \leq \Lambda$, the probability that $k_i=k_j$ is very small and less than $(1-\epsilon) \times 2^{-l}+\epsilon$; and (4) for any two independent key indices $i$ and $j$, knowing $i$, $j$, and $k_i$ does not reduce the amount of uncertainty about $k_j$ significantly, i.e., the conditional Shannon entropy $H(k_j |i,j,k_i)$ is at least as large as $(1-\epsilon)H(k_j | j)$. These security properties along with easy generation of each key $k_i$ from the keystore seed and the key index $i$ remove most challenges in distributing and managing a large number of random keys.
pp. 1529-1533
17:40 Secret-Key Agreement with Public Discussion over Multi-Antenna Transmitters with Amplitude Constraints
Zouheir Rezki (University of Idaho, USA); Mohamed-Slim Alouini (King Abdullah University of Science and Technology (KAUST), Saudi Arabia)
We consider secret-key agreement with public discussion over a multiple-input single output (MISO) Gaussian channel with an amplitude constraint. We prove that the capacity is achieved by a discrete input, i.e., an input whose support is sparse. The proof follows from the concavity of the conditional mutual information in terms of the input distribution and hence the KKT condition provides a necessary and sufficient condition for optimality. Then, a contradiction argument that rules out the non-sparsity of any optimal input's support is utilized. The latter approach is essential to apply the identity theorem in multidimensional setting as $\mathbb{R}^{n}$ is not an open subset $\mathbb{C}^{n}$.
pp. 1534-1538
18:00 Robust and Secure Identification
Holger Boche (Technical University Munich, Germany); Christian Deppe (University of Bielefeld, Germany)
We determine the identification capacity of compound channels with and without wiretapper. It turned out, that the secure capacity formula fulfill a dichotomy theorem. It is positive if its secure capacity is positive and equals the transmission capacity of the channel. Otherwise the capacity is zero. We analyze the (dis-)continuity and (super-)additivity of the capacities, which we determined. Alon gave in a conjecture about maximal violation for the additivity for capacity functions. We show that this maximal violation holds for the secure identification capacity. This is the first example of a capacity function, which has this behavior.
pp. 1539-1543

#### Tu4-8: Quantum IT 2

Room: K7+8
Chair: Joseph M. Renes (ETH Zurich, Switzerland)
16:40 Moderate deviation analysis for classical communication over quantum channels
Christopher Chubb (The University of Sydney, Australia); Vincent Y. F. Tan (National University of Singapore, Singapore); Marco Tomamichel (University of Technology Sydney, Australia)
We analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases. To characterise the fundamental tradeoff between decoding error, code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by Altug and Wagner as well as Polyanskiy and Verdu. We derive such a tradeoff for classical-quantum (as well as image-additive) channels in terms of the channel capacity and the channel dispersion, giving further evidence that the latter quantity characterises the necessary backoff from capacity when transmitting finite blocks of classical data. To derive these results we also study asymmetric binary quantum hypothesis testing in the moderate deviations regime. Due to the central importance of the latter task, we expect that our techniques will find further applications in the analysis of other quantum information processing tasks.
pp. 1544-1548
17:00 Quantum Information on Spectral Sets
Peter Harremoës (Niels Brock, Copenhagen Business College, Denmark)
For convex optimization problems Bregman divergences appear as regret functions. Such regret functions can be defined on any convex set, but if a sufficiency condition is added the regret function must be proportional to information divergence and the convex set must be spectral. Spectral set are sets where different orthogonal decompositions of a state into pure states have unique mixing coefficients. Only on such spectral sets it is possible to define well behaved information theoretic quantities like entropy and divergence. It is only possible to perform measurements in a reversible way if the state space is spectral. The most important spectral sets can be represented as positive elements of Jordan algebras with trace 1. This means that Jordan algebras provide a natural framework for studying quantum information.
pp. 1549-1553
17:20 Kolmogorov Amplification from Bell Correlation
Ämin Baumeler (Università della Svizzera Italiana, Switzerland); Charles Alexandre Bédard (Université de Montréal, Canada); Gilles Brassard (Université de Montréal & Canadian Institute for Advanced Research, Canada); Stefan Wolf (USI Lugano, Switzerland)
It was first observed by John Bell that quantum theory predicts correlations between measurement outcomes that lie beyond the explanatory power of local hidden variable theories. These correlations have traditionally been studied extensively in the probabilistic framework. A drawback of this perspective is that one is then forced to use in a single argument the outcomes of mutually-exclusive measurements. One of us has initiated an alternative approach, invoking only data at hand, in order to circumvent this issue. In this factual view, which is based on Kolmogorov complexity, we introduce mechanisms such as complexity amplification. We establish that this functionality is realizable, just as its probabilistic counterpart, hereby underlining that Bell correlations are a precious information-processing resource.
pp. 1554-1558
17:40 Degradable states and one-way entanglement distillation
Felix Leditzky (University of Colorado Boulder, USA); Nilanjana Datta (Cambridge, United Kingdom (Great Britain)); Graeme Smith (University of Colorado Boulder)
We derive an upper bound on the one-way distillable entanglement of bipartite quantum states. To this end, we revisit the notion of degradable, conjugate degradable, and antidegradable bipartite quantum states [Smith et al., IEEE Trans. on Inf. Th. 54.9 (2008), pp. 4208-4217]. We prove that for degradable and conjugate degradable states the one-way distillable entanglement is equal to the coherent information, and thus given by a single-letter formula. Furthermore, it is well-known that the one-way distillable entanglement of antidegradable states is zero. We use these results to derive an upper bound for arbitrary bipartite quantum states, which is based on a convex decomposition of a bipartite state into degradable and antidegradable states. This upper bound is always at least as good an upper bound as the entanglement of formation. Applying our bound to the qubit depolarizing channel, we obtain an upper bound on its quantum capacity that is strictly better than previously known bounds in the high noise regime. We also transfer the concept of approximate degradability [Sutter et al., arXiv:1412.0980 [quant-ph]] to quantum states and show that this yields another easily computable upper bound on the one-way distillable entanglement. Moreover, both methods of obtaining upper bounds on the one-way distillable entanglement can be combined into a generalized one.
pp. 1559-1562

#### Tu4-9: Compression 1

Room: K9
Chair: Faramarz Fekri (Georgia Institute of Technology, USA)
16:40 Recovery of Vertex Orderings in Dynamic Graphs
Abram Magner (UIUC, USA); Ananth Grama, Jithin K. Sreedharan and Wojciech Szpankowski (Purdue University, USA)
Many networks in the real world are dynamic in nature: nodes enter, exit, and make and break connections with one another as time passes. Several random graph models of these networks are such that nodes have well-defined arrival times. It is natural to ask if, for a given random graph model, we can recover the arrival order of nodes, given information about the structure of the graph. In this work, we give a rigorous formulation of the problem in a statistical learning framework and tie its feasibility, for a broad class of models, to several sets of permutations associated with the symmetries of the random graph model and graphs generated by it. Moreover, we show how the same quantities are fundamental to the study of the information content of graph structures. We then apply our general results to the special cases of the Erdős-R\'enyi and preferential attachment models to derive strong inapproximability results.
pp. 1563-1567
17:00 Variable-Length Lossy Compression Allowing Positive Overflow and Excess Distortion Probabilities
Shota Saito (Waseda University, Japan); Hideki Yagi (University of Electro-Communications, Japan); Toshiyasu Matsushima (Waseda University, Japan)
This paper investigates the problem of variable-length lossy source coding. We deal with the case where both the excess distortion probability and the overflow probability of codeword length are less than or equal to positive constants. The infimum of the thresholds on the overflow probability is characterized by a smooth max entropy-based quantity. Both non-asymptotic and asymptotic cases are analyzed. To show the achievability results, we do not utilize the random coding argument but give an explicit code construction.
pp. 1568-1572
17:20 On Lossy Compression of Binary Matrices
Ronit Bustin and Ofer Shayevitz (Tel Aviv University, Israel)
We consider lossy compression of random binary matrices under distortion constraints that strive to preserve the structure of the matrix. Specifically, we assume that matrix elements are statistically independent (but not necessarily identically distributed), and that the worst case row/column average distortion is to be controlled. We discuss a natural notion of matrix types termed (R;C)-type, and provide various results concerning its probability and cardinality, as well as a "Sanov-type" result, in the spirit of the method-of-types. We then derive bounds on the associated matrix rate distortion function via a suitable matrix version of the covering lemma.
pp. 1573-1577
17:40 Universal Lossless Compression of Graphical Data
Payam Delgosha (University of California, Berkeley, USA); Venkat Anantharam (University of California at Berkeley, USA)
Consider a data source comprised of a graph with marks on its edges and vertices. Examples of such data sources are social networks, biological data, web graphs, etc. Our goal is to design schemes that can efficiently compress such data without making assumptions about its stochastic properties, i.e. universal compression. To make sense of this, we employ the framework of local weak convergence, also called the objective method, which formalizes the notion of stationary stochastic processes indexed by graphs. We generalize a recently developed notion of entropy for such processes, due to Bordenave and Caputo, to the case of marked graphs, and use it to evaluate the efficiency of a compression scheme. The lossless compression scheme we propose in this paper is then proved to be universally optimal. It is also capable of performing local data queries in the compressed form.
pp. 1578-1582
18:00 Compressing data on graphs with clusters
Amir Asadi, Emmanuel Abbe and Sergio Verdú (Princeton University, USA)
This paper investigates the fundamental limits for compressing data on graphs, exploiting dependencies due to community structures in the graph. The source model, referred to as the data block model (DBM), is a mixture of discrete memoryless sources determined by the community structure of a stochastic block model (SBM). The main result gives the optimal expected length of a lossless compressor when the community signal is strong enough, a condition on the edge probabilities and the data distributions, which can take place below the exact recovery threshold of the SBM. This is derived in part by obtaining the threshold for exact recovery in SBMs with strong side information, a result of independent interest, which extends the CH-divergence threshold. Finally we discuss compressing data with almost exact recovery algorithms.
pp. 1583-1587

Room: Brussels

## Wednesday, June 28

### Wednesday, June 28, 08:30 - 09:30

#### WeP: Shannon Lecture: The Spirit of Information Theory - David Tse

David Tse
Room: Europa
Chair: Ruediger L Urbanke (EPFL, Switzerland)

### Wednesday, June 28, 09:50 - 11:10

#### We1-1: Iterative Decoding 1

Room: Europa
Chair: Albert Guillén i Fàbregas (ICREA and Universitat Pompeu Fabra & University of Cambridge, Spain)
09:50 Vector Approximate Message Passing
Sundeep Rangan (New York University, USA); Philip Schniter (The Ohio State University, USA); Alyson Fletcher (University of California, Los Angeles, USA)
The standard linear regression (SLR) problem is to recover a vector x0 from noisy linear observations y = Ax0 +w. The approximate message passing (AMP) algorithm recently proposed by Donoho, Maleki, and Montanari is a computationally efficient iterative approach to SLR that has a remarkable property: for large i.i.d. sub-Gaussian matrices A, its per- iteration behavior is rigorously characterized by a scalar state- evolution whose fixed points, when unique, are Bayes optimal. AMP, however, is fragile in that even small deviations from the i.i.d. sub-Gaussian model can cause the algorithm to diverge. This paper considers a "vector AMP" (VAMP) algorithm and shows that VAMP has a rigorous scalar state-evolution that holds under a much broader class of large random matrices A: those that are right-rotationally invariant. After performing an initial singular value decomposition (SVD) of A, the per-iteration complexity of VAMP is similar to that of AMP. In addition, the fixed points of VAMP's state evolution are consistent with the replica prediction of the minimum mean-squared error recently derived by Tulino, Caire, Verdu ́, and Shamai.
pp. 1588-1592
10:10 Generalized Approximate Message-Passing Decoder for Universal Sparse Superposition Codes
Erdem Biyik (Bilkent University, Turkey); Jean Barbier and Mohamad Dia (EPFL, Switzerland)
Sparse superposition (SS) codes were originally proposed as a capacity-achieving communication scheme over the additive white Gaussian noise channel (AWGNC) [1]. Very recently, it was discovered that these codes are universal, in the sense that they achieve capacity over any memoryless channel under generalized approximate message-passing (GAMP) decoding [2], although this decoder has never been stated for SS codes. In this contribution we introduce the GAMP decoder for SS codes, we confirm empirically the universality of this communication scheme through its study on various channels and we provide the main analysis tools: state evolution and potential. We also compare the performance of GAMP with the Bayes-optimal MMSE decoder. We empirically illustrate that despite the presence of a phase transition preventing GAMP to reach the optimal performance, spatial coupling allows to boost the performance that eventually tends to capacity in a proper limit. We also prove that, in contrast with the AWGNC case, SS codes for binary input channels have a vanishing error floor in the limit of large codewords. Moreover, the performance of Hadamard-based encoders is assessed for practical implementations.
pp. 1593-1597
10:30 Block Markov Superposition Transmission of BCH Codes with Iterative Hard-decision Decoding
Nina Lin, Suihua Cai and Xiao Ma (Sun Yat-sen University, P.R. China)
This paper is concerned with block Markov superposition transmission of BCH (BMST-BCH) codes. Compared with other BMST codes, BMST-BCH codes can achieve a lower error floor with an encoding memory of two, which is critical to reduce both delay and implementation complexity. To further reduce the implementation complexity, we propose a hard-decision sliding-window decoding algorithm, in which only binary and/or erasure messages are processed and exchanged between nodes. A fast simulation approach is proposed, with the help of the genie-aided lower bound and the density evolution analysis, to evaluate the performance of BMST-BCH codes at the BER of $10^{-15}$. BMST-BCH codes are constructed with overheads ranging from $15\%$ to $25\%$, exhibiting performances comparable to staircase codes with similar latencies. The proposed construction is more flexible to trade off latency against performance, and may find applications in optical transport networks as an attractive candidate.
pp. 1598-1602
10:50 Belief Propagation for Subgraph Detection with Imperfect Side-information
Arun Kadavankandy (Inria, EURECOM, France); Konstantin Avrachenkov (INRIA Sophia Antipolis, France); Laura Cottatellucci (EURECOM, France); Rajesh Sundaresan (Indian Institute of Science, India)
We propose a local message passing algorithm based on Belief Propagation (BP) to detect a small hidden Erdos-Renyi (ER) subgraph embedded in a larger sparse ER random graph in the presence of side-information. We consider side-information in the form of revealed subgraph nodes called cues, some of which may be erroneous. Namely, the revealed nodes may not all belong to the subgraph, and it is not known to the algorithm a priori which cues are correct and which are incorrect. We show that asymptotically as the graph size tends to infinity, the expected fraction of misclassified nodes approaches zero for any positive value of a parameter $\lambda,$ which represents the effective Signal-to-Noise Ratio of the detection problem. Previous works on subgraph detection using BP without side-information showed that BP fails to recover the subgraph when $\lambda < 1/e.$ Our results thus demonstrate the substantial gains in having even a small amount of side-information.
pp. 1603-1607

#### We1-2: Student Paper Awards Candidate Talks 1

Room: Brussels
Chair: Wei Yu (University of Toronto, Canada)
09:50 Multiplexing Zero-Error and Rare-Error Communications over a Noisy Channel with Feedback
Tibor Keresztfalvi (ETH Zurich, Switzerland); Amos Lapidoth (ETHZ, Switzerland)
Two independent data streams—the "zero-error stream" and the "rare-error stream"—are to be transmitted over a noisy discrete memoryless channel with feedback. Errors are tolerated only in the rare-error stream, provided that their probability tends to zero. Clearly the rate of the error-free stream cannot exceed the channel's zero-error feedback capacity, and the sum of the streams' rates cannot exceed the channel's Shannon capacity. Using a suitable coding scheme, these necessary conditions are shown to characterize all the achievable rate pairs. Planning for the worst—as is needed to achieve zero- error communication—and planning for the true channel—as is needed to communicate near the Shannon limit—are thus not incompatible.
pp. 1608-1612
10:10 The Exact Rate-Memory Tradeoff for Caching with Uncoded Prefetching
Qian Yu (University of Southern California, USA); Mohammad Ali Maddah-Ali (Bell Labs, Alcatel Lucent, USA); Salman Avestimehr (University of Southern California, USA)
We consider a cache network, where a single server is connected to multiple users via a shared bottleneck link. The server has a set of files, which can be cached by each user in a prefetching phase. In a following delivery phase, each user requests a file and the server needs to deliver users' demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of rate-memory tradeoff for this problem, by deriving the both the minimum average rate (for a uniform file popularity) and the minimum peak-rate required on the bottleneck link for a given cache size available at each user. We propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among users' demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we can also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without any coordination.
pp. 1613-1617
10:30 Greedy-Merge Degrading has Optimal Power-Law
Assaf Kartowsky and Ido Tal (Technion, Israel)
Consider a channel with a given input distribution. Our aim is to degrade it to a channel with at most L output letters. One such degradation method is the so called "greedy-merge" algorithm. We derive an upper bound on the reduction in mutual information between input and output. For fixed input alphabet size and variable L, the upper bound is within a constant factor of an algorithm-independent lower bound. Thus, we establish that greedy-merge is optimal in the power-law sense.
pp. 1618-1622
10:50 A Generic Transformation for Optimal Repair Bandwidth and Rebuilding Access in MDS Codes
Jie Li (Southwest Jiaotong University, P.R. China); Xiaohu Tang (Southwest Jiaotong University (SWJTU), P.R. China); Chao Tian (University of Tennessee Knoxville, USA)
We propose a generic transformation on maximum distance separable (MDS) codes, which can convert any non-binary (k+r,k) MDS code into another (k+r,k) MDS code with the following properties: 1) An arbitrarily chosen r nodes will have the optimal repair bandwidth and the optimal rebuilding access, 2) the repair bandwidth and rebuilding access efficiencies of all other nodes are maintained as in the code before the transformation, 3) it uses the same finite field as the code before the transformation, and 4) the sub-packetization is increased only by a factor of r. As two immediate applications of this powerful transformation, we show that 1) any non-binary MDS code with optimal repair bandwidth, or optimal rebuilding access, for only systematic nodes can be converted into an MDS code with the corresponding repair optimality for all nodes; and 2) any non-binary scalar MDS code can be converted to an MDS code with optimal repair bandwidth and rebuilding access for all nodes, or to an MDS code with optimal rebuilding access for all systematic nodes and moreover with the optimal sub-packetization, by applying the transformation multiple times.
pp. 1623-1627

#### We1-3: Coding for Storage and Streaming

Room: K2
Chair: Ashish Khisti (University of Toronto, Canada)
09:50 Multipermutation Ulam Sphere Analysis Toward Characterizing Maximal Code Size
Justin Kong and Manabu Hagiwara (Chiba University, Japan)
Permutation codes, in the form of rank modulation, have shown promise for applications such as flash memory. One of the metrics recently suggested as appropriate for rank modulation is the Ulam metric, which measures the minimum translocation distance between permutations. Multipermutation codes have also been proposed as a generalization of permutation codes that would improve code size (and consequently the code rate). In this paper we analyze the Ulam metric in the context of multipermutations, noting some similarities and differences between the Ulam metric in the context of permutations. We also consider sphere sizes for multipermutations under the Ulam metric and resulting bounds on code size.
pp. 1628-1632
10:10 Multiplexed FEC for Multiple Streams with Different Playout Deadlines
Ahmed Badr, Devin Lui and Ashish Khisti (University of Toronto, Canada); Wai-Tian Tan, Xiaoqing Zhu and John Apostolopoulos (Cisco Systems, USA)
We study a setting where two source streams with different decoding deadlines must be transmitted over a burst erasure channel. The source streams are multiplexed into a single stream of channel-packets at the encoder. The decoder must recover the source-packets within each stream sequentially, by their corresponding deadlines. We consider the burst-erasure channel model and characterize the capacity region for a certain range of system parameters. We show that the operation of the system can be dividing into three different regimes based on the relative values of decoding deadlines. We propose a coding scheme for each case. On the achievability side, we show that jointly coding across the two streams in a judicious manner can outperform the baseline scheme where we apply a single-stream code to each of the streams separately. On the converse side we develop information theoretic outer bounds on the capacity region. Interestingly we find that the capacity region exhibits a corner point" where we can transmit the urgent stream at a positive rate, yet attain a sum-rate equal to the capacity of the non-urgent stream.
pp. 1633-1637
10:30 A Code Equivalence between Streaming Network Coding and Streaming Index Coding
Ming Fai Wong and Michelle Effros (California Institute of Technology, USA); Michael Langberg (State University of New York at Buffalo, USA)
We consider a delay-constrained streaming model for communications and show that under this model, network coding and index coding problems are code equivalent. That is, any streaming network coding instance can be efficiently mapped to a corresponding acyclic streaming index coding instance such that an index code for the latter can be efficiently transformed into a network code for former. This reduction holds even for network coding instances that contain cycles, thereby proving the first known reduction from cyclic to finite acyclic network coding networks.
pp. 1638-1642
10:50 On the error probability of stochastic decision and stochastic decoding
Jun Muramatsu (NTT Corporation, Japan); Shigeki Miyake (NTT, Japan)
This paper investigates the error probability of a stochastic decision and the way in which it differs from the error probability of an optimal decision, i.e., the maximum a posteriori decision. This paper calls attention to the fact that the error probability of a stochastic decision with the a posteriori distribution is at most twice the error probability of the maximum a posteriori decision. It is shown that, by generating an independent identically distributed random sequence subject to the a posteriori distribution and making a decision that maximizes the a posteriori probability over the sequence, the error probability approaches exponentially the error probability of the maximum a posteriori decision as the sequence length increases. Using these ideas as a basis, we can construct stochastic decoders for source/channel codes.
pp. 1643-1647

#### We1-4: Zero Error Capacity

Room: K3
Chair: Alon Orlitsky (University of California, San Diego, USA)
09:50 The Birthday Problem and Zero-Error List Codes
Parham Noorzad and Michelle Effros (California Institute of Technology, USA); Michael Langberg (State University of New York at Buffalo, USA); Victoria Kostina (California Institute of Technology, USA)
As an attempt to bridge the gap between classical information theory and the combinatorial world of zero-error information theory, this paper studies the performance of randomly generated codebooks over discrete memoryless channels under a zero-error constraint. This study allows the application of tools from one area to the other. Furthermore, it leads to an information-theoretic formulation of the birthday problem, which is concerned with the probability that in a given population, a fixed number of people have the same birthday. Due to the lack of a closed-form expression for this probability when the distribution of birthdays is not uniform, the resulting computation is not feasible in some applications; the information-theoretic formulation, however, can be analyzed for all distributions.
pp. 1648-1652
10:10 The Zero-Error Capacity of a Collision Channel With Successive Interference Cancellation
Yijin Zhang (Nanjing University of Science and Technology, P.R. China); Yi Chen (The Chinese University of Hong Kong, Shenzhen, Hong Kong); Yuan-Hsun Lo (Xiamen University, P.R. China); Wing Shing Wong (The Chinese University of Hong Kong, P.R. China)
The collision channel without feedback (CCw/oFB) model depicts a scenario in which multiple users share a communication channel with random relative time offsets among their clocks. This paper considers an extension of this model, which allows the receiver to use successive interference cancellation (SIC) to iteratively cancel the interference caused by those collided packets that have been decoded by the receiver. We derive the zero-error capacity region of this channel in the slot-synchronous case, and present a zero-error capacity achieving scheme by joint protocol sequences and channel coding design. It is shown that the negative impact on the zero-error capacity due to a lack of time synchronization can be removed by SIC
pp. 1653-1657
10:30 An improved bound on the zero-error list-decoding capacity of the 4/3 channel
Marco Dalai (University of Brescia, Italy); Venkatesan Guruswami (Carnegie Mellon University, USA); Jaikumar Radhakrishnan (TIFR, Mumbai, India)
We prove a new, improved upper bound on the size of codes $C \subseteq \{1,2,3,4\}^n$ with the property that every four distinct codewords in $C$ have a coordinate where they all differ. Specifically, we show that such a code has size at most $2^{6n/19 + o(n)}$, or equivalently has rate bounded by $6/19 \le 0.3158$ (measured in bits). This improves the previous best upper bound of $0.3512$ due to (Arikan 1994), which in turn improved the $0.375$ bound that followed from general bounds for perfect hashing due to (Fredman and Koml\'{o}s, 1984) and (K\"{o}rner and Marton, 1988). The context for this problem is two-fold: zero-error list decoding capacity, where such codes give a way to communicate with no error on the 4/3 channel" when list-of-3 decoding is employed, and perfect hashing, where such codes give a perfect hash family of size $n$ mapping $C$ to $\{1,2,3,4\}$.
pp. 1658-1662

#### We1-5: Joint Source-Channel Coding 2

Room: K4
Chair: Sandeep Pradhan (University Michigan, USA)
09:50 Dependence Balance in Multiple Access Channels with Correlated Sources
Amos Lapidoth (ETHZ, Switzerland); Shirin Saeedi Bidokhti (Stanford University, USA); Michele A Wigger (Telecom ParisTech, France)
A necessary condition is established for the lossy transmission of correlated sources over memoryless multiple access channels (MAC). It is used to derive lower bounds on the symmetric distortions that are achievable over Gaussian and binary adder MACs. When specialized to symmetric Gaussian MACs and Gaussian sources, the new lower bound recovers Lapidoth and Tinguely's max-correlation lower bound (2010) for matched source and channel bandwidths, and it improves on it for bandwidth mismatch factors below one. An analogous condition is also derived for MACs with correlated sources and feedback.
pp. 1663-1667
10:10 On Minimum Energy for Robust Gaussian Joint Source-Channel Coding with a Distortion-Noise Profile
Erman Köken and Ertem Tuncel (UC Riverside, USA)
Minimum energy required to achieve a distortion-noise profile, i.e., a function indicating the maximum allowed distortion value for each noise level, is studied for robust transmission of Gaussian sources over Gaussian channels. It is shown that for the inversely linear profile, uncoded transmission is optimal. On the other hand, it turns out that exponential profiles are not achievable with finite energy. Finally, using a family of lower bounds and a proposed coding scheme, the minimum energy behavior for the square-law profile is understood up to a multiplicative constant.
pp. 1668-1672
10:30 Communicating Correlated Sources Over a MAC
The problem of characterizing sufficient conditions for communicating correlated sources over a MAC is considered. The technique of inducing source correlation onto channel inputs - due to Cover, El Gamal and Salehi [Nov, 1980] - is enhanced by the use of \textit{fixed B-L coding}. The performance of the proposed coding technique is characterized via single-letter expressions to derive a new set of sufficient conditions. The latter conditions are contained within those characterized in [Cover, El Gamal, Salehi], and are proven to be strictly less binding than those of the latter for certain examples.
pp. 1673-1677

#### We1-6: Spatial Coupling

Room: K5
Chair: Laurent Schmalen (Nokia Bell Labs, Germany)
09:50 Spatially Coupled LDLC: New Constructions
Svetlana Reznikov and Meir Feder (Tel-Aviv University, Israel)
Low Density Lattice Code (LDLC) uses a lattice with a sparse inverse matrix, which allows a linear complexity decoding. Spatially Coupled Low Density Lattice Code (SC-LDLC) is built by coupling some LDLCs and has a smaller Symbol Error Rate (SER) than the LDLC scheme for every tested block length n. In this paper, some new constructions of the spatially coupled low density lattice codes are introduced.
pp. 1678-1682
10:10 A Protograph-Based Design of Quasi-Cyclic Spatially Coupled LDPC Codes
Li Chen and Shiyuan Mo (Sun Yat-sen University, P.R. China); Daniel J. Costello, Jr. (University of Notre Dame, USA); David G. M. Mitchell (New Mexico State University, USA); Roxana Smarandache (University of Notre Dame, USA)
Spatially coupled (SC) low-density parity-check (LDPC) codes can achieve capacity approaching performance with low message recovery latency when using sliding window (SW) decoding. An SC-LDPC code constructed from a protograph can be generated by first coupling a chain of block protographs and then lifting the coupled protograph using permutation matrices. This paper introduces a systematic design of SC-LDPC codes to eliminate 4-cycles in the coupled protograph. Using a quasi-cyclic (QC) lifting, we obtain QC-SC-LDPC codes of girth at least eight. Coupling a chain of block protographs implies spreading edges from one protograph to the others. Our protograph-based design can be viewed as guiding the edge spreading and also the graph-lifting process. Simulation results show the design results in improved decoding performance, particularly in the error floor, compared to random designs.
pp. 1683-1687
10:30 Complexity-Optimized Concatenated LDGM-Staircase Codes
Lei Zhang and Frank R. Kschischang (University of Toronto, Canada)
A concatenated soft-decision channel coding scheme consisting of an inner LDGM code and an outer staircase code is proposed. The soft-decision LDGM code is used for error reduction while the majority of bit errors are corrected by the low complexity hard-decision staircase code. Decoding complexity of the concatenated code is quantified by a score based on the number of edges in the LDGM code Tanner graph, the number of decoding iterations, and the number of staircase code decoding operations. The inner LDGM ensemble is designed by solving an optimization problem, which minimizes the product of the average node degree and an estimate of the required number of decoding iterations. A search procedure is used to find the inner and outer code pair with lowest complexity. The design procedure results in a Pareto-frontier characterization of the trade-off between net coding-gain and complexity for the concatenated code. Simulations of code designs at rate 5/6 show that the proposed scheme achieves net coding-gains equivalent to existing soft-decision codes, with up to 57% reduction in complexity.
pp. 1688-1692
10:50 A Novel Combinatorial Framework to Construct Spatially-Coupled Codes: Minimum Overlap Partitioning
Homa Esfahanizadeh (University of California, Los Angeles, USA); Ahmed Hareedy (University of California, Los Angeles (UCLA), USA); Lara Dolecek (UCLA, USA)
Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention thanks to their capacity approaching performance. An SC code is constructed by partitioning an underlying block code into a number of components, and coupling these copies together. In this paper, we introduce a new partitioning scheme, namely minimum overlap partitioning, that outperforms previous methods. We also present a general approach for the enumeration of problematic objects in the error-floor area that can be applied to any circulant-based SC code and to a variety of partitioning schemes. Our results show that, compared to the decoupled block code, an SC code constructed by the minimum overlap partitioning has more than 1.5 and 3 orders of magnitude performance improvement for the memory 1 and 2, respectively. Additionally, it outperforms the existing method of partitioning via cutting vectors by at least half an order of magnitude; this performance advantage becomes more pronounced with increasing the memory.
pp. 1693-1697

#### We1-7: Security 3

Room: K6
Chair: Salim El Rouayheb (Illinois Institute of Technology, USA)
09:50 Secure wireless communication under spatial and local Gaussian noise assumptions
Masahito Hayashi (Nagoya University, Japan)
We consider wireless communication between Alice and Bob when the intermediate space between Alice and Bob is controlled by Eve. That is, our model divides the channel noise into two parts, the noise generated during the transmission and the noise generated in the detector. Eve is allowed to control the former, but is not allowed to do the latter. While the latter is assumed to be a Gaussian random variable, the former is not assumed to be a Gaussian random variable. In this situation, using backward reconciliation and the random sampling, we propose a protocol to generate secure keys between Alice and Bob under the assumption that Eve's detector has a Gaussian noise and Eve is out of Alice's neighborhood. In our protocol, the security criteria are quantitatively guaranteed even with finite block-length code based on the evaluation of error of the estimation of channel.
pp. 1698-1702
10:10 The Degraded Gaussian Multiple Access Wiretap Channel with Selfish Transmitters: A Coalitional Game Theory Perspective
Remi A Chou and Aylin Yener (Pennsylvania State University, USA)
We study the degraded Gaussian multiple access wiretap channel with selfish transmitters, i.e., they are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective protocol, instead of operating on their own. If yes, is there a protocol that satisfy all the participating transmitters, in the sense that no transmitter has an incentive to deviate from the protocol? We answer these questions in the positive utilizing coalitional game theory. In particular, we show that cooperation is in the best interest of all transmitters and that there exist protocols that incentivize all transmitters to participate. Furthermore, we determine a unique, fair, and stable achievable secrecy rate allocation.
pp. 1703-1707
10:30 MIMO Gaussian Wiretap Channels with Two Transmit Antennas: Optimal Precoding and Power Allocation
Mojtaba Vaezi (Princeton University, USA); Wonjae Shin (Seoul National University, Korea); H. Vincent Poor (Princeton University, USA); Jungwoo Lee (Seoul National University, Korea)
A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. It is shown that the secrecy capacity of this channel can be achieved by linear precoding. The optimal precoding and power allocation scheme achieving the secrecy capacity are developed subsequently, and the secrecy capacity is compared with the generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed precoding for this problem. Numerical results demonstrate that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precoding.
pp. 1708-1712
10:50 Computation of the Random Coding Secrecy Exponent for a Constant Composition Ensemble
Yutaka Jitsumatsu (Kyushu University, Japan)
Recently, Parizi, Telatar, and Merhav [1] determined the exact random coding secrecy exponents for a wiretap channel. In this study, we focus on the computation of such secrecy exponents. To obtain the exact random coding secrecy exponent for a constant composition random coding ensemble, optimization with respect to two stochastic matrices must be performed. Parizi et al. suggested that inner optimization is a convex optimization problem and therefore can be solved efficiently and that the outer optimization is not guaranteed to have convex structure and is solved by an exhaustive search. In this paper, we develop an efficient computation of the exact random coding secrecy exponent.
pp. 1713-1717

#### We1-8: Quantum IT 3

Room: K7+8
Chair: Min-Hsiu Hsieh (University of Technology Sydney, Australia)
09:50 Codes for Simultaneous Transmission of Quantum and Classical Information
Markus Grassl (Max-Plank-Institut für die Physik des Lichts, Germany); Sirui Lu (Tsinghua University, P.R. China); Bei Zeng (University of Guelph, Canada)
We consider the characterization as well as the construction of quantum codes that allow to transmit both quantum and classical information, which we refer to as hybrid codes'. We construct hybrid codes $[[n,k:m,d]]_q$ with length $n$ and distance $d$, that simultaneously transmit $k$ qudits and $m$ symbols from a classical alphabet of size $q$. Many good codes such as $[[7,1:1,3]]_2$, $[[9,2:2,3]]_2$, $[[10,3:2,3]]_2$, $[[11,4:2,3]]_2$, $[[11,1:2,4]]_2$, $[[13,1:4,4]]_2$, $[[13,1:1,5]]_2$, $[[14,1:2,5]]_2$, $[[15,1:3,5]]_2$, $[[19,9:1,4]]_2$, $[[20,9:2,4]]_2$, $[[21,9:3,4]]_2$, $[[22,9:4,4]]_2$. All these codes have better parameters than hybrid codes obtained from the best known stabilizer quantum code.
pp. 1718-1722
10:10 Belief propagation decoding of quantum channels by passing quantum messages
Joseph M. Renes (ETH Zurich, Switzerland)
We construct a belief propagation algorithm which passes quantum messages on the factor graph and is capable of decoding the classical-quantum channel with pure state outputs. This gives explicit decoding circuits whose number of gates is quadratic in the code length. We show that the decoder can be modified to work with polar codes for the pure state channel and as part of a decoder for transmitting quantum information over the amplitude damping channel. These yield the first explicit capacity-achieving decoders for non-Pauli channels.
pp. 1723-1727
10:30 Semidefinite programming converse bounds for classical communication over quantum channels
Xin Wang, Wei Xie and Runyao Duan (University of Technology Sydney, Australia)
We study the classical communication over quantum channels when assisted by no-signalling (NS) and PPT-preserving (PPT) codes. We first show that both the optimal success probability of a given transmission rate and one-shot $\epsilon$-error capacity can be formalized as semidefinite programs (SDPs) when assisted by NS and PPT codes. Based on this, we derive SDP finite blocklength converse bounds for general quantum channels, which also reduce to the converse bound of Polyanskiy, Poor, and Verdu for classical channels. Furthermore, we derive an SDP strong converse bound for the classical capacity of a general quantum channel: for any code with a rate exceeding this bound, the optimal success probability vanishes exponentially fast as the number of channel uses increases. In particular, applying our efficiently computable bound, we derive improved upper bounds to the classical capacity of the amplitude damping channels and also establish the strong converse property for a new class of quantum channels.
pp. 1728-1732
10:50 On the Feasibility Conditions of Quantum State Discrimination
Chung-Chin Lu (National Tsing Hua University, Taiwan); Shiuan-Hao Kuo (Silicon Motion, Inc., Taiwan)
In this paper, we consider the quantum unambiguous discrimination problem of a set of linearly independent pure states. With a constructive procedure, we establish a necessary and sufficient condition for feasible POVM measurements for unambiguous quantum state discrimination. We develop methods to calculate the optimal discrimination efficiencies for minimizing the inconclusive probability and the optimal discrimination efficiencies for the minimax criterion. Finally, we prove a necessary and sufficient condition to have a feasible POVM measurement which achieves the minimum inconclusive probability criterion and the minimax criterion simultaneously and show that geometrically uniform states with equal a priori probabilities meet this condition.
pp. 1733-1737

#### We1-9: Source Coding 3

Room: K9
Chair: Charalambos D Charalambous (University of Cyprus, Cyprus)
09:50 An Information-Theoretic Analysis of Deduplication
Urs Niesen (Qualcomm Research, USA)
Deduplication finds and removes long-range data duplicates. It is commonly used in cloud and enterprise server settings and has been successfully applied to primary, backup, and archival storage. Despite its practical importance as a source-coding technique, its analysis from the point of view of information theory is missing. This paper provides such an information-theoretic analysis of data deduplication. It introduces a new source model adapted to the deduplication setting. It formalizes both fixed and variable-length deduplication schemes, and it introduces a novel, multi-chunk deduplication scheme. It then provides an analysis of these three deduplication variants, emphasizing the importance of boundary synchronization between source blocks and deduplication chunks. The proposed multi-chunk deduplication scheme is shown to be order optimal under fairly mild assumptions.
pp. 1738-1742
10:10 Extended Gray-Wyner System with Complementary Causal Side Information
Cheuk Ting Li and Abbas El Gamal (Stanford University, USA)
We establish the rate region of an extended Gray-Wyner system for 2-DMS $(X,Y)$ with two additional decoders having complementary causal side information. This extension is interesting because in addition to the operationally significant extreme points of the Gray-Wyner rate region, which include Wyner's common information, G{\'a}cs-K{\"o}rner common information and information bottleneck, the rate region for the extended system also includes the K{\"o}rner graph entropy, the privacy funnel and excess functional information, as well as three new quantities of potential interest, as extreme points. To simplify the investigation of the 5-dimensional rate region of the extended Gray-Wyner system, we establish an equivalence of this region to a 3-dimensional mutual information region that consists of the set of all triples of the form $(I(X;U),\,I(Y;U),\,I(X,Y;U))$ for some $p_{U|X,Y}$. We further show that projections of this mutual information region yield the rate regions for many settings involving a 2-DMS, including lossless source coding with causal side information, distributed channel synthesis, and lossless source coding with a helper.
pp. 1743-1747
10:30 Variable-Length Resolvability for General Sources
Hideki Yagi and Te Sun Han (University of Electro-Communications, Japan)
We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding variable-length uniform random numbers, and the asymptotically minimum average length rate of the uniform random numbers, called the (variable-length) resolvability, is investigated. We first analyze the variable-length resolvability with the variational distance as an approximation measure. We then extend the analysis to the case under the divergence as an approximation measure. When the asymptotically exact approximation is required, it is shown that the resolvability under the two kinds of approximation measures coincides. We also analyze the second-order variable-length resolvability.
pp. 1748-1752
10:50 Universal Tree Source Coding Using Grammar-Based Compression
Markus Lohrey and Danny Hucke (University of Siegen, Germany)
We apply so-called tree straight-line programs to the problem of universal source coding for binary trees. We derive an upper bound on the maximal pointwise redundancy (or worst-case redundancy) that improve previous bounds on the average case redundancy obtained by Zhang, Yang, and Kieffer using directed acyclic graphs. Using this, we obtain universal codes for new classes of tree sources.
pp. 1753-1757

### Wednesday, June 28, 11:30 - 12:30

#### We2-1: Coding Techniques (Focus Session)

Room: Europa
Chair: Irina Bocharova (St. Petersburg University of Information Technologies, Mechanics and Optics, Russia)
11:30 Multi-Block Interleaved Codes for Local and Global Read Access
Yuval Cassuto (Technion, Israel); Evyatar Hemo (Technion - Institute of Technology, Israel); Sven Puchinger and Martin Bossert (Ulm University, Germany)
We define multi-block interleaved codes as codes that allow reading information from either a small sub-block or from a larger full block. The former offers faster access, while the latter provides better reliability. We specify the correction capability of the sub-block code through its gap t from optimal minimum distance, and look to have full-block minimum distance that grows with the parameter t. We construct two families of such codes when the number of sub-blocks is 3. The codes match the distance properties of known integrated-interleaving codes, but with the added feature of mapping the same number of information symbols to each sub-block. As such, they are the first codes that provide read access in multiple size granularities and correction capabilities.
pp. 1758-1762
11:50 Successive Cancellation Decoding of Single Parity-Check Product Codes
Mustafa Cemil Coşkun (Technische Universität München, Germany); Gianluigi Liva (DLR - German Aerospace Center, Germany); Alexandre Graell i Amat (Chalmers University of Technology, Sweden); Michael Lentmaier (Lund University, Sweden)
We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes by using recursive formulas. We analyze the error probability of SPC-PCs over the binary erasure channel under SC decoding. A bridge with the analysis of PCs introduced by Elias in 1954 is also established. Furthermore, bounds on the block error probability under SC decoding are provided, and compared to the bounds under the original decoding algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a lower block error probability than Elias' decoding.
pp. 1763-1767
12:10 Codes for Channels With Segmented Edits
Mahed Abroshan and Ramji Venkataramanan (University of Cambridge, United Kingdom (Great Britain)); Albert Guillén i Fàbregas (ICREA and Universitat Pompeu Fabra & University of Cambridge, Spain)
We consider insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. We further assume that there are no segment markers in the received sequence. We propose code constructions for the segmented deletion, segmented insertion, and segmented insertion-deletion channels based on subsets of VT codes chosen with pre-determined prefixes and/or suffixes. The proposed codes are zero-error, can be decoded segment-by-segment, and their rate scaling as the segment length increases is the same as that of the maximal code.
pp. 1768-1772

#### We2-2: Student Paper Awards Candidate Talks 2

Room: Brussels
Chair: Elza Erkip (New York University, USA)
11:30 A High-SNR Normal Approximation for Single-Antenna Rayleigh Block-Fading Channels
Alejandro Lancho and Tobias Koch (Universidad Carlos III de Madrid & Gregorio Marañón Health Research Institute, Spain); Giuseppe Durisi (Chalmers University of Technology, Sweden)
This paper concerns the maximal achievable rate at which data can be transmitted over a non-coherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. In particular, a high-SNR normal approximation of the maximal achievable rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals L over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate already at SNR values of 15 dB.
pp. 1773-1777
11:50 A Tight Rate Bound and a Matching Construction for Locally Recoverable Codes with Sequential Recovery From Any Number of Multiple Erasures
Balaji Srinivasan Babu (IISc, India); Ganesh Kini (Indian Institute of Science, India); P Vijay Kumar (Indian Institute of Science & University of Southern California, India)
An $[n,k]$ code $\mathcal{C}$ is said to be locally recoverable in the presence of a single erasure, and with locality parameter $r$, if each of the $n$ code symbols of $\mathcal{C}$ can be recovered by accessing at most $r$ other code symbols. An $[n,k]$ code is said to be a locally recoverable code with sequential recovery from $t$ erasures, if for any set of $s \leq t$ erasures, there is an $s$-step sequential recovery process, in which at each step, a single erased symbol is recovered by accessing at most $r$ other code symbols. This is equivalent to the requirement that for any set of $s \leq t$ erasures, the dual code contain a codeword whose support contains the coordinate of precisely one of the $s$ erased symbols. In this paper, a tight upper bound on the rate of such a code, for any value of number of erasures $t$ and any value $r \geq 3$, of the locality parameter is derived. This bound proves an earlier conjecture due to Song, Cai and Yuen. While the bound is valid irrespective of the field over which the code is defined, a matching construction of {\em binary} codes that are rate-optimal is also provided, again for any value of $t$ and any value $r\geq3$.
pp. 1778-1782
12:10 Feedback Capacity and Coding for the (0,k)-RLL Input-Constrained BEC
Ori Peled, Oron Sabag and Haim H Permuter (Ben-Gurion University, Israel)
The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the $(0,k)$-runlength limited (RLL) constraint, i.e., no more than $k$ consecutive zeros are allowed. The feedback capacity of this channel is derived for all $k\geq1$, \begin{equation*} C^\mathrm{fb}_{(0,k)}(\varepsilon) = \max\frac{\overline{\varepsilon}H_2(\delta_0)+\sum_{i=1}^{k-1}\left(\overline{\varepsilon}^{i+1}H_2(\delta_i)\prod_{m=0}^{i-1}\delta_m\right)}{1+\sum_{i=0}^{k-1}\left(\overline{\varepsilon}^{i+1} \prod_{m=0}^{i}\delta_m\right)}, \end{equation*} where $\varepsilon$ is the erasure probability, $\overline{\varepsilon}=1-\varepsilon$, $H_2(\cdot)$ is the binary entropy function and the maximization is only over $\delta_{k-1}$, while the other parameters $\delta_0,\ldots,\delta_{k-2}$ are simple functions of $\delta_{k-1}$. A simple coding scheme is constructed for all $k$, establishing that the feedback capacity can be achieved using variable length zero-error coding. In addition, it is shown that non-causal knowledge of the erasures at the encoder does not increase the feedback capacity.
pp. 1783-1787

#### We2-3: Crypto (Focus Session)

Room: K2
Chair: Natasa Zivic (University of Siegen, Germany)
11:30 Efficiency Lower Bounds for Commit-and-Prove Constructions
Chen-Da Liu Zhang and Christian Badertscher (ETH Zurich, Switzerland); Sandro Coretti (New York University, USA); Ueli Maurer (ETH Zurich, Switzerland)
Commitment schemes that come along with zero-knowledge proofs for relations among committed values are known as commit-and-prove functionalities or notarized envelopes. An important role in this context take equality proofs among commitments. They appear in various contexts of multi-party computation, circuit satisfiability or inclusion proofs. Using commit-and-prove functionalities for equality, we investigate black-box constructions of commit-and-prove functionalities for more complex relations. We are interested in the relationship between the soundness of such protocols and the number of additional commitments a protocol creates during a run. In particular, for the natural and quite general class of 3-round public-coin zero-knowledge protocols, it turns out that implementing an inequality proof, or any of the relations NAND, NOR, or XOR, essentially requires at least $2n$ additional commitments in order to achieve a soundness of $2^{-n}$. For concreteness, we revisit a protocol for inequality that exactly matches this bound.
pp. 1788-1792
11:50 Information Set Decoding with Soft Information and some cryptographic applications
Qian Guo (Lund University & Lund University, Sweden); Thomas Johansson, Erik Mårtensson and Paul Stankovski (Lund University, Sweden)
The class of information set decoding algorithms is the best known way of decoding general codes, i.e. codes that admit no special structure, in the Hamming metric. Stern's algorithm is the origin of the most efficient algorithms in this class. In this paper we consider the same decoding problem but for a channel with soft information. We give a version of Stern's algorithm for a channel with soft information that includes some novel steps of ordering vectors in lists, based on reliability values. We then demonstrate how this new algorithm can be used in a few cryptographic applications, including a very efficient attack on a recently proposed McEliece-type cryptosystem.
pp. 1793-1797
12:10 Statistical Decoding
Thomas Debris-Alazard (Inria Paris, France); Jean-Pierre Tillich (INRIA, France)
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoding techniques (ISD). A while ago a generic decoding algorithm which does not belong to this family was proposed: statistical decoding. It is a randomized algorithm that requires the computation of a large set of parity-check equations of moderate weight. We solve here several open problems related to this decoding algorithm. We give in particular the asymptotic complexity of this algorithm, give a rather efficient way of computing the parity-check equations needed for it inspired by ISD techniques and give a lower bound on its complexity showing that when it comes to decoding on the Gilbert-Varshamov bound it can never be better than Prange's algorithm.
pp. 1798-1802

#### We2-4: Security (Focus Session)

Room: K3
Chair: Andrew Thangaraj (IIT Madras, India)
11:30 Security of Helper Data Schemes for SRAM-PUF in Multiple Enrollment Scenarios
Lieneke Kusters and Tanya Ignatenko (Eindhoven University of Technology, The Netherlands); Frans MJ Willems (Technical University Eindhoven, The Netherlands); Roel Maes, Erik van der Sluis and Georgios. Selimis (Intrinsic-ID, The Netherlands)
Fuzzy commitment and syndrome-based schemes are two well-known helper data schemes used to bind and generate, respectively, a secret key to/from SRAM-PUF observations. To allow the decoder to reconstruct this secret key from a new (verification) observation of an SRAM-PUF, an encoder has to generate so-called helper data. This helper data is a function of an SRAM-PUF enrollment observation and, in case of fuzzy commitment, the secret key. The helper data is assumed to be public and thus must leak no information about the secret key. It is known that in the unbiased case both schemes can achieve secrecy capacity equal to the mutual information between enrollment and verification SRAM-PUF observations at negligible secrecy leakage, when a secret key is created for a single SRAM-PUF enrollment observation. We study here the situation when multiple SRAM-PUF observations are used to create different secret keys. First, we introduce a symmetry property for multiple SRAM-PUF observations. For such symmetric SRAM-PUFs, we show that, in both helper data schemes, the helper data corresponding to multiple SRAM-PUF observations provide no information about any of the secret keys.
pp. 1803-1807
11:50 New Models for Interference and Broadcast Channels with Confidential Messages
Mohamed Nafea (The Pennsylvania State University, USA); Aylin Yener (Pennsylvania State University, USA)
pp. 1808-1812
12:10 Secret Sharing with Optimal Decoding and Repair Bandwidth
Wentao Huang and Jehoshua Bruck (California Institute of Technology, USA)
This paper studies the communication efficiency of threshold secret sharing schemes. We construct a family of Shamir's schemes with asymptotically optimal decoding bandwidth for arbitrary parameters. We also construct a family of secret sharing schemes with both optimal decoding and optimal repair bandwidth for arbitrary parameters. The construction leads to a family of regenerating codes allowing centralized repair of multiple node failures with small sub-packetization.
pp. 1813-1817

#### We2-5: Network Information Theory (Focus Session)

Room: K5
Chair: Anthony Ephremides (University of Maryland, USA)
11:30 Towards an Algebraic Network Information Theory: Simultaneous Joint Typicality Decoding
Sung Hoon Lim (Korea Institute of Ocean Science and Technology, Korea); Chen Feng (University of British Columbia, Canada); Adriano Pastore (Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Spain); Bobak Nazer (Boston University, USA); Michael Gastpar (EPFL & University of California, Berkeley, Switzerland)
Recent work has employed joint typicality encoding and decoding of nested linear code ensembles to generalize the compute--forward strategy to discrete memoryless multiple-access channels (MACs). An appealing feature of these nested linear code ensembles is that the coding strategies and error probability bounds are conceptually similar to classical techniques for random i.i.d.\ code ensembles. In this paper, we consider the problem of recovering $K$ linearly independent combinations over a $K$-user MAC, i.e., recovering the messages in their entirety via nested linear codes. While the MAC rate region is well-understood for random i.i.d.\ code ensembles, new techniques are needed to handle the statistical dependencies between competing codeword $K$-tuples that occur in nested linear code ensembles. This is an important step towards characterizing the general case of recovering $L \leq K$ linear combinations.
pp. 1818-1822
11:50 On the Sub-optimality of Single-letter Coding in Multi-terminal Communications
We investigate binary block-codes (BBC). A BBC is defined as a vector of Boolean functions. We consider BBCs which are generated randomly, and using single-letter distributions. We characterize the vector of dependency spectrums of these BBCs. We use this vector to upper-bound the correlation between the outputs of two distributed BBCs. Finally, the upper-bound is used to show that the large blocklength single-letter coding schemes in the literature are sub-optimal in some multiterminal communication settings.
pp. 1823-1827
12:10 Coordination with Clustered Common Randomness in a Three-Terminal Line Network
Ishaque Ashar Kadampot and Matthieu Bloch (Georgia Institute of Technology, USA)
To achieve strong coordination in a network, nodes benefit from access to a source of common randomness. Most studies pertaining to strong coordination assume the existence of a source of common randomness accessible to all nodes in the network. This assumption, however, is not practical in a decentralized network. We analyze the problem of strong coordination in a three-terminal line network with common randomness available only at the first two nodes and assume that the actions of the first node are specified by an external agent. We use coding schemes developed for channel resolvability codes to characterize the strong coordination capacity region when the intermediate node is operating in a functional mode. A comparison of our coordination capacity region with a case in which all nodes have access to a common randomness shows that we have to increase the communication rate between the second and the third nodes to achieve the same coordination distribution.
pp. 1828-1832

#### We2-P: Recent Results Posters

Room: Foyer
Chair: Anke Schmeink (RWTH Aachen University, Germany)

### Wednesday, June 28, 12:45 - 13:45

#### WeA: Awards Session

Room: Europa
Chair: Ruediger L Urbanke (EPFL, Switzerland)

## Thursday, June 29

### Thursday, June 29, 08:30 - 09:30

#### ThP: Plenary Talk: The Flesh of Polar Codes - Emre Telatar

Emre Telatar
Room: Europa
Chair: Sennur Ulukus (University of Maryland, USA)

### Thursday, June 29, 09:50 - 11:10

#### Th1-1: Lattice Codes 1

Room: Europa
Chair: Stark Draper (University of Toronto, Canada)
09:50 Capacity Optimality of Lattice Codes in Common Message Gaussian Broadcast Channels with Coded Side Information
Lakshmi Prasad Natarajan (Indian Institute of Technology Hyderabad, India); Yi Hong and Emanuele Viterbo (Monash University, Australia)
Lattices possess elegant mathematical properties which have been previously used in the literature to show that structured codes can be efficient in a variety of communication scenarios. We consider the family of single-transmitter multiple-receiver Gaussian channels where the source transmits a set of common messages to all the receivers (multicast scenario), and each receiver has 'coded side information', i.e., prior information in the form of linear combinations of the messages. This channel model is motivated by applications to multi-terminal networks where the nodes may have access to coded versions of the messages from previous signal hops or through orthogonal channels. The capacity of this channel is known and follows from the work of Tuncel (2006), which is based on random coding arguments. In this paper, following the approach introduced by Erez and Zamir, we show that lattice codes are capacity-optimal for this family of channels. The structured coding scheme proposed in this paper is derived from Construction A lattices designed over prime fields, and utilizes 'algebraic binning' at the decoders to expurgate the channel code and obtain good lattice subcodes, for every possible set of linear combinations available as side information.
pp. 1833-1837
10:10 On the Communication Cost of Determining an Approximate Nearest Lattice Point
Maiara F. Bollauf (University of Campinas, Brazil); Vinay A Vaishampayan (City Univerity of New York, USA); Sueli I. R. Costa (University of Campinas-UNICAMP (Brazil), Brazil)
We consider the closest lattice point problem in a distributed network setting and study the communication cost and the error probability for computing an approximate nearest lattice point, using the nearest-plane algorithm, due to Babai. Two distinct communication models, centralized and interactive, are considered. The importance of proper basis selection is addressed. Assuming a reduced basis for a two-dimensional lattice, we determine the approximation error of the nearest plane algorithm. The communication cost for determining the Babai point, or equivalently, for constructing the rectangular nearest-plane partition, is calculated in the interactive setting. For the centralized model, an algorithm is presented for reducing the communication cost of the nearest plane algorithm in an arbitrary number of dimensions.
pp. 1838-1842
10:30 Communication Cost of Transforming a Nearest Plane Partition to the Voronoi Partition
Vinay A Vaishampayan (City Univerity of New York, USA); Maiara F. Bollauf (University of Campinas, Brazil)
We consider the problem of distributed computation of the nearest lattice point for a two dimensional lattice. An interactive model of communication is considered. We address the problem of reconfiguring a specific rectangular partition, a nearest plane, or Babai, partition, into the Voronoi partition. Expressions are derived for the error probability as a function of the total number of communicated bits. With an infinite number of allowed communication rounds, the average cost of achieving zero error probability is shown to be finite. For the interactive model, with a single round of communication, expressions are obtained for the error probability as a function of the bits exchanged. We observe that the error exponent depends on the lattice.
pp. 1843-1847
10:50 Compute-and-Forward over Block-Fading Channels Using Algebraic Lattices
Shanxiang Lyu, Antonio Campello and Cong Ling (Imperial College London, United Kingdom (Great Britain)); Jean-Claude Belfiore (Telecom Paristech & Huawei Technologies, France)
Previous approaches to compute-and-forward (C\&F) are mostly based on quantizing channel coefficients to integers. In this work, we investigate the C\&F strategy over block fading channels using Construction A over rings, so as to allow better quantization for the channels. Advantages in decoding error probabilities and computation rates are demonstrated, and the construction is shown to outperform the C\&F strategy over the integers $\mathbb{Z}$.
pp. 1848-1852

#### Th1-2: Polar Codes 2

Room: Brussels
Chair: Ruediger L Urbanke (EPFL, Switzerland)
09:50 Construction of Polar Codes with Sublinear Complexity
Marco Mondelli (Stanford University, USA); Hamed Hassani (University of Pennsylvania, USA); Ruediger L Urbanke (EPFL, Switzerland)
Consider the problem of constructing a polar code of block length N for the transmission over a given channel $W$. Typically this requires to compute the reliability of all the $N$ synthetic channels and then to include those that are sufficiently reliable. However, we know from [1], [2] that there is a partial order among the synthetic channels. Hence, it is natural to ask whether we can exploit it to reduce the computational burden of the construction problem. We show that, if we take advantage of the partial order [1], [2], we can construct a polar code by computing the reliability of roughly $N/\log^{3/2} N$ synthetic channels. Such a set of synthetic channels is universal, in the sense that it allows one to construct polar codes for any $W$, and it can be identified by solving a maximum matching problem on a bipartite graph. Our proof technique consists of reducing the construction problem to the problem of computing the maximum cardinality of an antichain for a suitable partially ordered set. As such, this method is general and it can be used to further improve the complexity of the construction problem in case a new partial order on the synthetic channels of polar codes is discovered.
pp. 1853-1857
10:10 On the Error Probability of Short Concatenated Polar and Cyclic Codes with Interleaving
Giacomo Ricciutelli, Marco Baldi and Franco Chiaraluce (Università Politecnica delle Marche, Italy); Gianluigi Liva (DLR - German Aerospace Center, Germany)
In this paper, the analysis of the performance of the concatenation of a (short) polar code with an outer binary linear block code is addressed from a distance spectrum viewpoint. The analysis targets the case where an outer cyclic code is employed together with an inner systematic polar code. A concatenated code ensemble is introduced placing an interleaver at the input of the polar encoder. The introduced ensemble allows deriving bounds on the achievable error rates under maximum likelihood decoding, by applying the union bound to the (expurgated) average weight enumerators. The analysis suggests the need of careful optimization of the outer code, at least in the short block length regime, to attain low error floors.
pp. 1858-1862
10:30 A Randomized Construction of Polar Subcodes
Peter Trifonov (Saint-Petersburg State Polytechnic University, Russia); Grigorii Trofimiuk (Peter the Great St. Petersburg Polytechnic University, Russia)
A method for construction of polar subcodes is presented, which aims on minimization of the number of low-weight codewords in the obtained codes, as well as on improved performance under list or sequential decoding with small list size. Simulation results are provided, which show that the obtained codes outperform LDPC and turbo codes.
pp. 1863-1867
10:50 On Design of CRC Codes for Polar Codes with Successive Cancellation List Decoding
Takumi Murata and Hideki Ochiai (Yokohama National University, Japan)
Concatenation of polar codes with cyclic redundancy check (CRC) codes, together with successive cancellation list (SCL) decoding, is known to be an effective approach that can significantly enhance the performance of the original polar codes. Most of the studies on the concatenation of CRC and polar codes, however, pay little attention to the structure of CRC codes themselves, even though the longer CRC may lead to loss in terms of information rate. In this work, we investigate the effect of CRC length on the CRC-concatenated polar code performance by developing an analytical bound for the frame error rate (FER) after the CRC-assisted list decoding. As a result, we reveal that there is a trade-off between the CRC length and FER performance, and for a given target FER, there is the minimum length of CRC that satisfies the FER constraint in high signal-to-noise ratio (SNR). The validity of our analytical framework is confirmed by extensive simulation over an additive white Gaussian noise (AWGN) channel. The results thus offer a useful guideline when designing CRC codes for polar codes with SCL decoding.
pp. 1868-1872

Room: K2
Chair: Shlomo (Shitz) Shamai (The Technion, Israel)
Mohamed Fadel (University of Texas at Dallas, USA); Aria Nosratinia (University of Texas, Dallas, USA)
The broadcast channel under delayed, mixed, hybrid, or no CSIT is a subject of much interest but has been studied only under i.i.d. fading and perfect CSIR for all users. Models that go beyond i.i.d. fading and perfect CSIR are of practical importance since users may experience unequal fading block-length (coherence time) and unequal CSIR availability due to different mobility and scattering environment. This paper studies a two-user MISO broadcast channel with hybrid CSIR, where one static user (with slower fading) has CSIR and one dynamic user (with faster fading) does not have free CSIR. Under this hybrid CSIR condition, the paper studies the degrees of freedom under various CSIT scenarios: no, delayed, and hybrid CSIT. For no CSIT, we provide an outer bound that meets the achievable degrees of freedom region when the coherence times of the users are the same. For both delayed and hybrid CSIT, the achievable regions partially meet their corresponding outer bounds, and furthermore the corresponding gaps decrease with the dynamic user coherence time.
pp. 1873-1877
10:10 Application of Yamamoto-Itoh Coding Scheme to Discrete Memoryless Broadcast Channels
Hirosuke Yamamoto and Shintaro Hara (The University of Tokyo, Japan)
The Yamamoto-Itoh (YI) scheme is a simple two phase coding scheme for discrete memoryless channels with noiseless feedback, which can attain the so-called Burnashev error-exponent. In this paper, we show how we can apply the YI scheme to discrete memoryless broadcast channels, and derive the achievable error-exponents region of the YI scheme for given coding rates.;
pp. 1878-1882
10:30 Coding Across Heterogeneous Parallel Erasure Broadcast Channels is Useful
Sunghyun Kim (ETRI, Korea); Soheil Mohajer (University of Minnesota, USA); Changho Suh (KAIST, Korea)
Motivated by recent efforts to harness millimeter-wave (mmWave) bands, known to have high outage probabilities, we explore a $K$-user parallel packet-erasure broadcast channel that consists of orthogonal subchannels prone to packet-erasures. Our main result is two-fold. First, in the homogeneous channel where all subchannels have the same erasure probability, we show that the separation principle holds, i.e., coding across subchannels provides no gain. Second, in the heterogeneous channel where the subchannels have different erasure probabilities, we devise a scheme that employs coding across subchannels and show that the principle fails to hold, i.e., coding across subchannels provides a gain. Inspired by this finding, we demonstrate our scheme to be effective in harnessing the mmWave bands. Compared to the current approach in the 4G systems which allocates subchannels to users exclusively, we show that our scheme offers a huge gain. We find the gain to be significant in scenarios where the erasure probabilities are largely different, and importantly to increase with the growth of $K$. Our result calls for joint coding schemes in future wireless systems to meet growing mobile data demands.
pp. 1883-1887
10:50 Rate Splitting and Superposition Coding for Concurrent Groupcasting over the Broadcast Channel: A General Framework
Henry Romero (MIT Lincoln Laboratory, USA); Mahesh K Varanasi (University of Colorado, USA)
A general inner bound is given for the discrete memoryless broadcast channel with an arbitrary number of users and general message sets, a setting that accounts for the most general form of concurrent groupcasting, with up to exponentially many messages intended for any set of subsets of receivers. Achievability is based on superposition coding and rate-splitting, where each receiver jointly decodes both its desired messages as well as the partial interference assigned to it via rate-splitting. The proof of achievability builds on the techniques for the description and analysis of superposition coding recently developed by the authors for the multiple access channel with general messages.
pp. 1888-1892

#### Th1-4: Private Information Retrieval

Room: K3
Chair: Michael Gastpar (EPFL & University of California, Berkeley, Switzerland)
09:50 Private Information Retrieval from MDS Coded Data with Colluding Servers: Settling a Conjecture by Freij-Hollanti et al
Hua Sun (University of California, Irvine, USA); Syed Ali Jafar (University of California Irvine, USA)
A (K,N,T,Kc) instance of the MDS-TPIR problem is comprised of K messages and N distributed servers. Each message is separately encoded through a (Kc,N) MDS storage code. A user wishes to retrieve one message, as efficiently as possible, while revealing no information about the desired message index to any colluding set of up to T servers. The fundamental limit on the efficiency of retrieval, i.e., the capacity of MDS-TPIR is known only at the extremes where either T or Kc belongs to {1,N}. The focus of this work is a recent conjecture by Freij-Hollanti, Gnilke, Hollanti and Karpuk which offers a general capacity expression for MDS-TPIR. We prove that the conjecture is false by presenting as a counterexample a PIR scheme for the setting (K,N,T,Kc) = (2,4,2,2), which achieves the rate 3/5, exceeding the conjectured capacity, 4/7.
pp. 1893-1897
10:10 Multi-Message Private Information Retrieval
Karim A. Banawan and Sennur Ulukus (University of Maryland, USA)
We consider the problem of multi-message private information retrieval (MPIR) from $N$ non-communicating replicated databases. In MPIR, the user is interested in retrieving $P$ messages out of $M$ stored messages without leaking the identity of the retrieved messages. The information-theoretic sum capacity of MPIR $C_s^P$ is the maximum number of desired message symbols that can be retrieved privately per downloaded symbol. For the case $P \geq \frac{M}{2}$, we determine the exact sum capacity of MPIR as $C_s^P=\frac{1}{1+\frac{M-P}{PN}}$. For $P \leq \frac{M}{2}$, we develop lower and upper bounds for all $M,P,N$. These bounds match if the number of messages $M$ is an integer multiple of the number of desired messages $P$, in which case, $C_s^P=\frac{1-\frac{1}{N}}{1-(\frac{1}{N})^{M/P}}$. Our results indicate that joint retrieval of desired messages is more efficient than successive use of single-message retrieval schemes.
pp. 1898-1902
10:30 Robust Private Information Retrieval on Coded Data
Razane Tajeddine (Aalto University, Finland); Salim El Rouayheb (Illinois Institute of Technology, USA)
We consider the problem of designing PIR scheme on coded data when certain nodes are unresponsive. We provide the construction of $\nu$-robust PIR schemes that can tolerate up to $\nu$ unresponsive nodes. These schemes are adaptive and universally optimal in the sense of achieving (asymptotically) optimal download cost for any number of unresponsive nodes up to $\nu$.
pp. 1903-1907
10:50 Private Information Retrieval Schemes for Coded Data with Arbitrary Collusion Patterns
Razane Tajeddine, Oliver Gnilke, David Karpuk, Ragnar Freij-Hollanti and Camilla Hollanti (Aalto University, Finland); Salim El Rouayheb (Illinois Institute of Technology, USA)
In Private Information Retrieval (PIR), one wants to download a file from a database without revealing to the database which file is being downloaded. Much attention has been paid to the case of the database being encoded across several servers, subsets of which can collude to attempt to deduce the requested file. With the goal of studying the achievable PIR rates in realistic scenarios, we generalize results for coded data from the case of all subsets of servers of size $t$ colluding, to arbitrary subsets of the servers. We investigate the effectiveness of previous strategies in this new scenario, and present new results in the case where the servers are partitioned into disjoint colluding groups.
pp. 1908-1912

#### Th1-5: Rate Distortion Theory 2

Room: K4
Chair: Tsachy Weissman (Stanford University, USA)
09:50 A Distortion Based Approach for Protecting Inferences
Chi-Yo Tsai (UCLA, USA); Gaurav Kumar Agarwal (University of California Los Angeles, USA); Christina Fragouli (UCLA, USA); Suhas Diggavi (University of California Los Angeles, USA)
Eavesdropping attacks in inference systems aim to learn not the raw data, but the system inferences to predict and manipulate system actions. We argue that conventional entropy measures can be ambiguous on the adversary's estimation abilities, and adopt instead a distortion based framework. We show that requiring perfect distortion-based security is more frugal than requiring perfect entropy- based secrecy even for block length 1 codes, offering in some cases unbounded gains. Within this framework, we design algorithms that enable to efficiently use shared randomness, and show that each shared random key is exponentially useful in security.
pp. 1913-1917
10:10 Rate-Distortion Regions of Instances of Cascade Source Coding with Side Information
Chien-Yi Wang (Télécom ParisTech, France); Abdellatif Zaidi (Université Paris-Est Marne La Vallée, France)
In this work, we study a three-terminal cascade source coding problem with side information $Y_1$ known to the source encoder and the first user, and side information $Y_2$ known only to the second user. Each user wants to reconstruct some desired function of the source, lossily, to within some fidelity level. We establish single-letter characterization of the rate-distortion region of this model in some important special cases, including when the reconstruction is lossless at the first user. We then establish a connection among the studied model and the so-called side information-scalable source coding problem (i.e., Heegard-Berger problem with side information and successive refinement) to infer single-letter characterization of the rate-distortion region of some instances of the latter problem. In contrast with most previous related works, the results of this paper hold irrespective of the ordering among the source and side information sequences, which are then arbitrarily correlated.
pp. 1918-1922
10:30 The Rate-Distortion Function for Successive Refinement of Abstract Sources
Victoria Kostina (California Institute of Technology, USA); Ertem Tuncel (UC Riverside, USA)
In successive refinement of information, the decoder refines its representation of the source progressively as it receives more encoded bits. The rate-distortion region of successive refinement describes the minimum rates required to attain the target distortions at each decoding stage. In this paper, we derive a parametric characterization of the rate-distortion region for successive refinement of abstract sources. Our characterization extends Csiszár's result to successive refinement, and generalizes a result by Tuncel and Rose, applicable for finite alphabet sources, to abstract sources. The new characterization leads to a family of outer bounds to the rate-distortion region. It also enables new nonasymptotic converse bounds.
pp. 1923-1927
10:50 Rate-Distortion Tradeoffs under Kernel-Based Distortion Measures
Kazuho Watanabe (Toyohashi University of Technology, Japan)
Kernel methods have been used for turning linear learning algorithms into nonlinear ones. These nonlinear algorithms measures distances between data points by the distance in the kernel-induced feature space. In lossy data compression, the optimal tradeoff between the number of quantized points and the incurred distortion is characterized by the rate-distortion function. However, the rate-distortion functions associated with distortion measures involving kernel feature mapping have yet to be analysed. We consider two reconstruction schemes, reconstruction in input space and reconstruction in feature space, and provide bounds to the rate-distortion functions for these schemes. Comparison of the derived bounds to the quantizer performance obtained by the kernel K-means method suggests that the rate-distortion bounds for input space and feature space reconstructions are informative at low and high distortion levels, respectively.
pp. 1928-1932

#### Th1-6: Coding for Insertion and Deletion Channels 1

Room: K5
Chair: Joseph Jean Boutros (Texas A&M University, USA)
09:50 Coding for the Permutation Channel with Insertions, Deletions, Substitutions, and Erasures
Mladen Kovačević and Vincent Y. F. Tan (National University of Singapore, Singapore)
This paper is motivated by the error-control problem in communication channels in which the transmitted sequences are subjected to random permutations, in addition to being impaired with insertions, deletions, substitutions, and erasures of symbols. Bounds on the size of optimal codes in this setting are derived, and their asymptotic behavior examined in the fixed-minimum-distance regime. A family of codes correcting these types of errors is described and is shown to be asymptotically optimal for some sets of parameters. The corresponding error-detection problem is also analyzed.
pp. 1933-1937
10:10 Perfect Codes for Single Balanced Adjacent Deletions
Manabu Hagiwara (Chiba University, Japan)
Two classes of perfect codes for single balanced adjacent deletions are provided. These classes are inspired by Levenshtein's work on binary perfect codes for single standard deletion. One of the classes is defined via the inversion number and the other is defined via Levenshtein codes. The first half of this paper is devoted to the proof of perfectness and the other is devoted to discussion on the other properties of the provided codes.
pp. 1938-1942
10:30 Timing-Drift Channel Model and Marker-Based Error Correction Coding
Haruhiko Kaneko (Tokyo Institute of Technology, Japan)
Several types of insertion/deletion/substitution error correction codings have been proposed for channels with imperfect synchronization. Most of the conventional coding schemes assume insertion/deletion errors of bit granularity, while in some applications, e.g. bit patterned media recording, insertion/deletion errors occur as a result of accumulation of small synchronization errors. This paper considers a fractional insertion/deletion error channel in which a fraction of bit (i.e., $1/\nu$-bit) is inserted and deleted, and describes application of conventional marker-based IDS error correction coding to the channel. Also simulation results show bit error rates of the marker-based coding.
pp. 1943-1947
10:50 Limits to List Decoding of Insertions and Deletions
Antonia Wachter-Zeh (Technical University of Munich (TUM), Germany)
List decoding of insertions and deletions in the Levenshtein metric is considered. In this paper, a Johnson-like upper bound on the maximum list size when decoding in the Levenshtein metric is derived. This bound depends only on the length and minimum Levenshtein distance of the code, the length of the received word, and the alphabet size. It shows that polynomial-time list decoding beyond half the Levenshtein distance is possible for many parameters. For example, list decod- ing of two insertions/deletions with the well-known Varshamov- Tenengolts (VT) codes is feasible. Further, we also show a lower bound on list decoding VT codes and an efficient list decoding algorithm for two insertions/deletions with VT codes.
pp. 1948-1952

#### Th1-7: Security 4

Room: K6
Chair: Lifeng Lai (University of California, Davis, USA)
09:50 The Gelfand-Pinsker wiretap channel: Higher secrecy rates via a novel superposition code
Ziv Goldfeld (Ben Gurion University, Israel); Paul Cuff (Princeton University, USA); Haim H Permuter (Ben-Gurion University, Israel)
We study the state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. This model subsumes all other instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence both for reliability and security purposes. A lower bound on the secrecy-capacity, that improves upon the previously best known result by Chen and Han Vinck, is derived based on a novel superposition coding scheme. The improvement over the Chen and Han Vinck result is strict for some SD-WTCs. Specializing the lower bound to the case where CSI is also available to the decoder reveals that it is at least as good as the achievable formula by Chia and El-Gamal, which is already known to outperform the adaptation of the Chen and Han Vinck code to the encoder and decoder CSI scenario. The results are derived under the strict semantic-security metric that requires negligible information leakage for all message distributions. The proof of achievability relies on a stronger version of the soft-covering lemma for superposition codes.
pp. 1953-1957
10:10 The Gaussian Multiple Access Wiretap Channel when the Eavesdropper can Arbitrarily Jam
Remi A Chou and Aylin Yener (Pennsylvania State University, USA)
We study the Gaussian multiple access channel in presence of an adversary, who is simultaneously able to eavesdrop and jam, i.e., an active wiretapper. We assume that the adversary has a power constraint, which she can utilize to have any arbitrary jamming strategy. The multiple access channel between the legitimate transmitters and the receiver thus becomes arbitrarily varying. We derive inner and outer bounds on the secrecy rate region of our model. In the case of a degraded channel, we characterize the optimal secrecy sum-rate, and within 0.5 bits per channel use the optimal individual rate constraints. As a special case, we obtain the secrecy capacity of the point-to-point Gaussian wiretap channel when the eavesdropper is able to arbitrarily jam.
pp. 1958-1962
10:30 Secrecy Capacity of the First-Order Autoregressive Moving Average Gaussian Channel with Feedback
Chong Li (Qualcomm R&D, USA); Yingbin Liang (Syracuse University, USA)
In this paper, we consider the first-order autoregressive moving average Gaussian channel with perfect causal feedback where an eavesdropper receives noisy observations of the channel inputs and outputs. We show that the secrecy capacity is equal to the feedback capacity without the presence of eavesdropper. Furthermore, we explicitly construct the secrecy capacity-achieving feedback code, which is deterministic and simple to implement.
pp. 1963-1967
10:50 Asymptotic Converse Bound for Secret Key Capacity in Hidden Markov Model
Mohammad Reza Khalili Shoja, George T Amariucai and Zhengdao Wang (Iowa State University, USA); Shuangqing Wei (Louisiana State University, USA); Jing Deng (University of North Carolina at Greensboro, USA)
Secret key establishment from common randomness has been traditionally investigated under certain limiting assumptions, of which the most ubiquitous appears to be that the information available to all parties comes in the form of independent and identically distributed (i.i.d.) samples of some correlated random variables. Unfortunately, models employing the i.i.d assumption are often not accurate representations of real scenarios. A more capable model would represent the available information as correlated hidden Markov models (HMMs), based on the same underlying Markov chain. Such a model accurately reflects the scenario where all parties have access to imperfect observations of the same source random process, exhibiting a certain time dependency. In this paper, we derive a computationally-efficient asymptotic converse bound for the secret key capacity of the correlated-HMM scenario. The main obstacle, not only for our model, but also for other non-i.i.d cases, is the computational complexity. We address this by converting the initial bound to a product of Markov random matrices, and using recent results regarding its convergence to a Lyapunov exponent. The methods developed in the paper are easily extensible to derive a secret-key capacity lower bound.
pp. 1968-1972

#### Th1-8: Quantum IT 4

Room: K7+8
Chair: Stefan Wolf (USI Lugano, Switzerland)
09:50 Compression for quantum population coding
Yuxiang Yang, Ge Bai and Giulio Chiribella (The University of Hong Kong, Hong Kong); Masahito Hayashi (Nagoya University, Japan)
We study the compression of arbitrary parametric families of n identically prepared finite-dimensional quantum states, in a setting that can be regarded as a quantum analogue of population coding. For a family with f free parameters, we propose an asymptotically faithful protocol that requires a memory of overall size (f/2)log n. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of the optimal compression of n identically prepared displaced thermal states. Our protocol achieves the ultimate bound predicted by quantum Shannon theory. In addition, we explore the minimum requirement for quantum memory: On the one hand, the amount of quantum memory used by our protocol can be made arbitrarily small compared to the overall memory cost; on the other hand, any protocol using only classical memory cannot be faithful.
pp. 1973-1977
10:10 Moderate Deviations for Quantum Hypothesis Testing and a Martingale Inequality
Hao-Chung Cheng (National Taiwan University, Taiwan); Min-Hsiu Hsieh (University of Technology Sydney, Australia)
We study the asymptotic behavior of the type-I error in quantum hypothesis testing when the exponent of the type-II error approaches the quantum relative entropy sufficiently slowly. Our result shows that the moderate deviation principle holds for the testing problem if the quantum relative variance is positive. Our proof strategy employs strong large deviation theory and a martingale inequality.
pp. 1978-1982
10:30 Classical-Quantum Arbitrarily Varying Wiretap Channel: Secret Message Transmission under Jamming Attacks
Minglai Cai (Technische Universität München, Germany); Holger Boche (Technical University Munich, Germany); Christian Deppe (University of Bielefeld, Germany); Janis Noetzel (Technische Universität Dresden, Germany)
We analyze arbitrarily varying classical-quantum wiretap channels. These channels are subject to two attacks at the same time: one passive (eavesdropping), and one active (jamming). We progress on previous works by introducing a reduced class of allowed codes that fulfills a more stringent secrecy requirement than earlier definitions. In addition, we prove that non-symmetrizability of the legal link is sufficient for equality of the deterministic and the common randomness assisted secrecy capacities. At last, we focus on analytic properties of both secrecy capacities: We completely characterize their discontinuity points, and their super-activation properties.
pp. 1983-1987
10:50 Quantum Markov Chains and Logarithmic Trace Inequalities
David Sutter (ETH Zurich, Switzerland); Mario Berta (California Institute of Technology, USA); Marco Tomamichel (University of Technology Sydney, Australia)
A Markov chain is a tripartite quantum state $\rho_{ABC}$ where there exists a recovery map $R_{B\to BC}$ such that $\rho_{ABC}=R_{B\to BC}(\rho_{AB})$. More generally, an approximate Markov chain $\rho_{ABC}$ is a state whose distance to the closest recovered state $R_{B\to BC}(\rho_{AB})$ is small. Recently it has been shown that this distance can be bounded from above by the conditional mutual information $I(A:C|B)_{\rho}$ of the state. We improve on this connection by deriving the first bound that is tight in the commutative case and features an explicit and universal recovery map. The key tool in our proof is a multivariate extension of the Golden-Thompson inequality, which allows us to extend logarithmic trace inequalities from two to arbitrarily many matrices.
pp. 1988-1992

#### Th1-9: Source Coding 4

Room: K9
Chair: Yasutada Oohama (University of Electro-Communications, Japan)
Annina Bracher (Swiss Re, Switzerland); Amos Lapidoth (ETHZ, Switzerland); Christoph Pfister (ETH Zurich, Switzerland)
The rate region of the task-encoding problem for two correlated sources is characterized using a novel parametric family of dependence measures. The converse uses a new expression for the $\rho$-th moment of the list size, which is derived using the relative $\alpha$-entropy.
pp. 1993-1997
10:10 Performance Limits on the Classification of Kronecker-structured Models
Ishan Jindal and Matthew Nokleby (Wayne State University, USA)
Kronecker-structured (K-S) models recently have been proposed for the efficient representation, processing, and classification of multidimensional signals such as images and video. Because they are tailored to the multi-dimensional structure of the target images, K-S models show improved performance in compression and reconstruction over more general (union of) subspace models. In this paper, we study the classification performance of Kronecker-structured models in two asymptotic regimes. First, we study the diversity order, the slope of the error probability as the signal noise power goes to zero. We derive an exact expression for the diversity order as a function of the signal and subspace dimensions of a K-S model. Next, we study the classification capacity, the maximum rate at which the number of classes can grow as the signal dimension goes to infinity. We derive upper and lower bounds on the prelog factor of the classification capacity. Finally, we evaluate the empirical classification performance of K-S models, showing that they agree with the diversity order analysis.
pp. 1998-2002
10:30 The Redundancy Gains of Almost Lossless Universal Source Coding over Envelope Families
Jorge F Silva (University of Chile, Chile); Pablo Piantanida (CentraleSupélec-CNRS-Université Paris-Sud, France)
The problem of almost lossless universal coding is revisited in this work. We study uniform rate of convergence for distortion and redundancy over a family of envelope distributions. In particular, we show that an almost lossless coding scheme offers faster rate of convergence for the (minimax) redundancy compared with the well-known information radius developed for the lossless case at the expense of tolerating a non-zero distortion that vanishes to zero as the block-length grows. Our results show that even when lossless universality is feasible, an almost lossless scheme can still offer different regimes on the rates of convergence of the redundancy versus the distortion.
pp. 2003-2007
10:50 Universal Sampling Rate Distortion
Vinay Praneeth Boda (University of Maryland, College Park, USA); Prakash Narayan (University of Maryland, USA)
We examine the coordinated and universal rate-efficient sampling of a subset of correlated discrete memoryless sources followed by lossy compression of the sampled sources. The goal is to reconstruct a predesignated subset of sources within a specified level of distortion. The combined sampling mechanism and rate distortion code are universal in that they are devised to perform robustly without exact knowledge of the underlying probability distribution of the sources. Single-letter characterizations are provided for a universal sampling rate distortion function for fixed-set and independent random sampling.
pp. 2008-2012

### Thursday, June 29, 11:30 - 12:50

#### Th2-1: Coding Techniques 3

Room: Europa
Chair: Vladimir Sidorenko (Technical University of Munich, Germany)
11:30 Cooling Codes: Thermal-Management Coding for High-Performance Interconnects
Tuvi Etzion (Technion-Israel Institute of Technology, Israel); Alexander Vardy (University of California San Diego, USA); Yeow Meng Chee and Han Mao Kiah (Nanyang Technological University, Singapore)
High temperatures have dramatic negative effects on interconnect performance. Numerous techniques have been proposed to reduce the power dissipation of on-chip buses but they fall short of fully addressing the thermal challenges posed by high-performance interconnects. We introduce new efficient coding schemes that directly control the peak temperature of a bus by effectively cooling its hottest wires. This is achieved by avoiding state transitions on the hottest wires for as long as necessary until their temperature drops off. At the same time, we reduce the average power consumption by ensuring that the total number of state transitions on all the wires is bounded. Our solutions call for redundancy: we use $n > k$ wires to encode a given $k$-bit bus. Therefore, it is important to determine the minimum possible number of wires $n$ needed to encode $k$ bits while satisfying the desired properties. We provide full analysis in each case, and show that the number of additional wires required to cool the $t$ hottest wires is negligible when $k$ is large. Moreover, the resulting encoders and decoders are fully practical. They do not require significant computational overhead and can be implemented without sacrificing a large circuit area.
pp. 2013-2017
11:50 Recursive Block Markov Superposition Transmission of Short Codes
Shancheng Zhao (Jinan University, P.R. China); Qin Huang (Beihang University, Beijing, P.R. China); Xiao Ma (Sun Yat-sen University, P.R. China); Baoming Bai (Xidian University, P.R. China)
Extensive studies have demonstrated the effectiveness of constructing capacity-approaching codes by block Markov superposition transmission (BMST). However, to achieve high performance, BMST codes typically require large encoding memories and large decoding window sizes, which result in increased decoding complexity and decoding latency. To address this issue, we introduce the recursive BMST (rBMST), in which block-oriented feedback convolutional code is used instead of the block-oriented feedforward convolutional code. We propose to use a modified extrinsic information transfer (EXIT) chart analysis to study the convergence behavior of rBMST codes. On one hand, rBMST code shares most merits of BMST code, including near-capacity performance, low-complexity encoding, and flexible construction. On the other hand, compared with BMST code, rBMST code requires a smaller encoding memory, hence a lower decoding complexity, to approach the capacity. In particular, analytical results show that, rBMST code ensemble with encoding memory three reveals a lower error-floor than the BMST code ensemble with encoding memory twelve.
pp. 2018-2022
12:10 Complete Characterization of the Solvability of PAPR Reduction for OFDM by Tone Reservation
Holger Boche (Technical University Munich, Germany); Ullrich J Mönich and Ezra Tampubolon (Technische Universität München, Germany)
In this paper we analyze the peak-to-average power ratio (PAPR) reduction by tone reservation for orthogonal frequency division multiplexing (OFDM) schemes. In addition to the strong solvability of the PAPR reduction problem, where the PAPR has to be bounded by some constant, we consider a weaker form of solvability, where only the boundedness of the peak value of the signal is required. We show that for OFDM both forms of solvability are equivalent. Further, we show that in the case where the PAPR problem is not solvable, the set of input signals that lead to an unbounded OFDM signal is a residual set. As a consequence, if the upper density of the carriers, used for information transmission, is positive, the set of input signals that lead to a bounded OFDM signal is a meager set.
pp. 2023-2027
12:30 Construction of q-ary Constant Weight Sequences using a Knuth-like Approach
Elie Ngomseu Mambou and Theo G. Swart (University of Johannesburg, South Africa)
We present an encoding and decoding scheme for constant weight sequences, that is, given an information sequence, the construction results in a sequence of specific weight within a certain range. The scheme uses a prefix design that is based on Gray codes. Furthermore, by adding redundant symbols we extend the range of weight values for output sequences, which is useful for some applications.
pp. 2028-2032

#### Th2-2: Locally Repairable Codes 3

Room: Brussels
Chair: P Vijay Kumar (Indian Institute of Science & University of Southern California, India)
11:30 Bounds and Constructions for Linear Locally Repairable Codes over Binary Fields
Anyu Wang (Institute of Information Engineering, Chinese Academy of Sciences, P.R. China); Zhifang Zhang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.R. China); Dongdai Lin (Institute of Information Engineering, Chinese Academy of Sciences, P.R. China)
For binary $[n,k,d]$ linear locally repairable codes (LRCs), two new upper bounds on $k$ are derived. The first one applies to LRCs with disjoint local repair groups, for general values of $n,d$ and locality $r$, containing some previously known bounds as special cases. The second one is based on solving an optimization problem and applies to LRCs with arbitrary structure of local repair groups. Particularly, an explicit bound is derived from the second bound when $d\geq 5$. A specific comparison shows this explicit bound outperforms the Cadambe-Mazumdar bound for $5\leq d\leq 8$ and large values of $n$. Moreover, a construction of binary linear LRCs with $d\geq6$ attaining our second bound is provided.
pp. 2033-2037
11:50 Locally Repairable Codes with Multiple \\ $(r_{i}, \delta_{i})$-Localities
Bin Chen (South China Normal University, P.R. China); Shutao Xia and Jie Hao (Tsinghua University, P.R. China)
In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with \emph{$(r, \delta)$-locality} are further proposed. Since hot data is not uncommon in a distributed storage system, both Zeh et al. and Kadhe et al. focus on the LRCs with \emph{multiple localities or unequal localities} (ML-LRCs) recently, which said that the localities among the code symbols can be different. ML-LRCs are attractive and useful in reducing repair cost for hot data. In this paper, we generalize the ML-LRCs to the $(r,\delta)$-locality case of multiple node failures, and define an LRC with multiple $(r_{i}, \delta_{i})_{i\in [s]}$ localities ($s\ge 2$), where $r_{1}\leq r_{2}\leq\dots\leq r_{s}$ and $\delta_{1}\geq\delta_{2}\geq\dots\geq\delta_{s}\geq2$. Such codes ensure that some hot data could be repaired more quickly and have better failure-tolerance in certain cases because of relatively smaller $r_{i}$ and larger $\delta_{i}$. Then, we derive a Singleton-like upper bound on the minimum distance for the proposed LRCs by employing the regenerating-set technique. Finally, we obtain a class of explicit and structured constructions of optimal ML-LRCs, and further extend them to the cases of multiple $(r_{i}, \delta)_{i\in [s]}$ localities.
pp. 2038-2042
12:10 epsilon-MSR Codes with Small Sub-packetization
Ankit Singh Rawat (Massachusetts Institute of Technology, USA); Itzhak Tamo (Tel Aviv University, Israel); Venkatesan Guruswami (Carnegie Mellon University, USA); Klim Efremenko (Tel Aviv University, Israel)
Minimum storage regenerating (MSR) codes form a special class of maximum distance separable (MDS) codes by providing mechanisms for exact regeneration of a single code block in their codewords by downloading the minimum amount of information from the remaining code blocks. As a result, the MSR codes find application to distributed storage systems to enable node repairs with the optimal repair bandwidth. However, the construction of exact-repairable MSR codes requires working with a large sub-packetization level, which restricts the employment of these codes in practice. This paper explores exact-repairable MDS codes that significantly reduce the required sub-packetization level by achieving slightly sub-optimal repair bandwidth as compared to the MSR codes. This paper presents a general approach to combine an MSR code with large sub-packetization level with a code with large enough minimum distance to construct exact-repairable MDS codes with small sub-packetization level and near-optimal repair bandwidth. For a given number of parity blocks, the codes constructed using this approach have their sub-packetization level scaling logarithmically with the code length. In addition, the obtained codes require field size linear in the code length and ensure load balancing among the intact code blocks in terms of the information downloaded from these blocks during a node repair.
pp. 2043-2047
12:30 An Explicit, Coupled-Layer Construction of a High-Rate MSR Code with Low Sub-Packetization Level, Small Field Size and $d<(n-1)$
Birenjith Padmakumari Sasidharan and Myna Vajha (Indian Institute of Science, India); P Vijay Kumar (Indian Institute of Science & University of Southern California, India)
This paper presents an explicit construction for an $((n=2qt,k=2q(t-1),d=n-(q+1)), (\alpha = q(2q)^{t-1},\beta = \frac{\alpha}{q}))$ regenerating code over a field $\mathbb{F}_Q$ operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate $k/n$ as close to $1$ as desired, sub-packetization level $\alpha \leq r^{\frac{n}{r}}$ for $r=(n-k)$, field size $Q$ no larger than $n$ and where all code symbols can be repaired with the same minimum data download. This is the first-known construction of such an MSR code for $d<(n-1)$.

#### Th2-3: Multicell and Cloud Radio

Room: K2
Chair: Salman Avestimehr (University of Southern California, USA)
11:30 An Upper Bound on the Sum Capacity of the Downlink Multicell Processing with Finite Backhaul Capacity
Tianyu Yang, Nan Liu and Wei Kang (Southeast University, P.R. China); Shlomo (Shitz) Shamai (The Technion, Israel)
In this paper, we study upper bounds on the sum capacity of the downlink multicell processing model with finite backhaul capacity for the simple case of 2 base stations and 2 mobile users. It is modeled as a two-user multiple access diamond channel. It consists of a first hop from the central processor to the base stations via orthogonal links of finite capacity, and the second hop from the base stations to the mobile users via a Gaussian interference channel. The converse is derived using the converse tools of the multiple access diamond channel and that of the Gaussian MIMO broadcast channel. Through numerical results, it is shown that our upper bound improves upon the existing upper bound greatly in the medium backhaul capacity range, and as a result, the gap between the upper bounds and the sum rate of the time-sharing of the known achievable schemes is significantly reduced.
pp. 2053-2057
11:50 Capacity Bounds on the Downlink of Symmetric, Multi-Relay, Single Receiver C-RAN Networks
Shirin Saeedi Bidokhti (Stanford University, USA); Gerhard Kramer (Technical University of Munich, Germany); Shlomo (Shitz) Shamai (The Technion, Israel)
The downlink of symmetric Cloud Radio Access Networks (C-RAN) with multiple relays and a single receiver is studied. Lower and upper bounds are derived on the capacity. The lower bound is achieved by Marton's coding which facilitates dependence among the multiple-access channel inputs. The upper bound uses Ozarow's technique to augment the system with an auxiliary random variable. The bounds are studied over scalar Gaussian C-RANs and are shown to meet and characterize the capacity for interesting regimes of operation.
pp. 2058-2062
12:10 On the Capacity of Cloud Radio Access Networks
Shouvik Ganguly (University of California, San Diego); Young-Han Kim (UCSD, USA)
Uplink and downlink cloud radio access networks are modeled as two-hop K-user L-relay networks, whereby small base-stations act as relays and are connected to a central processor via orthogonal links of finite capacity. Simplified versions of noisy network coding and distributed decode-forward are used to establish inner bounds on the capacity region for uplink and downlink communications, respectively. Through a careful analysis, the uplink inner bound is shown to achieve the cutset bound on the capacity region universally within O(log L) bits per user. The downlink inner bound achieves the cutset bound with a slightly looser gap of O(log(KL)). These tight per-user gap results are extended to the situations in which the nodes have multiple antennas.
pp. 2063-2067
12:30 On the Capacity of Cloud Radio Access Networks with Oblivious Relaying
Inaki Estella (Huawei Technologies Co., Ltd., France); Abdellatif Zaidi (Université Paris-Est Marne La Vallée, France); Giuseppe Caire (Technische Universität Berlin, Germany); Shlomo (Shitz) Shamai (The Technion, Israel)
We study the transmission over a network in which users send information to a remote destination through relay nodes that are connected to the destination via finite-capacity error-free links, i.e., a cloud radio access network. The relays are constrained to operate without knowledge of the users codebooks, i.e., they perform oblivious processing -- The destination, or central processor, however, is informed about the users' codebooks. We establish a single-letter characterization of the capacity region of this model for a class of discrete memoryless channels in which the outputs at the relay nodes are independent given the users' inputs. We show that both relaying à-la Cover-El Gamal, i.e., compress-and-forward with joint decompression and decoding, and noisy network coding'', are optimal. The proof of the converse part establishes, and utilizes, connections with the Chief Executive Officer (CEO) source coding problem under logarithmic loss distortion measure. Extensions to general discrete memoryless channels are also investigated. In this case, we establish inner and outer bounds on the capacity region. For memoryless Gaussian channels within the studied class of channels, we characterize the capacity under Gaussian channel inputs.
pp. 2068-2072

#### Th2-4: Channel Capacity 3

Room: K3
Chair: Muriel Médard (MIT, USA)
11:30 Intrinsic Capacity
Shengtian Yang (Zhejiang Gongshang University, P.R. China); Rui Xu, Jun Chen and Jian-Kang Zhang (McMaster University, Canada)
Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are in general not unique, each giving rise to a specific intrinsic-state distribution. In this paper we study the maximum and the minimum capacities of a channel when the realization of its intrinsic state is causally available at the encoder and/or the decoder. Several conclusive results are obtained for binary-input channels and binary-output channels. Byproducts of our investigation include a generalization of the Birkhoff-von Neumann theorem and a condition on the uselessness of causal state information at the encoder.
pp. 2073-2077
11:50 Gaussian Channels with Minimum Amplitude Constraints: When is Optimal Input Binary?
Zhengwei Ni and Mehul Motani (National University of Singapore, Singapore)
In this paper, we consider a scalar Gaussian Channel with minimum amplitude constraint, and investigate when the capacity-achieving input is binary. First, we study the case that the input satisfies both minimum and peak amplitude constraints and find that the optimal input is discrete. Then, for a given minimum amplitude, we find sufficient conditions that the peak amplitude constraint must satisfy such that the optimal input is binary and when it is not binary. Similarly, for a given peak amplitude, we find sufficient conditions that the minimum amplitude constraint must satisfy such that the optimal input is binary and when it is not binary. Finally, we find that when the input satisfies minimum amplitude and average power constraints, the optimal input is not binary, regardless of whether there is also a peak amplitude constraint.
pp. 2078-2082
12:10 On the Achievable Rate of Bandlimited Continuous-Time 1-Bit Quantized AWGN Channels
Sandra Bender and Meik Dörpinghaus (TU Dresden, Germany); Gerhard Fettweis (Technische Universität Dresden, Germany)
We consider a continuous-time bandlimited additive white Gaussian noise channel with 1-bit output quantization. On such a channel the information is carried by the temporal distances of the zero-crossings of the transmit signal. The set of input signals is constrained by the bandwidth of the channel and an average power constraint. Under a set of assumptions, we derive a lower bound on the capacity by lower-bounding the achievable rate for a given set of waveforms with exponentially distributed zero-crossing distances. We focus on the behaviour in the high signal-to-noise ratio regime and characterize the achievable rate depending on the available bandwidth and the signal-to-noise ratio.
pp. 2083-2087
12:30 Single-Bit Quantization of Binary-Input, Continuous-Output Channels
Brian Michael Kurkoski (Japan Advanced Institute of Science and Technology (JAIST), Japan); Hideki Yagi (University of Electro-Communications, Japan)
A binary-input, memoryless channel with a continuous-valued output quantized to one bit is considered. For arbitrary noise models, conditions on an optimal quantizer, in the sense of maximizing mutual information between the channel input and the quantizer output, are given. This result is obtained by considering the backward'' channel and applying Burshtein et al.'s theorem on optimal classification. In this backward channel, there exists an optimal quantizer for which the quantizer preimage is convex. It is possible no optimal forward quantizer is convex, but by working with the backward channel, this optimal quantizer may be found.
pp. 2088-2092

#### Th2-5: Estimation 1

Room: K4
Chair: H. Vincent Poor (Princeton University, USA)
11:30 Lower Bounds on Parameter Modulation-Estimation Under Bandwidth Constraints
Nir Weinberger and Neri Merhav (Technion, Israel)
The problem of modulating the value of a parameter onto a band-limited signal to be transmitted over a continuous-time, additive white Gaussian noise (AWGN) channel, and estimating this parameter at the receiver, is considered. The performance is measured by the mean power-$\alpha$ error (MP$\alpha$E), which is defined as the worst-case $\alpha$th order moment of the absolute estimation error. The optimal exponential decay rate of the MP$\alpha$E as a function of the transmission time, is investigated. Two upper (converse) bounds on the MP$\alpha$E exponent are derived, on the basis of known bounds for the AWGN channel of inputs with unlimited bandwidth. The bounds are computed for typical values of the error moment and the signal-to-noise ratio (SNR), and the SNR asymptotics of the different bounds are analyzed. The new bounds are compared to known converse and achievability bounds, which were derived from channel coding considerations.
pp. 2093-2097
11:50 Multi-Layer Generalized Linear Estimation
Andre Manoel (Neurospin, CEA, Université Paris-Saclay, France); Florent Krzakala (Ecole Normale Superieure, France); Marc Mézard (École Normale Supérieure, France); Lenka Zdeborova (Institut de Physique Theorique IPhT, CEA Saclay and CNRS, France)
We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using standard but non-rigorous methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP) algorithm for computing marginal probabilities of the corresponding estimation problem and derive the associated state evolution equations to analyze its performance. We also give the expression of the asymptotic free energy and the minimal information-theoretically achievable reconstruction error. Finally, we present some applications of this measurement model for compressed sensing and perceptron learning with structured matrices/patterns, and for a simple model of estimation of latent variables in an auto-encoder.
pp. 2098-2102
12:10 Minimax Optimal Estimators for Additive Scalar Functionals of Discrete Distributions
Kazuto Fukuchi (University of Tsukuba & Graduate School of Systems and Information Engineering, Japan); Jun Sakuma (University of Tsukuba, Japan)
In this paper, we consider estimators for an {\em additive functional} of $\phi$, which is defined as $\theta(P;\phi)=\sum_{i=1}^k\phi(p_i)$, from $n$ i.i.d. random samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size $k$. We propose a minimax optimal estimator for the estimation problem of the additive functional. We reveal that the minimax optimal rate is characterized by the divergence speed of the fourth derivative of $\phi$ if the divergence speed is high. As a result, we show there is no consistent estimator if the divergence speed of the fourth derivative of $\phi$ is larger than $p^{-4}$. Furthermore, if the divergence speed of the fourth derivative of $\phi$ is $p^{4-\alpha}$ for $\alpha \in (0,1)$, the minimax optimal rate is obtained within a universal multiplicative constant as $\frac{k^2}{(n\ln n)^{2\alpha}} + \frac{k^{2-2\alpha}}{n}$.
pp. 2103-2107
12:30 I-MMSE relations in random linear estimation and a sub-extensive interpolation method
Jean Barbier and Nicolas Macris (EPFL, Switzerland)
Consider random linear estimation with Gaussian measurement matrices and noise. One can compute infinitesimal variations of the mutual information under infinitesimal variations of the signal-to-noise ratio or of the measurement rate. We discuss how each variation is related to the minimum mean-square error and deduce that the two variations are directly connected through a very simple identity. The main technical ingredient is a new interpolation method called "sub-extensive interpolation method". We use it to provide a new proof of an I-MMSE relation recently found by Reeves and Pfister [1] when the measurement rate is varied. Our proof makes it clear that this relation is intimately related to another I-MMSE relation also recently proved in [2]. One can directly verify that the identity relating the two types of variation of mutual information is indeed consistent with the one letter replica symmetric formula for the mutual information, first derived by Tanaka [3] for binary signals, and recently proved in more generality in [1,2,4,5] (by independent methods). However our proof is independent of any knowledge of Tanaka's formula.
pp. 2108-2112

#### Th2-6: MIMO 3

Room: K5
Chair: Hamid Jafarkhani (University of California, Irvine, USA)
11:30 Multi-Antenna Coded Caching
Seyed Pooya Shariatpanahi (Institute for Research in Fundamental Sciences (IPM), Iran); Giuseppe Caire (Technische Universität Berlin, Germany); Babak Hossein Khalaj (Sharif University of Technology, Iran)
In this paper we consider a single-cell downlink scenario where a multiple-antenna base station delivers contents to multiple cache-enabled user terminals. Based on the multicasting opportunities provided by the so-called Coded Caching technique, we investigate three delivery approaches. Our baseline scheme employs the coded caching technique on top of max-min fair multicasting. The second one consists of a joint design of Zero-Forcing (ZF) and coded caching, where the coded chunks are formed in the signal domain (complex field). The third scheme is similar to the second one with the difference that the coded chunks are formed in the data domain (finite field). We derive closed-form rate expressions where our results suggest that the latter two schemes surpass the first one in terms of Degrees of Freedom (DoF). However, at the intermediate SNR regime forming coded chunks in the signal domain results in power loss, and will deteriorate throughput of the second scheme. The main message of our paper is that the schemes performing well in terms of DoF may not be directly appropriate for intermediate SNR regimes, and modified schemes should be employed.
pp. 2113-2117
11:50 Optimally-Tuned Nonparametric Linear Equalization for Massive MU-MIMO Systems
Ramina Ghods, Charles Jeon and Gulnar Mirza (Cornell University, USA); Arian Maleki (Columbia University, USA); Christoph Studer (Cornell University, USA)
This paper deals with linear equalization in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. We first provide simple conditions on the antenna configuration for which the well-known linear minimum mean-square error (L-MMSE) equalizer provides near-optimal spectral efficiency, and we analyze its performance in the presence of parameter mismatches in the signal and/or noise powers. We then propose a novel, optimally-tuned NOnParametric Equalizer (NOPE) for massive MU-MIMO systems, which avoids knowledge of the transmit signal and noise powers altogether. We show that NOPE achieves the same performance as that of the L-MMSE equalizer in the large-antenna limit, and we demonstrate its efficacy in realistic, finite-dimensional systems. From a practical perspective, NOPE is computationally efficient and avoids dedicated training that is typically required for parameter estimation.
pp. 2118-2122
12:10 Rate Bounds on $4$-group fast decodable space-time code
Bharath A Sethuraman (California State University, Northridge, USA)
It is known that the maximum number of groups into which space-time codes from division algebras can be partitioned so that the resulting vectorized representations, for any channel matrix, break off into pairwise orthogonal subsets, is four. Such partitions are key to fast decodability of codes. In this paper we study the rate of such $4$-group fast decodable codes, and show that if the codes arise from $n\times n$ matrices, then the maximum data rate, measured in number of real symbols per transmitted matrix, is $2n$. We give examples of codes that meet this bound.
pp. 2123-2127

#### Th2-7: Security 5

Room: K6
Chair: Sidharth Jaggi (Chinese University of Hong Kong, Hong Kong)
11:30 Games on Linear Deterministic Channels with Eavesdroppers
Ruijie Xu, Hao Ge and Randall A Berry (Northwestern University, USA)
We consider adding secrecy constraints to a model of information theoretic games introduced in earlier works. In these games, each user autonomously selects their encoding and decoding strategy with the objective of maximizing their own secure rate in the presence of a single eavesdropper. We study the Nash equilibrium regions for such games when the users are communicating over linear deterministic models of a multiple access channel and an interference channel. In particular, we show that for interference channels, the presence of an eavesdropper results in significantly different equilibrium properties than when an eavesdropper is not present.
pp. 2128-2132
11:50 A New Broadcast Wiretap Channel Model
Mohamed Nafea (The Pennsylvania State University, USA); Aylin Yener (Pennsylvania State University, USA)
A new broadcast wiretap channel (B-WTC) with a wiretapper who noiselessly taps into a fixed-length subset of the transmitted symbols of her choice, and observes the remainder through a noisy channel, is studied. An achievable strong secrecy rate region which extends Marton's inner bound to the proposed setting, is derived. Strong secrecy capacity regions for two classes of the new B-WTC, namely the new B-WTC with deterministic receivers, and the new B-WTC with degraded receivers and more noisy wiretapper, are identified. These results extend the recently proposed new wiretap channel model to the broadcast setting.
pp. 2133-2137
12:10 Secrecy-Reliability Tradeoff for Semi-Deterministic Wiretap Channels at Finite Blocklength
Wei Yang (Princeton University, USA); Rafael F. Schaefer (Technische Universität Berlin, Germany); H. Vincent Poor (Princeton University, USA)
This paper studies the maximum secrecy rate for a semi-deterministic wiretap channel, in which the channel between the transmitter and legitimate receiver is deterministic, while that between the transmitter and the eavesdropper is a discrete memoryless channel. For a given decoding error probability and information leakage (measured by the variational distance), the optimal second-order secrecy rate is derived. Unlike the secrecy capacity, the second-order secrecy rate characterizes the optimal tradeoff between secrecy and reliability at finite blocklength.
pp. 2138-2142
12:30 On Secure Asymmetric Multilevel Diversity Coding Systems
Congduan Li (City University of Hong Kong, Hong Kong); Xuan Guang (The Chinese University of Hong Kong, P.R. China); Chee Wei Tan (City University of Hong Kong, Hong Kong); Raymond W. Yeung (The Chinese University of Hong Kong, Hong Kong)
Whether superposition (source separation) is optimal for the asymmetric multilevel diversity coding systems (AMDCS) with perfect secrecy is answered in this paper by studying a non-trivial example. Threshold perfect secrecy is added to the AMDCS model. The eavesdropper may have access to any one but not more than one subset of the channels but can get nothing about the sources, as long as the size of the subset is not above the security level. The secure AMDCS (S-AMDCS) with five sources, four encoders and security level two is solved and it is shown that linear codes are optimal for this instance. However, in contrast with the secure symmetric multilevel diversity coding systems (S-SMDCS), superposition is shown to be not optimal for S-AMDCS in general from this counterexample.
pp. 2143-2147

#### Th2-8: Compressed Sensing 3

Room: K7+8
Chair: Tareq Y. Al-Naffouri (King Abdullah University of Science and Technology, USA)
11:30 Dynamical Functional Theory for Compressed Sensing
Burak Çakmak (Aalborg University, Denmark); Manfred Opper (KI / TU Berlin, Germany); Ole Winther (Technical University of Denmark, Denmark); Bernard Henri Fleury (Aalborg University, Denmark)
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix ensemble. By construction, the fixed points of the algorithm obey the Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way that the resulting fields become Gaussian random variables allowing for an explicit analysis. The asymptotic statistics of these fields are consistent with those obtained for the replica ansatz of the compressed sensing problem.
pp. 2148-2152
11:50 Compressed Sensing under Optimal Quantization
Alon Kipnis (Stanford University, USA); Galen Reeves (Duke University, USA); Yonina C. Eldar (Technion-Israel Institute of Technology, Israel); Andrea Goldsmith (Stanford University, USA)
We consider the problem of recovering a sparse vector from a quantized or a lossy compressed version of its noisy random linear projections. We characterize the minimal distortion in this recovery as a function of the sampling ratio, the sparsity rate, the noise intensity and the total number of bits in the quantized representation. We first derive a singe-letter expression that can be seen as the indirect distortion-rate function of the sparse source observed through a Gaussian channel whose signal-to-noise ratio is derived from these parameters. Under the replica symmetry postulation, we prove that there exists a quantization scheme that attains this expression in the asymptotic regime of large system dimensions. In addition, we prove a converse demonstrating that the MMSE in estimating any fixed sub-block of the source from the quantized measurements at a fixed number of bits does not exceed this expression as the system dimensions go to infinity. Thus, under these conditions, the expression we derive describes the excess distortion incurred in encoding the source vector from its noisy random linear projections in lieu of the full source information.
pp. 2153-2157
12:10 Noisy Tensor Completion for Tensors with a Sparse Canonical Polyadic Factor
Swayambhoo Jain, Alexander Gutierrez and Jarvis D. Haupt (University of Minnesota, USA)
In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDECOMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and then instantiate these bounds for the case of additive white Gaussian noise. We also provide an ADMM-type algorithm for solving the complexity-regularized maximum likelihood problem and validate the theoretical finding via experiments on synthetic data set.
pp. 2158-2162
12:30 Compressed Sensing of Compressible Signals
Sajjad Beygi (University of Southern California, USA); Shirin Jalali (Bell Labs, USA); Arian Maleki (Columbia University, USA); Urbashi Mitra (University of Southern California, USA)
A novel low-complexity robust-to-noise iterative algorithm named compression-based gradient descent (C-GD) algorithm is proposed. C-GD is a generic compressed sensing recovery algorithm, that at its core, employs compression codes, such as JPEG2000 and MPEG4. Through using compression codes, C-GD strongly generalizes the scope of structures used by compressed sensing recovery algorithms beyond sparsity or low-rankness. The squared error of the proposed method and its associated convergence is characterized and predicts the strong performance of C-GD. Numerical results suggest that C-GD, when combined with state-of-the-art compression codes, either outperforms or performs comparably to modern compressed sensing recovery methods.
pp. 2163-2167

#### Th2-9: Statistics 1

Room: K9
Chair: Andrew R Barron (Yale University, USA)
11:30 Budget-Optimal Clustering via Crowdsourcing
Ravi Kiran Raman and Lav R. Varshney (University of Illinois at Urbana-Champaign, USA)
This paper defines and studies the problem of universal clustering using responses of crowd workers, without knowledge of worker reliability or task difficulty. We model stochastic worker response distributions by incorporating traits of memory for similar objects and traits of distance among differing objects. We are particularly interested in two limiting worker types—temporary and long-term workers, without and with memory respectively. We first define clustering algorithms for these limiting cases and then integrate them into an algorithm for the unified worker model. We prove asymptotic consistency of the algorithms and establish sufficient conditions on the sample complexity of the algorithm. Converse arguments establish necessary conditions on sample complexity, proving that the defined algorithms are asymptotically order-optimal in cost.
pp. 2168-2172
11:50 Universal Joint Image Clustering and Registration using Partition Information
Ravi Kiran Raman and Lav R. Varshney (University of Illinois at Urbana-Champaign, USA)
The problem of joint clustering and registration of images is studied in a universal setting. We define universal joint clustering and registration algorithms using multivariate information functionals. We first study the problem of registering two images using maximum mutual information and prove its asymptotic optimality. We then show the shortcomings of pairwise registration in multi-image registration, and design an asymptotically optimal algorithm based on multiinformation. Finally, we define a novel multivariate information functional to perform joint clustering and registration of images, and prove consistency of the algorithm.
pp. 2173-2177
12:10 How to Find a Joint Probability Distribution of Minimum Entropy (almost) given the Marginals
Ferdinando Cicalese (University of Verona, Italy); Luisa Gargano (University of Salerno, Italy); Ugo Vaccaro (University of Salerno, USA)
Given two discrete random variables $X$ and $Y$, with probability distributions $p=(p_1,..., p_n)$ and $q=(q_1,..., q_m)$, respectively, denote by $C(p,q)$ the set of all joint distributions of $X$ and $Y$ (couplings) of $p$ and $q$, that is, the set of all bivariate probability distributions that have $p$ and $q$ as marginals. In this paper, we study the problem of finding the joint probability distribution in $C(p,q)$ of minimum entropy (equivalently, the joint probability distribution that maximizes the mutual information between $X$ and $Y$), and we discuss several situations where the need for this kind of optimization naturally arises. Since the optimization problem is known to be NP-hard, we give an efficient algorithm to find a joint probability distribution in $C(p,q)$ with entropy exceeding the minimum possible by at most 1, thus providing an approximation algorithm with additive approximation factor of 1. We also discuss some related consequences of our findings.
pp. 2178-2182
12:30 On the Fundamental Statistical Limit of Community Detection in Random Hypergraphs
Chung-Yi Lin, I Chien and I-Hsiang Wang (National Taiwan University, Taiwan)
The problem of community detection in random hyper graphs is considered. We extend the Stochastic Block Model (SBM) from graphs to hypergraphs with d-uniform hyperedges, which we term "d-wise hyper stochastic block model" (d-hSBM), and consider a homogeneous and approximately equal-sized K community case. For d=3, we fully characterize the exponentially decaying rate of the minimax risk in recovering the underlying communities, where the loss function is the mis-match ratio between the true community assignment and the recovered one. It turns out that the rate function is a weighted combination of several divergence terms, each of which is the Renyi divergence of order 1/2 between two Bernoulli distributions. The Bernoulli distributions involved in the characterization of the rate function are those governing the random instantiation of hyperedges in d-hSBM. The lower bound is set by finding a smaller parameter space where we can analyze the risk, while the upper bound is achieved with the Maximum Likelihood estimator. The technical contribution is to show that upper bound has the same decaying rate as the lower bound, which involves careful bounding of the various probabilities of errors. Finally, we relate the minimax risk to the recovery criterion under the Bayesian framework and derive a threshold condition for exact recovery.
pp. 2183-2187

Room: K1

Room: Brussels

### Thursday, June 29, 14:40 - 16:20

#### Th3-1: Coding Theory 3

Room: Amsterdam
Chair: Antonia Wachter-Zeh (Technical University of Munich (TUM), Germany)
14:40 Multiset combinatorial batch codes
Hui Zhang (Technion - Israel Institute of Technology, Israel); Eitan Yaakobi (Technion, Israel); Natalia Silberstein (Yahoo! Labs, Israel)
Batch codes, first introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai, mimic a distributed storage of a set of $n$ data items on $m$ servers, in such a way that any batch of $k$ data items can be retrieved by reading at most some $t$ symbols from each server. Combinatorial batch codes, are replication-based batch codes in which each server stores a subset of the data items. In this paper, we propose a generalization of combinatorial batch codes, called multiset combinatorial batch codes (MCBC), in which $n$ data items are stored in $m$ servers, such that any multiset request of $k$ items, where any item is requested at most $r$ times, can be retrieved by reading at most $t$ items from each server. The setup of this new family of codes is motivated by recent work on codes which enable high availability and parallel reads in distributed storage systems. The main problem under this paradigm is to minimize the number of items stored in the servers, given the values of $n,m,k,r,t$, which is denoted by $N(n,k,m,t;r)$. We first give a necessary and sufficient condition for the existence of MCBCs. Then, we present several bounds on $N(n,k,m,t;r)$ and constructions of MCBCs. In particular, we determine the value of $N(n,k,m,1;r)$ for any $n\geq \left\lfloor\frac{k-1}{r}\right\rfloor{m\choose k-1}-(m-k+1)A(m,4,k-2)$, where $A(m,4,k-2)$ is the maximum size of a binary constant weight code of length $m$, distance four and weight $k-2$. We also determine the exact value of $N(n,k,m,1;r)$ when $r\in\{k,k-1\}$ or $k=m$.
pp. 2188-2192
15:00 Structured Spherical Codes With Asymptotically Optimal Distance Distributions
Robert M. Taylor, Jr. and Lamine Mili (Virginia Tech, USA); Amir I Zaghloul (US Army Research Laboratory & Virginia Tech, USA)
We introduce a new geometric construction of cyclic group codes in odd-dimensional spaces formed by intersecting even-dimensional constant curvature curves with hyperplanes of one less dimension. This allows us to recast the cyclic group code as a uniform sampling of a constant curvature curve whereby the design of the constant curvature curve controls code performance. Using a tool from knot theory known as the circumradius function, we derive properties of cyclic group codes from properties of the constant curvature curve passing through every point of the spherical code. By relating the distribution of the squared circumradius function of the connecting curve to the distribution of the pairwise distances of the cyclic group code, we show that the distance spectrum of cyclic group codes achieves optimality in the sense of matching the random spherical code distance distribution bound as the block length grows large.
pp. 2193-2197
15:20 Weight Spectrum of Quasi-Perfect Binary Codes with Distance 4
Valentin Afanassiev (Intitute Problems of Information Transmission, Russia); Alexander Davydov (Institute for Information Transmission Problem, Russia)
We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. For example, extended Hamming code and Panchenko code are the known members of this class. Also, it is known that in many cases Panchenko code has the minimal number of weight 4 codewords. We give exact recursive formulas for the weight spectrum of quasi-perfect codes and their dual codes. As an example of application of the weight spectrum we derive a lower estimate for the conditional probability of correction of erasure patterns of high weights (equal to or greater than code distance).
pp. 2198-2202
15:40 Kronecker Product and Tiling of Permutation Arrays for Hamming Distances
Sergey Bereg, Luis Gerardo Mojica de la Vega, Linda Morales and I. Hal Sudborough (University of Texas at Dallas, USA)
We give improved lower bounds for M(n,d), for various positive integers d and n with d<n, where M(n,d) is the largest number of permutations on n symbols with pairwise Hamming distance at least d. Permutation arrays are used for constructing error correcting permutation codes, which have been proposed for power-line communications. We describe two techniques, which use Kronecker products and a "tiling" operation. Our techniques improve the size of permutation arrays, and improve lower bounds on M(n,d), for infinitely many n and d, d<n.
pp. 2203-2207
16:00 Performance of Spinal Codes with Sliding Window Decoding
Weiqiang Yang (Xidian University, P.R. China); Ying Li (University of Xidian, P.R. China); Xiaopu Yu (Xidian University, P.R. China)
In this paper, we focus on the finite-length performance of spinal codes with a sliding window decoder over binary erasure channel. An expression of the error probability of spinal codes is derived. Particularly, we also derive an expression of the error probability of spinal codes with some known tail bits, which can improve the error-control performance. Moreover, easier-to-compute upper and lower bounds on the error probability are also provided. Simulation results show that the error-control performance can be improved by introducing known tail bits and the performance becomes better with the increase of the maximum window length. Finally, the derived bounds can well evaluate the error performance of spinal codes.
pp. 2208-2212

#### Th3-2: Coding for Distributed Storage 2

Room: Brussels
Chair: Joerg Kliewer (New Jersey Institute of Technology, USA)
14:40 Secure Regenerating Codes for Hybrid Cloud Storage Systems
Islam Samy and Gokhan Calis (University of Arizona, USA); O. Ozan Koyluoglu (University of California, Berkeley, USA)
We study the scenario of hybrid cloud storage where the client utilizes both an off-site and a local storage. The former is a distributed storage system (DSS) with the presence of an eavesdropper that has access to the content stored in and downloaded to some subset of nodes. The latter (local) storage is utilized to store a secret key to secure the stored file against the eavesdropper. We introduce two possibilities to utilize local storage (secret key) in enhancing the DSS. First, the key can be used to increase the maximum file size stored in the DSS. We propose an upper bound for this scenario and show constructions achieving it. Second, the key can be used to decrease the number of contacted nodes required to reconstruct the file at the client. We extend the product matrix (PM) framework and construct codes that enables efficient data access. Our analysis includes both minimum repair bandwidth regenerating (MBR) and minimum storage regenerating (MSR) codes.
pp. 2213-2217
15:00 Centralized Multi-Node Repair for Minimum Storage Regenerating Codes
Marwen Zorgui (University of California, Irvine, USA); Zhiying Wang (UC Irvine, USA)
In distributed storage, erasure codes are widely used to provide data reliability, where every codeword symbol corresponds to one storage node. The network traffic cost during the repair of node failures, called repair bandwidth, is an important metric in code design. In particular, minimum storage regenerating (MSR) codes are maximum distance separable (MDS) codes that have optimal repair bandwidth. In this paper, we generalize the problem to minimum storage multi-node regenerating (MSMR) codes, which are MDS codes with optimal repair bandwidth for $e$ node failures. We describe a general framework for converting MSR codes to MSMR codes. The repair strategy for $e$ failures is similar to that for single failure, however certain extra requirements need to be satisfied by the repairing functions for single failure. Then we apply this framework to product-matrix codes and interference alignment codes.
pp. 2218-2222
15:20 GDSP: A Graphical Perspective on the Distributed Storage Systems
Saeid Sahraei (EPFL, Switzerland); Michael Gastpar (EPFL & University of California, Berkeley, Switzerland)
The classical distributed storage problem can be modeled by a k-uniform {\it complete} hyper-graph where vertices represent servers and hyper-edges represent users. Hence each hyper-edge should be able to recover the full file using only the memories of the vertices associated with it. This paper considers the generalization of this problem to {\it arbitrary} hyper-graphs and to the case of multiple files, where each user is only interested in one, a problem we will refer to as the graphical distributed storage problem (GDSP). Specifically, we make progress in the analysis of minimum-storage codes for two main subproblems of the GDSP which extend the classical model in two independent directions: the case of an arbitrary graph with multiple files, and the case of an arbitrary hyper-graph with a single file.
pp. 2223-2227
15:40 Distributed Storage Allocation for Multi-Class Data
Koosha Pourtahmasi Roshandeh, Moslem Noori, Masoud Ardakani and Chintha Tellambura (University of Alberta, Canada)
Distributed storage systems (DSSs) provide a scalable solution for reliably storing massive amounts of data coming from various sources. Heterogeneity of these data sources often means different data classes (types) exist in a DSS, each needing a different level of quality of service (QoS). As a result, efficient data storage and retrieval processes that satisfy various QoS requirements are needed. This paper studies storage allocation, meaning how the data of different classes is spread over storage nodes, for a multi-class DSS. More specifically, assuming a probabilistic access to the storage nodes, we aim at maximizing the weighted sum of the probability of successful data recovery of data classes. Solving this optimization problem for a general setup is intractable. Thus, we find the optimal storage allocation when the data of each class is spread minimally over the nodes, i.e. minimal spreading allocation (MSA). Then, by comparing the performance of the optimal MSA with the performance upper bound, we show that the optimal MSA is indeed the optimal storage allocation in many practical cases. Numerical examples are also presented for better illustration of the results.
pp. 2228-2232

#### Th3-3: Relaying

Room: K2
Chair: Roy Yates (Rutgers University, USA)
14:40 The Capacity-distortion Function for Multihop Channels with State
Amir Salimi (University of Southern California); Wenyi Zhang (University of Science and Technology of China, P.R. China); Satish Vedantam and Urbashi Mitra (University of Southern California, USA)
We consider a joint communication and channel estimation problem over a multi-hop relay network with discrete-memoryless channel states. The state information on each link is not available either for the senders or the receivers. Each receiver in the network needs to construct an estimation of channel states with certain fidelity constraint, as well as helping the destination to decode the message reliably. First, we study a two-hop network where channel states on each hop are independent. We then show that a decode-and-Forward strategy, in conjunction with a compress-and-forward strategy achieves the entire capacity-distortion region. We also prove an achievable rate when the channel states are correlated. We extend the result to a multi-hop network, where each node is intended to reconstruct channel state information from $L$ previous links.
pp. 2233-2237
15:00 The Geometry of the Relay Channel
Xiugang Wu, Leighton Barnes and Ayfer Özgür (Stanford University, USA)
Consider a memoryless relay channel, where the channel from the relay to the destination is an isolated bit pipe of capacity $C_0$. Let $C(C_0)$ denote the capacity of this channel as a function of $C_0$. What is the critical value of $C_0$ such that $C(C_0)$ first equals $C(\infty)$? This is a long-standing open problem posed by Cover and named The Capacity of the Relay Channel,'' in Open Problems in Communication and Computation, Springer-Verlag, 1987. In our recent work, we answered this question in the case when the channels from the source to the relay and destination are symmetric, which is the original assumption imposed by Cover, and when these channels are Gaussian. We showed that $C(C_0)$ can not equal to $C(\infty)$ unless $C_0=\infty$, regardless of the SNR of the Gaussian channels, while the cut-set bound would suggest that $C(\infty)$ can be achieved at finite $C_0$. In this paper, we show that our techniques for solving Cover's problem can be naturally extended to the general Gaussian case, where the channels from the source to the relay and destination may be asymmetric, and prove an upper bound on the capacity $C(C_0)$ of a general Gaussian relay channel for any $C_0$. This upper bound immediately implies that our previous conclusion, i.e. $C(C_0)$ can not equal to $C(\infty)$ unless $C_0=\infty$, also holds in the asymmetric case. Our approach is geometric and relies on a strengthening of the isoperimetric inequality on the sphere by using the Riesz rearrangement inequality.
pp. 2238-2242
15:20 The CF-DF Approach for Relay Networks Based on Multiple Descriptions with the Shared Binning
Leila Ghabeli (Department of Electrical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran)
Decode-and-forward (DF) and compress-and-forward (CF) are well-known strategies to transmit information over the relay channel. There are several methods which generalize these strategies to relay networks, among them, the unified CF-DF strategy is one with relatively good performance and less complexity. In this method the nodes are divided into two groups: DF relay nodes and CF relay nodes, where the DF relay nodes fully utilize the help of the CF relay nodes. Here we present a modified CF-DF approach in which the CF relay nodes form multiple description coding. This method let different DF relay nodes and the destination receive the relay observation at different quality levels. In comparison with similar approaches, here the key point is that we use the shared binning for all descriptions at a CF relay node. This strategy reduces the complexity of the obtained achievable rate and yielding the better performance at the same time. Simulation results for Gaussian relay networks show that our proposed achievable rate includes the previously proposed ones.
pp. 2243-2247

#### Th3-4: Guessing

Room: K3
Chair: Neri Merhav (Technion, Israel)
14:40 Making Recommendations Bandwidth Aware
Linqi Song (University of California, Los Angeles, USA); Christina Fragouli (UCLA, USA)
This paper asks how much we can gain in terms of bandwidth and user satisfaction, if recommender systems became bandwidth aware and took into account not only the user preferences, but also the fact that they may need to serve these users under bandwidth constraints, as is the case over wireless networks. We formulate this as a new problem in the context of index coding: we relax the index coding requirements to capture scenaria where each client has preferences associated with messages. The client is satisfied to receive any message she does not already have, with a satisfaction proportional to her preference for that message. We consistently find, over a number of scenaria we sample, that although the optimization problems are in general NP-hard, significant bandwidth savings are possible even when restricted to polynomial time algorithms.
pp. 2248-2252
15:00 The Effect of Bias on the Guesswork of Hash Functions
Yair Yona and Suhas Diggavi (University of California Los Angeles, USA)
In this work we analyze the average guesswork for the problem of hashed passwords cracking (i.e., finding a password that has the same hash value as the actual password). We focus on the following two cases: Averaging over all strategies of guessing passwords one by one for any hash function that has effective distribution (i.e., the fraction of mappings to any bin) which is i.i.d. Bernoulli$(p)$, and averaging over all hash functions whose effective distribution is i.i.d. Bernoulli$(p)$ for any strategy of guessing passwords one by one. We analyze the average guesswork under both online and offline attacks by deriving upper and lower bounds on the average guesswork as a function of the bins to which passwords are mapped, along with the most likely average guesswork, that is, the average guesswork of the most likely set of bins. Furthermore, we provide a concentration result that shows that the probability mass function of the guesswork is concentrated around its mean value. These results give quantifiable bounds for the effect of bias as well as the number of users on the average guesswork of a hash function, and show that increasing the number of users has a far worse effect than bias in terms of the average guesswork.
pp. 2253-2257
15:20 Guessing With Limited Memory
Wasim Huleihel (MIT, USA); Salman Salamatian (Massachusetts Institute of Technology, USA); Muriel Médard (MIT, USA)
Suppose that we wish to guess the realization $x$ of a discrete random variable $X$ taking values in a finite set, by asking sequential questions of the form Is $X$ equal to $x$?", exhausting the elements of $X$ until the answer is Yes" [1,2]. If the distribution of $X$ is known to the guesser, and the guesser has memory of his previous queries then the best strategy is to guess in decreasing order of probabilities. In this paper, we consider the problem of a memoryless guesser, namely, each new guess is independent of the previous guesses. We consider also the scenario of a guesser with a bounded number of guesses. For both cases we derive the optimal guessing strategies, and show new connections to R\'enyi entropy.
pp. 2258-2262
15:40 Centralized vs Decentralized Multi-Agent Guesswork
Salman Salamatian (Massachusetts Institute of Technology, USA); Ahmad Beirami (MIT, USA); Asaf Cohen (Ben-Gurion University of the Negev, Israel); Muriel Médard (MIT, USA)
We study a notion of guesswork, where multiple agents intend to launch a coordinated brute-force attack to find a single binary secret string, and each agent has access to side information generated through either a BEC or a BSC. The average number of trials required to find the secret string grows exponentially with the length of the string, and the rate of the growth is called the guesswork exponent. We compute the guesswork exponent for several multi-agent attacks, and show that a multi-agent attack reduces the guesswork exponent compared to a single agent, even when the agents do not exchange information to coordinate their attack, and try to individually guess the secret string using a predetermined scheme in a decentralized fashion. Further, we show that the guesswork exponent of two agents who do coordinate their attack is strictly smaller than that of any finite number of agents individually performing decentralized guesswork.
pp. 2263-2267

#### Th3-5: Detection and Estimation 3

Room: K4
Chair: Alfred Hero III (University of Michigan, USA)
14:40 Asymptotic Optimality of D-CuSum for Quickest Change Detection under Transient Dynamics
Shaofeng Zou (University of Illinois at Urbana Champaign, USA); Georgios Fellouris and Venugopal Veeravalli (University of Illinois at Urbana-Champaign, USA)
The problem of quickest change detection (QCD) under transient dynamics is studied, in which the change from the initial distribution to the final persistent distribution does not happen instantaneously, but after a series of cascading transient phases. It is assumed that the durations of the transient phases are deterministic but unknown. The goal is to detect the change as quickly as possible subject to a constraint on the average run length to false alarm. The dynamic CuSum (D-CuSum) algorithm is investigated, which is based on reformulating the QCD problem into a dynamic composite hypothesis testing problem, and has a recursion that facilitates implementation. We show that this algorithm is adaptive to the unknown change point, as well as the unknown transient duration. And under mild conditions of the pre-change and post-change distributions, its asymptotic optimality is demonstrated for all possible asymptotic regimes as the transient duration and the average run length to false alarm go to infinity.
pp. 2268-2272
15:00 Sketched Covariance Testing: A Compression-Statistics Tradeoff
Gautam Dasarathy (Rice University, USA); Parikshit Shah (Yahoo Research, USA); Richard Baraniuk (Rice University, USA)
Hypothesis testing of covariance matrices is an important problem in multivariate analysis. Given n data samples and a covariance matrix Σ0, the goal is to determine whether or not the data is consistent with this matrix. In this paper we introduce a framework that we call Sketched Covariance Testing, where the data is provided after being compressed by multiplying by a "sketching" matrix A. We propose a statistical test in this setting and quantify an achievable sample complexity as a function of the amount of compression. Our result reveals an intriguing tradeoff between the compression ratio and the statistical information required for reliable hypothesis testing; the sample complexity increases as the fourth power of amount of compression.
pp. 2273-2277
15:20 Error bounds for Bregman Denoising and Structured Natural Parameter Estimation
Amin Jalali (Wisconsin Institute for Discovery, USA); James Saunderson (University of Washington, USA); Maryam Fazel (Univiversity of Washington, USA); Babak Hassibi (California Institute of Technology, USA)
We analyze an estimator based on the Bregman divergence for recovery of structured models from additive noise. The estimator can be seen as a regularized maximum likelihood estimator for an exponential family where the natural parameter is assumed to be structured. For all such Bregman denoising estimators, we provide an error bound for a natural associated error measure. Our error bound makes it possible to analyze a wide range of estimators, such as those in proximal denoising and inverse covariance matrix estimation, in a unified manner. In the case of proximal denoising, we exactly recover the existing tight normalized mean squared error bounds. In sparse precision matrix estimation, our bounds provide optimal scaling with interpretable constants in terms of the associated error measure. Lastly, we give a numerical example for the multivariate Gaussian distribution to showcase the Bregman denoiser and the bound.
pp. 2278-2282
15:40 On Random Sampling with Nodes Attraction: The Case of Gauss-Poisson Process
Flavio Zabini and Gianni Pasolini (University of Bologna, Italy); Andrea Conti (ENDIF University of Ferrara, WiLAB University of Bologna, Italy)
The deployment of sensing nodes is crucial for appli- cations relying on the reconstruction of spatial fields. Theoretical analysis usually assumes that nodes are distributed according to a homogeneous Poisson point process (PPP), in which nodes positions are stochastically independent. However, realistic scenarios for crowd sourcing and Internet of Things call for clustered layouts of sensing nodes, for which homogeneous PPP is not appropriate. This paper analyzes sampling and reconstruction of finite-energy signals in Rd, with samples gathered in space according to a Gauss-Poisson point process (G-PPP), which has been recently proposed to model node spatial distribution with attraction (as in clustering). In particular, it is shown that attraction between nodes modeled by G-PPP reduces the reconstruction accuracy with respect the case of homogeneous PPP with the same intensity. This represents the opposite case of the repulsion effect, which was investigated in a previous work relying on Ginibre point process sampling.
pp. 2283-2287
16:00 Low-rank, Sparse and Line Constrained Estimation: Applications to Target Tracking and Convergence
Amr Elnakeeb and Urbashi Mitra (University of Southern California, USA)
In this paper, the incorporation of a line constraint is considered for structured estimation. In particular, multiple forms of structure on matrices are extended from low-rank and sparsity. The line constraint is introduced via a rotation that yields a secondary low rank condition. The proposed method is applied to single object tracking in video wherein the trajectory can be parameterized as a line. The optimization is solved via the Augmented Lagrange Multiplier method. Measurable performance improvement is observed over previous background subtraction methods that do not exploit the line structure. An aggregated error is proven to converge to zero and a boundedness analysis is conducted which suggests that the iterative algorithm is convergent.
pp. 2288-2292

#### Th3-6: Multiple Access Feedback

Room: K5
Chair: Lalitha Sankar (Arizona State University, USA)
14:40 Two-User Downlink Non-Orthogonal Multiple Access with Limited Feedback
Xiaoyi Liu and Hamid Jafarkhani (University of California, Irvine, USA)
In this paper, we analyze downlink non-orthogonal multiple access (NOMA) networks with limited feedback. Our goal is to derive appropriate transmission rates for rate adaptation and minimize outage probability of minimum rate for the constant-rate data service, based on distributed channel feedback information from two receivers. We propose an efficient quantizer with variable-length encoding that approaches the best performance of the case where perfect channel state information is available everywhere. We prove that in the typical application with two receivers, the losses in the minimum rate and outage probability decay at least exponentially with the minimum feedback rate. Furthermore, we analyze the diversity gain and provide a sufficient condition for the quantizer to achieve the maximum diversity order.
pp. 2293-2297
15:00 Role of Feedback in Modulo-Sum Computation over Erasure Multiple-Access Channels
I-Hsiang Wang (National Taiwan University, Taiwan); Shih-Chun Lin (National Taiwan University of Science and Technology, Taiwan); Yu-Chih Huang (National Taipei University, Taiwan)
The problem of computing the modulo-sum of messages over a finite-field erasure multiple access channel (MAC) is studied, and the role of feedback for function computation is explored. Our main contribution is two-fold. First, a new outer bound on the non-feedback computation capacity is proved, which strictly improves the state of the art by Khisti, Hern, and Narayanan. The new outer bound answers a previously unsettled question in the affirmative: delayed state feedback strictly increases computation capacity for the two-user erasure MAC universally. The proof leverages the subset entropy inequality by Madiman and Tetali. Second, focusing on the family of linear coding schemes with hybrid-ARQ-type retransmissions, we develop the optimal computation rate with delayed state feedback. For the considered family of schemes, it is always sub-optimal to compute modulo-sum by decoding all messages first. This is in contrast to the non-feedback case by Khisti et al. where sometimes the aforementioned "decode- all" strategy can reach the best known achievable rates.
pp. 2298-2302
15:20 On the Necessity of Structured Codes for Communications over MAC with Feedback
Mohsen Heidari Khoozani and Farhad Shirani (University of Michigan, USA); Sandeep Pradhan (University Michigan, USA)
The problem of three-user multiple-access channel (MAC) with noiseless feedback is investigated. A new coding strategy is presented. The coding scheme builds upon the natural extension of the Cover-Leung (CL) scheme [1]; and uses quasi-linear codes. A new single-letter achievable rate region is derived. The new achievable region strictly contains the CL region. This is shown through an example. In this example, the coding scheme achieves optimality in terms of transmission rates. It is shown that any optimality achieving scheme for this example must have a specific algebraic structure. Particularly, the codebooks must be closed under binary addition.
pp. 2303-2307
15:40 On the Gaussian MAC with Stop-Feedback
Lan V. Truong and Vincent Y. F. Tan (National University of Singapore, Singapore)
We characterize the information theoretic limits of the Gaussian multiple access channel (MAC) when variable-length stop-feedback is available at the encoder and a non-vanishing error probability is permitted. Due to the continuous nature of the channel and the presence of expected power constraints, we need to develop new achievability and converse techniques. Due to the multi-terminal nature of the channel model, we are faced with the need to bound the asymptotic behavior of the expected value of the maximum of several stopping times. We do so by leveraging tools from renewal theory developed by Gut, Lai and Siegmund.
pp. 2308-2312

#### Th3-7: Communications 3

Room: K6
Chair: Ralf R. Müller (Friedrich-Alexander Universität Erlangen-Nürnberg, Germany)
14:40 Probabilistic Shaping and Non-Binary Codes
Joseph Jean Boutros (Texas A&M University, USA); Fanny Jardel (Nokia Bell Labs, Germany); Cyril Measson (Nokia & Qualcomm, EPFL, France)
We generalize probabilistic amplitude shaping (PAS) with binary codes [1] to the case of non-binary codes defined over prime finite fields. Firstly, we introduce probabilistic shaping via time sharing where shaping applies to information symbols only. Then, we design circular quadrature amplitude modulations (CQAM) that allow to directly generalize PAS to prime finite fields with full shaping. [1] G. Böcherer, F. Steiner, and P. Schulte, "Bandwidth efficient and rate-matched Low-Density Parity-Check coded modulation," IEEE Trans. Commun., vol. 63, no. 12, pp. 4651-4665, Dec. 2015.
pp. 2313-2317
15:00 Successive Local and Successive Global Omniscience
Anoosheh Heidarzadeh and Alex Sprintson (Texas A&M University, USA)
This paper considers two generalizations of the cooperative data exchange problem, referred to as the \emph{successive local omniscience} (SLO) and the successive global omniscience (SGO). The users are divided into $\ell$ nested sub-groups. Each user initially knows a subset of packets in a ground set $X$ of size $k$, and all users wish to learn all packets in $X$. The users exchange their packets by broadcasting coded or uncoded packets. In SLO or SGO, in the $l$th ($1\leq l\leq \ell$) round of transmissions, the $l$th smallest sub-group of users need to learn all packets they collectively hold or all packets in $X$, respectively. The problem is to find the minimum sum-rate (i.e., the total transmission rate by all users) for each round, subject to minimizing the sum-rate for the previous round. To solve this problem, we use a linear-programming approach. For the cases in which the packets are randomly distributed among users, we construct a system of linear equations whose solution characterizes the minimum sum-rate for each round with high probability as $k$ tends to infinity. Moreover, for the special case of two nested groups, we derive closed-form expressions, which hold with high probability as $k$ tends to infinity, for the minimum sum-rate for each round.
pp. 2318-2322
15:20 Noncoherent Massive Space-Time Codes with PSK Modulation for Uplink Network Communications
Jian-Kang Zhang (McMaster University, Canada); Shuangzhi Li and Xiaomin Mu (Zhengzhou University, P.R. China)
We consider a multi-user massive MIMO uplink system in which there are multiple users with each having a single antenna and one base station (BS) with a large number of antennas. It is assumed that each user and BS have neither small scale nor large scale channel state information. For such a noncoherent system, we systematically design a series of absolutely additively uniquely decomposable constellation pairs (AAUDCPs) using the phase-shift keying (PSK) constellations such that when any linear combination of two PSK constellation points with positive weighting coefficients is received, each individual PSK signal can be uniquely decoded. With this, a novel noncoherent massive space-time block code with PSK modulation is developed for the system. In a noise-free case, we prove that when the number of antenna at BS grows to infinite, the transmitted symbols and uplink channel can be uniquely determined if the channel coherence time is at least equal to the number of users. In a noisy case, a robust Euclidean distance receiver is developed for efficiently and effectively estimating both the channel coefficients and the transmitted signals.
pp. 2323-2327
15:40 FPLinQ: A Cooperative Spectrum Sharing Strategy for Device-to-Device Communications
Kaiming Shen and Wei Yu (University of Toronto, Canada)
Interference management is a fundamental problem for the device-to-device (D2D) network, in which transmitter and receiver pairs may be arbitrarily located geographically with full frequency reuse, so active links may severely interfere with each other. This paper devises a new optimization strategy called FPLinQ that coordinates link scheduling decisions together with power control among the interfering links throughout the network. Scheduling and power optimization for the interference channel are challenging combinatorial and nonconvex optimization problems. This paper proposes a fractional programming (FP) approach that derives a problem reformulation whereby the optimization variables are determined analytically in each iterative step. As compared to the existing works of FlashLinQ, ITLinQ and ITLinQ+, a merit of the proposed strategy is that it does not require tuning of design parameters. FPLinQ shows significant performance advantage as compared to the benchmarks in maximizing system throughput in a typical D2D network.
pp. 2328-2332
16:00 On the Effective Rate of MISO/TAS Systems in Rayleigh Fading
Yazan H. Al-Badarneh, Costas N Georghiades and Carlos Mejia (Texas A&M University, USA)
The effective rate is an important metric that takes delay quality of service (QoS) requirements into consideration while analyzing the performance of wireless systems. In this paper we analyze the effective rate of multiple-input single-output (MISO) systems with transmit antenna selection (TAS) subject to Rayleigh fading. Specifically, we derive a closed-form expression for the effective rate of MISO/ TAS systems. We also derive closed form expressions for the effective rate in asymptotically high and low signal-to-noise ratio (SNR) regimes. Furthermore, we analyze the effective rate of MISO/ TAS systems with large of number of transmit antennas and derive an asymptotic closed-form expression for it.
pp. 2333-2337

#### Th3-8: Compressed Sensing 4

Room: K7+8
Chair: Bernard Henri Fleury (Aalborg University, Denmark)
14:40 Generalized Expectation Consistent Signal Recovery for Nonlinear Measurements
Hengtao He (Southeast University, P.R. China); Chao-Kai Wen (National Sun Yat-sen University, Taiwan); Shi Jin (Southeast University, P.R. China)
In this paper, we propose a generalized expectation consistent signal recovery algorithm to estimate the signal $\mathbf{x}$ from the nonlinear measurements of a linear transform output $\mathbf{z}=\mathbf{A}\mathbf{x}$. This estimation problem has been encountered in many applications, such as communications with front-end impairments, compressed sensing, and phase retrieval. The proposed algorithm extends the prior art called generalized turbo signal recovery from a partial discrete Fourier transform matrix $\mathbf{A}$ to a class of general matrices. Numerical results show the excellent agreement of the proposed algorithm with the theoretical Bayesian-optimal estimator derived using the replica method.
pp. 2338-2342
15:00 Universality of the Elastic Net Error
Andrea Montanari and Phan Minh Nguyen (Stanford University, USA)
We consider the problem of reconstructing a vector $\boldsymbol{x}_{0}\in\mathbb{R}^{n}$ from noisy linear observations $\boldsymbol{y}=\boldsymbol{A}\boldsymbol{x}_{0}+\boldsymbol{w}$, where $\boldsymbol{A}\in\mathbb{R}^{m\times n}$ is a known operator and $\boldsymbol{w}$ is a noise vector, using the elastic net method. Assuming that $\boldsymbol{A}$ is random with independent and identically distributed entries, and under suitable moment conditions, we prove the following universality result. In the high-dimensional asymptotics $n\to\infty$ and $\frac{m}{n}\to\delta>0$, the normalized error of the elastic net minimizer converges in probability to a limit, that does not depend on the exact distribution that the entries are drawn from. We also provide an explicit formula for the limit.
pp. 2343-2347
15:20 Using Mutual Information for Designing the Measurement Matrix in Phase Retrieval Problems
Nir Shlezinger (Ben Gurion University, Israel); Ron Dabora (Ben-Gurion University, Israel); Yonina C. Eldar (Technion-Israel Institute of Technology, Israel)
In the phase retrieval problem, the observations consist of the magnitude of a linear transformation of the signal of interest (SOI) with additive noise, where the linear transformation is typically referred to as measurement matrix. The objective is then to reconstruct the SOI from the observations up to an inherent phase ambiguity. Many works on phase retrieval assume that the measurement matrix is a random Gaussian matrix, which in the noiseless scenario with sufficiently many measurements guarantees uniqueness of the mapping between the SOI and the observations. However, in many applications, e.g., optical imaging, the measurement matrix corresponds to the underlying physical setup, and is therefore a deterministic matrix with structure constraints. In this work we study the design of deterministic measurement matrices, aimed at maximizing the mutual information between the SOI and the observations. We characterize necessary conditions for the optimal measurement matrix, and propose a practical design method for measurement matrices corresponding to masked Fourier measurements. Simulation tests of the proposed method show that it achieves the same performance as random Gaussian matrices for various phase recovery algorithms.
pp. 2348-2352
15:40 Information Theoretic Limits for Linear Prediction with Graph-Structured Sparsity
Adarsh Barik, Jean Honorio and Mohit Tawarmalani (Purdue University, USA)
We analyze the necessary number of samples for sparse vector recovery in a noisy linear prediction setup. This model includes problems such as linear regression and classification. We focus on structured graph models. In particular, we prove that sufficient number of samples for the weighted graph model proposed by Hegde and others is also necessary. We use the Fano's inequality on well constructed ensembles as our main tool in establishing information theoretic lower bounds.
pp. 2353-2357
16:00 Improved Bounds for Universal One-bit Compressive Sensing
Jayadev Acharya (Cornell University, USA); Arnab Bhattacharyya (Indian Institute of Science, India); Pritish Kamath (Massachusetts Institute of Technology, USA)
Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in "one-bit compressive sensing", measurements are quantized to one bit, their signs. In this work, our contributions are as follows: 1. We show how to recover the support of sparse high-dimensional vectors in the 1-bit compressive sensing framework with an asymptotically near-optimal number of measurements. We do this by showing an equivalence between the task of support recovery using 1-bit compressive sensing and a well-studied combinatorial object known as Union Free Families. 2. We also improve the bounds on the number of measurements for approximately recovering vectors from 1-bit compressive sensing measurements. All our results are about universal measurements, namely the measurement schemes that work simultaneously for all sparse vectors. Our improved bounds naturally lead the way to suggest several interesting open problems.
pp. 2358-2362

#### Th3-9: Signal Processing

Room: K9
Chair: Negar Kiyavash (University of Illinois at Urbana-Champaign, USA)
14:40 Principal Pivot Transforms on Radix-2 DFT-type Matrices
Sian-Jheng Lin (University of Science and Technology of China, P.R. China); Amira Alloum (Nokia Bell Labs, France); Tareq Y. Al-Naffouri (King Abdullah University of Science and Technology, USA)
In this paper, we discuss the principal pivot transforms (PPT) on a family of matrices, called the radix-2 DFT-type matrices. Given a transformation matrix, the PPT of the matrix is a transformation matrix with exchanging some entries between the input array and the output array. The radix-2 DFT-type matrices form a classification of matrices such that the transformations by the matrices can be calculated via radix-2 butterflies. A number of well-known matrices, such as radix-2 DFT matrices and Hadamard matrices, belong to this classification. In this paper, the sufficient conditions for the PPTs on radix-2 DFT-type matrices are given, such that their transformations can also be computed in $O(n\lg n)$. Then based on the results above, an encoding algorithm for systematic Reed-Solomon (RS) codes in $O(n\lg n)$ field operations is presented.
pp. 2363-2367
Daniel L Pimentel-Alarcon, Aritra Biswas and Claudia Solis-Lemus (University of Wisconsin-Madison, USA)
This paper studies the following question: where should an adversary place an outlier of a given magnitude in order to maximize the error of the subspace estimated by PCA? We give the exact location of this "worst" possible outlier, and the exact expression of the maximum possible error. Equivalently, we determine the information-theoretic bounds on how much an outlier can "tilt" a subspace in its direction. This in turn provides universal (worst-case) error bounds for PCA under arbitrary noisy settings. Our results also have several implications on adaptive PCA, online PCA, and rank-one updates. We illustrate our results with a subspace tracking experiment.
pp. 2368-2372
15:20 Characterization of the stability range of the Hilbert transform with applications to spectral factorization
Holger Boche (Technical University Munich, Germany); Volker Pohl (Technische Universität München, Germany)
The Hilbert transform plays an important role in many different applications. Especially in the area of detection and estimation it is closely related to the calculation of the spectral factorization. Generally, it is not possible to calculate the Hilbert transform in closed form. Therefore approximation methods are applied. This paper studies the stability of a general class of approximation algorithms for the Hilbert transform which contains all traditional numerical integration methods. To this end, the paper introduces a scale of signal spaces with finite energy in which a factor $(\log n)^{\beta}$ measures the concentration of the signal energy in its Fourier coefficients $c_{n}$. It will be shown that if the energy concentration is two weak, i.e. if $0 \leq \beta \leq 1$, then every approximation method diverges. Conversely, if the energy concentration is sufficiently good, i.e. if $\beta > 1$, convergent approximation methods do exist and we give a natural characterization of all convergent methods.
pp. 2373-2377
15:40 Mellin-Transform-Based New Results of the Joint Statistics of Partial Products of Ordered Random Variables
Sung Sik Nam and Young-Chai Ko (Korea University, Korea); Mohamed-Slim Alouini (King Abdullah University of Science and Technology (KAUST), Saudi Arabia)
Order statistics find applications in various areas including communications and signal processing. In this paper, we introduce new results of the joint statistics of partial products of ordered random variables (RVs) based on a Mellin-transform-based unified analytical framework. With the proposed approach, we can systematically derive the joint statistics of any partial products of ordered statistics, in terms of the Mellin transform and the probability density function (PDF). Our Mellin-transform-based approach can apply when all the K-ordered RVs are involved even for more complicated cases, when only the Ks (Ks <K) best RVs are also considered. In addition, the closed-form expressions for the exponential RV special case are presented. As an application example, these results can apply to the performance analysis of various wireless communication systems over fading channels.
pp. 2378-2382
16:00 Optimal Sensor Selection in the Presence of Noise and Interference
Afshin Abdi and Faramarz Fekri (Georgia Institute of Technology, USA)
The sensor selection problem arises in many applications ranging from sensor networks for event detection to determining concentrations of bio-markers for disease detection. In this paper, we assume that in addition to noise, there exist interference signals (which can be correlated with the desired signals) corrupting the measurements. We consider two different criteria to measure the performance of the selected sensors; average error and minimax analysis. For each case, the cost function is defined over the reconstruction algorithm (or matrix in the linear case), which in turn, explicitly determines the selected sensors. Therefore, minimizing the cost function with some sparsity constraints on the reconstruction algorithm results in the best subset of sensors and as to how we recover the desired signals from the selected measurements. In this paper, we consider the problem for the linear measurement system in various settings and derive the optimization problems. Finally, we propose various methods to solve these problems, and show the effectiveness of the proposed algorithms through simulations.
pp. 2383-2387

### Thursday, June 29, 16:40 - 18:20

#### Th4-1: Network Coding 2

Room: Amsterdam
Chair: Ron M. Roth (Technion, Israel)
16:40 Circular-shift Linear Network Coding
Qifu T Sun and Hanqi Tang (University of Science and Technology Beijing, P.R. China); Zongpeng Li (University of Calgary, Canada); Xiaolong Yang (University of Science & Technology Beijing, P.R. China); Keping Long (University of Science and Technology Beijing, P.R. China)
We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations at intermediate nodes consist of only circular-shifts and bit-wise addition (XOR). Departing from existing literature, we systematically formulate circular-shift LNC as a special type of vector LNC, where the local encoding kernels of an $L$-dimensional circular-shift linear code of degree $\delta$ are summation of at most $\delta$ cyclic-permutation matrices of size $L$. Under this framework, an intrinsic connection between scalar LNC and circular-shift LNC is established. In consequence, for some block lengths $L$, an $(L-1, L)$-fractional circular-shift linear solution of arbitrary degree $\delta$ can be efficiently constructed on a multicast network. With different $\delta$, the constructed solution has an interesting encoding-decoding complexity tradeoff, and when $\delta = (L-1)/2$, it requires fewer binary operations for both encoding and decoding processes compared with scalar LNC. While the constructed $(L-1, L)$-fractional solution has one-bit redundancy per edge transmission, we show that this is inevitable, and that circular-shift LNC is insufficient to achieve the exact capacity of multicast networks.
pp. 2388-2392
17:00 Coding for Networks of Compound Channels
Fariba Abbasi (Sharif Institute of Technology, Iran); Mayank Bakshi (The Chinese University of Hong Kong, Hong Kong)
In this paper, we consider networks where every edge is a compound channel whose transition probability is determined by a global network state. We examine the setting where each edge corresponds to a Binary Symmetric Channel, and the sum of the transition probabilities for all edges satisfies an overall global upper bound. We first consider networks with exactly one source and one sink. For such networks, we show that capacity is given by the smallest min-cut among all permitted networks. We show that routing along with end-to-end error correction is optimal for such networks. Next, we consider networks with one source and multiple sinks with multicast demands. We give upper and lower bounds on the capacity of such networks. The coding strategy that leads to our lower bound is intriguing -- it involves both end-to-end error correction across the network as well as link-by-link error correction.
pp. 2393-2397
17:20 Distributed Decoding of Convolutional Network Error Correction Codes
Hengjie Yang and Wangmei Guo (Xidian University, P.R. China)
The decoding problem is addressed in this paper for the scenario that convolutional codes are employed at the source node of the network with linear or convolutional network coding for error correction. Since network errors may disperse or neutralize due to network coding, decoding cannot be done at sink nodes merely based on the minimum Hamming distance between the received and sent sequence. Source decoding is proposed in previous work by multiplying the inverse of the network transfer matrix, where the inverse is hard to compute and sometimes the result is noncausal. Starting from the Maximum A Posteriori (MAP) decoding criterion, we find that it is equivalent to the minimum error weight under our model. Inspired by classical Viterbi algorithm, we propose a Viterbi-like decoding algorithm based on the minimum error weight of combined error vectors, which can be carried out directly at sink nodes and can correct any network errors within the capability of convolutional network error correction codes (CNECC). We then study the distributed decoding of CNECC and give a sufficient condition that is able to realize such a decoding process with the proposed algorithm.
pp. 2398-2402
17:40 Multiuser Rate-Diverse Network-Coded Multiple Access
Haoyuan Pan, Lu Lu and Soung Chang Liew (The Chinese University of Hong Kong, Hong Kong)
This paper presents the first Network-Coded Multiple Access (NCMA) system with multiple users adopting different signal modulations, referred to as rate-diverse NCMA. A distinguishing feature of NCMA is the joint use of physical-layer network coding (PNC) and multiuser decoding (MUD) to boost throughput of multipacket reception systems. In previous NCMA systems, users adopt the same modulation regardless of their individual channel conditions. This leads to suboptimal throughput for many practical scenarios, especially when different users have widely varying channel conditions. A rate-diverse NCMA system allows different users to use modulations that are commensurate with their channel conditions. A key challenge is the design of PNC mapping and decoding mechanisms in NCMA when different users adopt different modulations. While there have been past work on non-channel-coded rate-diverse PNC, this paper is the first attempt to design channel-coded rate-diverse PNC to ensure the reliability of the overall NCMA system. Specifically, we put forth a symbol-splitting channel coding and modulation design so that PNC/NCMA can work over different modulations. We implemented our rate-diverse NCMA system on software-defined radios. Experimental results show that the throughput of rate-diverse NCMA can outperform the state-of-the-art rate-homogeneous NCMA by 80%. Overall, the introduction of rate diversity significantly boosts the NCMA system throughput in practical scenarios.
pp. 2403-2407

#### Th4-2: Coded Computation

Room: Brussels
Chair: Helmut Bölcskei (ETH Zurich, Switzerland)
16:40 Coded convolution for parallel and distributed computing within a deadline
Sanghamitra Dutta (Carnegie Mellon University, USA); Viveck Cadambe (Pennsylvania State University, USA); Pulkit Grover (Carnegie Mellon University, USA)
We consider the problem of computing the convolution of two long vectors using parallel processors in the presence of stragglers''. Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation in time-critical distributed systems. We first show that splitting the vectors into smaller pieces and using a linear code to encode these pieces provides improved resilience against stragglers than replication-based schemes under a simple, worst-case straggler analysis. We then demonstrate that under commonly used models of computation time, coding can dramatically improve the probability of finishing the computation within a target deadline'' time. As opposed to the more commonly used technique of expected computation time analysis, we quantify the exponents of the probability of failure in the limit of large deadlines. Our exponent metric captures the probability of failing to finish before a specified deadline time, i.e. , the behavior of the tail''. Moreover, our technique also allows for simple closed form expressions for more general models of computation time, e.g. shifted Weibull models instead of only shifted exponentials. Thus, through this problem of coded convolution, we establish the utility of a novel asymptotic failure exponent analysis for distributed systems.
pp. 2408-2412
17:00 Coded Computation over Heterogeneous Clusters
Amirhossein Reisizadeh (University of California, Santa Barbara, USA); Saurav Prakash (University of Southern California, USA); Ramtin Pedarsani (University of California, Santa Barbara, USA); Salman Avestimehr (University of Southern California, USA)
In large-scale distributed computing clusters, such as Amazon EC2, there are several types of "system noise" that can result in major degradation of performance: system failures, bottlenecks due to limited communication bandwidth, latency due to straggler nodes, etc. On the other hand, these systems enjoy abundance of redundancy -- a vast number of computing nodes and large storage capacity. There have been recent results that demonstrate the impact of coding for efficient utilization of computation and storage redundancy to alleviate the effect of stragglers and communication bottlenecks in homogeneous clusters. In this paper, we focus on general heterogeneous distributed computing clusters consisting of a variety of computing machines with different capabilities. We propose a coding framework for speeding up distributed computing in heterogeneous clusters with straggling servers by trading redundancy for reducing the latency of computation. In particular, we propose Heterogeneous Coded Matrix Multiplication (HCMM) algorithm for performing distributed matrix multiplication over heterogeneous clusters that is provably asymptotically optimal. Moreover, if the number of worker nodes in the cluster is $n$, we show that HCMM is $\Theta(\log n)$ times faster than any uncoded scheme. We further provide numerical results demonstrating significant speedups of up to $49\%$ and $34\%$ for HCMM in comparison to the "uncoded" and "homogeneous coded" schemes, respectively.
pp. 2413-2417
17:20 Coded Computation for Multicore Setups
Kangwook Lee (KAIST, Korea); Ramtin Pedarsani (University of California, Santa Barbara, USA); Dimitris Papailiopoulos (UW-Madison, USA); Kannan Ramchandran (University of California at Berkeley, USA)
Consider a distributed computing setup consisting of a mater node and $n$ worker nodes, each equipped with $p$ cores, and a function $f(x) = g(f_1(x),f_2(x),..,f_k(x))$, where each $f_i$ can be computed independently of the rest. Assuming that the worker computational times have exponential tails, what is the minimum possible time for computing $f$? Can we use coding theory principles to speed up this distributed computation? Unlike the case where the local functions are linear (recently studied in [1]), in the non-linear case, it is not clear if traditional codes can provide any gains due to the high density of the parities. To resolve this problem, we propose the use of codes with sparse generator matrices for assigning local functions to different cores, and provide design guidelines for optimal constructions that minimize the runtime. We show that our coding solution offers (up to a constant factor) optimal performance, and has a provable unbounded gap compared to any uncoded schemes.
pp. 2418-2422
17:40 High-Dimensional Coded Matrix Multiplication
Kangwook Lee and Changho Suh (KAIST, Korea); Kannan Ramchandran (University of California at Berkeley, USA)
Coded computation is a framework for providing redundancy in distributed computing systems to make them robust to slower nodes, or stragglers. In [1], the authors propose a coded computation scheme based on maximum distance separable (MDS) codes for computing the product of two matrices, and this scheme is suitable for the case where one of the matrices is small enough to fit into a single compute node. In this work, we study coded computation involving large matrix multiplication where both matrices are large, and propose a new coded computation scheme, which we call product-coded matrix multiplication. Our analysis reveals interesting insights into which schemes perform best in which regimes. When the number of backup workers scales sub-linearly in the size of the product, the product-coded scheme achieves the best run-time performance. On the other hand, when the number of backup workers scales linearly in the size of the product, the MDS-coded scheme achieves the fundamental limit on the run-time performance. Further, we propose a novel application of low-density-parity-check (LDPC) codes to achieve linear-time decoding complexity, thus allowing our proposed solutions to scale gracefully.
pp. 2423-2427

#### Th4-3: Coded Caching 1

Room: K2
Chair: Giuseppe Caire (Technische Universität Berlin, Germany)
16:40 Coded Caching with Partial Adaptive Matching
Jad Hachem (University of California, Los Angeles, USA); Nikhil Karamchandani and Sharayu Moharir (Indian Institute of Technology Bombay, India); Suhas Diggavi (University of California Los Angeles, USA)
We study the coded caching problem when we are allowed to match users to caches based on their requested files. We focus on the case where caches are divided into clusters and each user can be assigned to a unique cache from a specific cluster. We show that neither the coded delivery strategy (approximately optimal when the user-cache assignment is pre-fixed) nor the uncoded replication strategy (approximately optimal when all caches belong to a single cluster) is sufficient for all memory regimes. We propose a hybrid solution that combines ideas from both schemes and that performs strictly better than both. Finally, we show that this hybrid strategy is approximately optimal in most memory regimes.
pp. 2428-2432
17:00 Improved Converses and Gap-Results for Coded Caching
Chien-Yi Wang (Télécom ParisTech, France); Shirin Saeedi Bidokhti (Stanford University, USA); Michele A Wigger (Telecom ParisTech, France)
Improved lower bounds on the worst-case and the average-case rate-memory tradeoffs for the Maddah-Ali\&Niesen coded-caching scenario are presented. For any number of users and files and for arbitrary cache sizes, the multiplicative gap between the exact rate-memory tradeoff and the new lower bound is less than 2.315 in the worst-case scenario and less than 2.507 in the average-case scenario.
pp. 2433-2437
17:20 Coded Caching for Combination Networks with Cache-Aided Relays
Ahmed A Zewail and Aylin Yener (Pennsylvania State University, USA)
We study a two-hop cache-aided network, where a layer of relay nodes connects a server and a set of end users, i.e., a combination network. We consider the case where both the relay nodes and the end users have caching capabilities. We provide upper and lower bounds which are applicable to any combination network, noting that previous work had focused on models where the relays do not have caches as well as schemes that were suitable for a special class of combination networks. Utilizing maximum distance separable (MDS) codes, we jointly optimize the placement and the delivery phases, demonstrating the impact of cache memories in alleviating the delivery load over the two hop communications. Moreover, we show how cooperation between the relay nodes and the end users can effectively replace the server during the delivery phase whenever the total memory at each end user and its connected relay nodes is sufficient to store the database.
pp. 2438-2442
17:40 Asynchronous Coded Caching
Hooshang Ghasemi and Aditya Ramamoorthy (Iowa State University, USA)
Coded caching is a technique that promises huge reductions in network traffic in content-delivery networks. However, the original formulation and several subsequent contributions in the area, assume that the file requests from the users are synchronized, i.e., they arrive at the server at the same time. In this work we formulate and study the coded caching problem when the file requests from the users arrive at different times. We assume that each user also has a prescribed deadline by which they want their request to be completed. In the offline case, we assume that the server knows the arrival times before starting transmission and in the online case, the user requests are revealed to the server over time. We present a LP formulation for the offline case that minimizes the overall rate subject to constraint that each user meets his/her deadline. While the online case is much harder, we demonstrate that in the case when the server wishes to minimize the overall completion time, the online solution can be as good as the offline solution. Our simulation results indicate that in the presence of mild asynchronism, much of the benefit of coded caching can still be leveraged.
pp. 2443-2447
18:00 Decentralized Coded Caching in Wireless Networks: Trade-off between Storage and Latency
Antonious Girgis (Nile University, Egypt); Ozgur Ercetin (Sabanci University, Turkey); Mohammed Nafie (Cairo University & Nile University, Egypt); Tamer ElBatt (Faculty of Engineering, Cairo University & WINC, Nile University, Egypt)
This paper studies the decentralized coded caching for a Fog Radio Access Network (F-RAN), whereby two edge-nodes (ENs) connected to a cloud server via fronthaul links with limited capacity are serving the requests of $K_r$ users. We consider all ENs and users are equipped with caches. A decentralized content placement is proposed to independently store contents at each network node during the off-peak hours. After that, we design a coded delivery scheme in order to deliver the user demands during the peak-hours under the objective of minimizing the normalized delivery time (NDT), which refers to the worst case delivery latency. An information-theoretic lower bound on the minimum NDT is derived for arbitrary number of ENs and users. We evaluate numerically the performance of the decentralized scheme. Additionally, we prove the approximate optimality of the decentralized scheme for a special case when the caches are only available at the ENs.
pp. 2448-2452

#### Th4-4: Shannon Theory and Molecular

Room: K3
Chair: Olivier Lévêque (EPFL, Switzerland)
16:40 A Characterization of the Shannon Ordering of Communication Channels
Rajai Nasser (École Polytechnique Fédérale de Lausanne, Switzerland)
The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that $W'$ contains $W$ if and only if $W$ is the skew-composition of $W'$ with a convex-product channel. This fact is used to derive a characterization of the Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two channels are said to be Shannon-equivalent if each one is contained in the other. We investigate the topologies that can be constructed on the space of Shannon-equivalent channels. We introduce the strong topology and the BRM metric on this space. Finally, we study the continuity of a few channel parameters and operations under the strong topology.
pp. 2453-2457
17:00 On the Input-Degradedness and Input-Equivalence Between Channels
Rajai Nasser (École Polytechnique Fédérale de Lausanne, Switzerland)
A channel $W$ is said to be input-degraded from another channel $W'$ if $W$ can be simulated from $W'$ by randomization at the input. We provide a necessary and sufficient condition for a channel to be input-degraded from another one. We show that any decoder that is good for $W'$ is also good for $W$. We provide two characterizations for input-degradedness, one of which is similar to the Blackwell-Sherman-Stein theorem. We say that two channels are input-equivalent if they are input-degraded from each other. We study the topologies that can be constructed on the space of input-equivalent channels, and we investigate their properties. Moreover, we study the continuity of several channel parameters and operations under these topologies.
pp. 2458-2462
17:20 Models and information-theoretic bounds for nanopore sequencing
Wei Mao and Suhas Diggavi (University of California Los Angeles, USA); Sreeram Kannan (University of Washington Seattle, USA)
Nanopore sequencing is an emerging new technology for sequencing DNA, which can read long fragments of DNA (ca. 50,000 bases) unlike most current sequencers which can only read hundreds of bases. While nanopore sequencers can acquire long reads, the high error rates ($\approx$ 30%) pose a technical challenge. In a nanopore sequencer, a DNA is migrated through a nanopore and current variations are measured. The DNA sequence is inferred from this observed current pattern using an algorithm called a base-caller. In this paper, we propose a mathematical model for the channel'' from the input DNA sequence to the observed current, and calculate bounds on the information extraction capacity of the nanopore sequencer. This model incorporates impairments like inter-symbol interference, deletions, as well as random response. The practical application of such information bounds is two-fold: (1) benchmarking present base-calling algorithms, and (2) offering an optimization objective for designing better nanopore sequencers.
pp. 2463-2467
17:40 Less Noisy Domination by Symmetric Channels
Anuran Makur (Massachusetts Institute of Technology, USA); Yury Polyanskiy (MIT, USA)
Consider the family of all q-ary symmetric channels (q-SCs) with capacities decreasing from log(q) to 0. This paper addresses the following question: what is the member of this family with the smallest capacity that dominates a given channel V in the "less noisy" preorder sense. When the q-SCs are replaced by q-ary erasure channels, this question is known as the "strong data processing inequality." We provide several equivalent characterizations of the less noisy preorder in terms of chi-squared-divergence, Loewner (PSD) partial order, and spectral radius. We then illustrate a simple criterion for domination by a q-SC based on degradation, and mention special improvements for the case where V is an additive noise channel over an Abelian group of order q. Finally, as an application, we discuss how logarithmic Sobolev inequalities for q-SCs, which are well-studied, can be transported to an arbitrary channel V.
pp. 2468-2472
18:00 Capacity of Molecular Channels with Imperfect Particle-Intensity Modulation and Detection
Nariman Farsad (Stanford University, USA); Christopher Rose (Brown University, USA); Muriel Médard (MIT, USA); Andrea Goldsmith (Stanford University, USA)
This work introduces the particle-intensity channel (PIC) as a model for molecular communication systems and characterizes the properties of the optimal input distribution and the capacity limits for this system. In the PIC, the transmitter encodes information, in symbols of a given duration, based on the number of particles released, and the receiver detects and decodes the message based on the number of particles detected during the symbol interval. In this channel, the transmitter may be unable to control precisely the number of particles released, and the receiver may not detect all the particles that arrive. We demonstrate that the optimal input distribution for this channel always has mass points at zero and the maximum number of particles that can be released. We then consider diffusive particle transport, derive the capacity expression when the input distribution is binary, and show conditions under which the binary input is capacity-achieving. In particular, we demonstrate that when the transmitter cannot generate particles at a high rate, the optimal input distribution is binary.
pp. 2473-2477

#### Th4-5: Bounds 3

Room: K4
Chair: I-Hsiang Wang (National Taiwan University, Taiwan)
16:40 Information-theoretic Limits of Subspace Clustering
Kwangjun Ahn, Kangwook Lee and Changho Suh (KAIST, Korea)
Subspace clustering is a celebrated problem that comes up in a variety of applications such as motion segmentation and face clustering. The goal of the problem is to find clusters in different subspaces from similarity measurements across data points. While the algorithmic aspect of this problem has been extensively studied in the literature, the information-theoretic limit on the number of similarities required for reliable clustering has been unknown. In this paper, we translate the problem into an instance of community recovery in hypergraphs, and characterize the sharp threshold on the limit required for exact subspace clustering. Moreover, we present a computationally efficient algorithm that achieves the fundamental limit.
pp. 2478-2482
17:00 The Error Exponent of Sparse Regression Codes with AMP Decoding
Cynthia Rush (Columbia University); Ramji Venkataramanan (University of Cambridge, United Kingdom (Great Britain))
Sparse regression codes (SPARCs) are a recent class of codes for reliable communication over the AWGN channel at rates approaching the channel capacity. Approximate message passing (AMP) decoding, a computationally efficient technique for decoding SPARCs, has been proven to be asymptotically capacity-achieving for the AWGN channel. In this paper, we refine the asymptotic results by deriving a large deviations bound on the probability of AMP decoding error. This bound shows that for an appropriate choice of code parameters and any fixed rate smaller than the AWGN capacity, the probability of decoding error decays exponentially in $n/(\log n)^{2T}$, where T is the number of AMP iterations required for successful decoding. The number of iterations T is proportional to the inverse of the logarithm of the ratio of channel capacity to rate. For the above choice of code parameters, the complexity of the AMP decoder scales as a low-order polynomial in the block length n.
pp. 2483-2487
17:20 Lower Bounds on the Number of Write Operations by Index-less Indexed Flash Code with Inversion Cells
Akira Yamawaki, Hiroshi Kamabe and Shan Lu (Gifu University, Japan)
Index-less indexed flash code (ILIFC) is a coding scheme for flash memories in which one bit of a data sequence is stored in a slice consisting of several cells but the index of the bit is stored implicitly. Although several modified ILIFC schemes have been proposed, in this study we consider an ILIFC with inversion cells (I-ILIFC). The I-ILIFC reduces the total number of cell level changes at each write request. Computer simulation is used to show that the I-ILIFC improves the average performance of ILIFC in many cases. This paper presents our derivation of the lower bound on the number of write operations by I-ILIFC. Additionally, we consider another lower bound thereon and show that the threshold of the code length that determines whether the I-ILIFC improves the worst-case performance of the ILIFC is smaller than that in the first lower bound. Lastly, we analyze the asymptotic performance of the I-ILIFC in the worst case.
pp. 2488-2492
17:40 Partial Data Extraction via Noisy Histogram Queries: Information Theoretic Bounds
Wei-Ning Chen and I-Hsiang Wang (National Taiwan University, Taiwan)
The problem of extracting data via noisy histogram queries is investigated. A data set is a collection of items, and each item carries a piece of categorical data taking values in a finite alphabet. Data analysts are allowed to query the data set by specifying a subset and then obtain the histogram of the queried subset. The histogram released by the curator, however, is perturbed by some noise with magnitude $\delta_n$. The reconstruction is successful if the Hamming distance between the reconstructed data set and the actual data set is less than a tolerance parameter $k_n$. In this work, we prove several sharp upper and lower bounds on the minimum query complexity $T_n^*$ for successful reconstruction, which depends on the noise level $\delta_n$ and the tolerance level $k_n$. We first show that if the noise-tolerance condition $\delta_n=O(kn^(1/2))$ is satisfied, the minimum query complexity $T_n^∗=\Theta(n/log n)$, where the achievability is based on random sampling and the converse is based on counting and packing arguments. On the other hand, if $\delta_n=\Omega(kn^(1+\epsilon)/2)$ for some $\epsilon > 0$, we prove that $T_n^∗ = \omega(n^p)$ for any positive integer $p$. In words, no querying methods with Poly($n$) query complexity can successfully reconstruct the data set in that regime. This impossibility result is established by a novel combinatorial lower bound on $T_n^∗$ (converse).
pp. 2493-2497
18:00 Asymptotics of the Error Probability in Quasi-Static Binary Symmetric Channels
Josep Font-Segura and Alfonso Martinez (Universitat Pompeu Fabra, Spain); Albert Guillén i Fàbregas (ICREA and Universitat Pompeu Fabra & University of Cambridge, Spain)
This paper provides an asymptotic expansion of the error probability, as the codeword length n goes to infinity, in quasi-static binary symmetric channels. After the leading term, namely the outage probability, the following two terms are found to be proportional to (log n)/n and 1/n respectively. Explicit characterizations of the respective coefficients are given. The resulting expansion gives an accurate approximation to the random-coding union for even small codeword lengths.
pp. 2498-2502

#### Th4-6: Wireless Networks 2

Room: K5
Chair: Randall A Berry (Northwestern University, USA)
16:40 Commitment in regulatory spectrum games: Examining the first-player advantage
Vidya Muthukumar and Anant Sahai (UC Berkeley, USA)
Recent advances in dynamic spectrum sharing have led to renewed focus on the structure of regulatory games between a primary, incumbent user and a secondary, opportunistic user of a spectrum band. The primary user has to decide to what extent it invokes the services of the regulator, and the secondary user has to decide how to operate in the spectrum band. This paper builds on a mathematical model for light-handed regulation using spectrum jails" to show that the order of play and amount of commitment matters. A primary that can commit to its strategy before the game is able to reduce its equilibrium cost, even when the secondary best responds to the committed strategy. We compare the ensuing Stackelberg game with the simultaneous primary-secondary game. We also introduce a new concept of \textit{partial} commitment by which the primary can only commit to a range of strategies using a finite number of bits. We show explicitly that the more the primary commits to, the more it benefits, and that Stackelberg commitment can be understood as a limit of infinite commitment bits".
pp. 2503-2507
17:00 Inferring Network Topology from Information Cascades
Feng Ji, Wenchang Tang and Wee Peng Tay (Nanyang Technological University, Singapore); Edwin K. P. Chong (Colorado State University, USA)
We study the problem of inferring the graph structure of a network using knowledge of information cascades in the network. Unlike previous studies, which assume knowledge of the distributions of information diffusion across edges in the network, we only require that diffusion along different edges in the network be independent together with limited information on their distributions (e.g., just the means). We introduce the concept of a separating vertex set for a graph, which is a set of vertices in which for any two given distinct vertices of the graph, one can find a vertex whose distance to them are different. We show that a necessary condition for reconstructing a tree perfectly using distance information between pairs of vertices is given by the size of an observed separating vertex set. We then propose an algorithm to recover the tree structure using infection times, whose differences have means corresponding to the distance between two vertices. To improve the accuracy, we propose the concept of redundant vertices, which allows us to perform averaging to better estimate the distance between two vertices. Though the theory is developed mainly for trees, we demonstrate how the algorithm can be extended heuristically to general graphs. Simulation results suggest that our proposed algorithm performs better than some current state-of-the-art network reconstruction methods.
pp. 2508-2512
17:20 Statistical beamforming for the large antenna broadcast channel
Vasanthan Raghavan (Qualcomm, Inc., USA); Junil Choi (POSTECH, Korea); David Love (Purdue University, USA)
This paper studies the broadcast channel with M antennas at the base-station and M single antenna users. Most of the works in the literature assume perfect channel state information at both ends of each link. In this work, we assume that these links are spatially correlated and only the long-term statistical information corresponding to the covariance matrices of the links are available at both ends. We are interested in the design of beamforming vectors for data transmission to the M users to maximize the ergodic sum-rate obtained by treating interference as noise. In the simpler M = 2 setting, prior work has shown the optimality of a generalized eigenvector beamformer structure for this problem. However, these results are not easily extendable to the general M user setting. We overcome these difficulties by first establishing a tractable approximation for the ergodic sum-rate in terms of the beamforming vectors and covariance matrices that is surprisingly asymptotically tight in M. We then cast the sum-rate approximation maximization problem as a manifold optimization and illustrate the optimality of the generalized eigenvector structure in the general M user setting.
pp. 2513-2517
Quy Hong Le (Technische Universitaet Darmstadt, Germany); Hussein Al-Shatri and Anja Klein (TU Darmstadt, Germany)
pp. 2518-2522
18:00 Scalable Spectrum Allocation for Large Networks Based on Sparse Optimization
Binnan Zhuang (Samsung Semiconductor, Inc., USA); Dongning Guo, Ermin Wei and Michael Honig (Northwestern University, USA)
Joint allocation of spectrum and user association is considered for a large cellular network. The objective is to optimize a network utility function such as average delay given traffic statistics collected over a slow timescale. A key challenge is scalability: given $n$ Access Points (APs), there are $O(2^n)$ ways in which the APs can share the spectrum. The number of variables is reduced from $O(2^n)$ to $O(nk)$, where $k$ is the number of users, by optimizing over local overlapping neighborhoods, defined by interference conditions, and by exploiting the existence of sparse solutions in which the spectrum is divided into $k+1$ segments. We reformulate the problem by optimizing the assignment of subsets of active APs to those segments. An $\ell_0$ constraint enforces a one-to-one mapping of subsets to spectrum, and an iterative (reweighted $\ell_1$) algorithm is used to find an approximate solution. Numerical results for a network with 100 APs serving several hundred users show the proposed method achieves a substantial increase in total throughput relative to benchmark schemes.
pp. 2523-2527

#### Th4-7: Random Access Channels

Room: K6
Chair: Robert Calderbank (Duke University, USA)
16:40 A perspective on massive random-access
Yury Polyanskiy (MIT, USA)
This paper discusses the contemporary problem of providing multiple-access (MAC) to massive number of uncoordinated users. First, we define a random-access code for $K_a$-user Gaussian MAC to be a collection of norm-constrained vectors such that the noisy sum of any $K_a$ of them can be decoded with a given (suitably defined) probability of error. An achievability bound for existence of such codes is proposed and compared against popular practical solutions: ALOHA, coded slotted ALOHA, CDMA, and treating interference as noise. It is found out that as the number of users increases existing solutions become vastly energy-inefficient. Second, we discuss the asymptotic (in blocklength) problem of coding for a $K$-user Gaussian MAC when $K$ is proportional to blocklength and each user's payload is fixed. It is discovered that the energy-per-bit vs. spectral efficiency exhibits a rather curious tradeoff in this case.
pp. 2528-2532
17:00 Low Complexity Schemes for the Random Access Gaussian Channel
Or Ordentlich and Yury Polyanskiy (MIT, USA)
We consider an uncoordinated Gaussian multiple access channel with a relatively large number of active users within each block. A low complexity coding scheme is proposed, which is based on a combination of compute-and-forward and coding for a binary adder channel. For a wide regime of parameters of practical interest, the energy-per-bit required by each user in the proposed scheme is significantly smaller than that required by popular solutions such as slotted-ALOHA and treating interference as noise.
pp. 2533-2537
17:20 Multi-Cell Aware Opportunistic Random Access
Huifa Lin and Won-Yong Shin (Dankook University, Korea)
We propose a decentralized multi-cell aware opportunistic random access (MA-ORA) protocol that almost achieves the optimal throughput scaling in a $K$-cell random access network with one access point (AP) and $N$ users in each cell. Under our MA-ORA protocol, users opportunistically transmit with a predefined physical layer data rate in a decentralized manner if the desired signal power to the serving AP is sufficiently large and the generating interference power to other APs is sufficiently small. It is proved that the aggregate throughput scales as $\frac{K}{e}(1-\epsilon)\log(\text{SNR} \log N)$ in a high signal-to-noise ratio (SNR) regime if $N$ scales faster than $\text{SNR}^\frac{K-1}{1-\delta}$ for small constants $\epsilon,\delta>0$. Our analytical result is validated by computer simulations.
pp. 2538-2542
17:40 Multi-Channel Random Access with Replications
Olga Galinina (Tampere University of Technology, Finland); Andrey Turlikov (Saint-Petersburg State University of Aerospace Instrumentation, Russia); Sergey Andreev and Yevgeni Koucheryavy (Tampere University of Technology, Finland)
This paper considers a class of multi-channel random access algorithms, where contending devices may send multiple copies (replicas) of their messages to the central base station. We first develop a hypothetical algorithm that delivers a lower estimate for the access delay performance within this class. Further, we propose a feasible access control algorithm achieving low access delay by sending multiple message replicas, which potentially approaches the hypothetical case. The resulting performance is readily approximated by a simple lower bound, which is derived for a large number of channels.
pp. 2543-2547

#### Th4-8: Index Coding 1

Room: K7+8
Chair: Lawrence Ong (The University of Newcastle, Australia)
16:40 Private Broadcasting: an Index Coding Approach
Mohammed Karmoose (UCLA, USA); Linqi Song (University of California, Los Angeles, USA); Martina Cardone (University of Califonia, Los Angeles, USA); Christina Fragouli (UCLA, USA)
Using a broadcast channel to transmit clients' data requests may impose privacy risks. In this paper, we tackle such privacy concerns in the index coding framework. We show how a curious client can infer some information about the requests and side information of other clients by learning the encoding matrix used by the server. We propose an information-theoretic metric to measure the level of privacy and show how encoding matrices can be designed to achieve specific privacy guarantees. We then consider a special scenario for which we design a transmission scheme and derive the achieved levels of privacy in closed-form. We also derive upper bounds and we compare them to the levels of privacy achieved by our scheme, highlighting that an inherent trade-off exists between protecting privacy of the request and of the side information of the clients.
pp. 2548-2552
17:00 Golden-Coded Index Coding
Yu-Chih Huang (National Taipei University, Taiwan); Yi Hong and Emanuele Viterbo (Monash University, Australia)
We study the problem of constructing good space-time codes for broadcasting K independent messages over a MIMO network to L users, where each user demands all the messages and already has a subset of messages as side information. As a first attempt, we consider the 2x2 case and propose golden-coded index coding by partitioning the golden codes into K subcodes, one for each message. The proposed scheme is shown to have the property that for any side information configuration, the minimum determinant of the code increases exponentially with the amount of information contained in the side information.
pp. 2553-2557
17:20 Generalized Index Coding Problem and Discrete Polymatroids
Anoop Thomas and B. Sundar Rajan (Indian Institute of Science, India)
The index coding problem has been generalized recently to accommodate receivers which demand functions of messages and which possess functions of messages. The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids. For vector linear index codes discrete polymatroids which can be viewed as a generalization of the matroids was used. It was shown that a vector linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions. In this work we explore the connections between generalized index coding and discrete polymatroids. The conditions that needs to be satisfied by a representable discrete polymatroid for a generalized index coding problem to have a vector linear solution is established. From a discrete polymatroid we construct an index coding problem with coded side information and show that if the index coding problem has a certain optimal length solution then the discrete polymatroid satisfies certain properties. Furthermore, from a matroid we construct a similar generalized index coding problem and show that it has a binary scalar linear solution of optimal length if and only if the matroid is binary representable.
pp. 2558-2562
17:40 A Pliable Index Coding Approach to Data Shuffling
Linqi Song (University of California, Los Angeles, USA); Christina Fragouli (UCLA, USA); Tianchu Zhao (Tsinghua University, P.R. China)
A promising research area that has recently emerged, is on how to use index coding to improve the communication efficiency in distributed computing systems, especially for data shuffling in iterative computations. In this paper, we posit that pliable index coding can offer a more efficient framework for data shuffling, as it can better leverage the many possible shuffling choices to reduce the number of transmissions. We theoretically analyze pliable index coding under data shuffling constraints, and design an hierarchical data-shuffling scheme that uses pliable index coding as a component. We find benefits up to $O(ns/m)$ over index coding, where $ns/m$ is the average number of workers caching a message, and $m$, $n$, and $s$ are the numbers of messages, workers, and cache size, respectively.
pp. 2563-2567

#### Th4-9: Compression 2

Room: K9
Chair: Stefano Rini (National Chiao Tung University, Taiwan)
16:40 Fixed-Length-Parsing Universal Compression with Side Information
Yeohee Im and Sergio Verdú (Princeton University, USA)
This paper presents a fixed-length-parsing universal compression algorithm for settings where compressor and decompressor share the same side information. We prove the optimality of the algorithm for any stationary processes. Furthermore, strategies to modify the algorithm are suggested in order to lower the data compression rate.
pp. 2568-2572
17:00 Coding Theorems for the Compress and Estimate Source Coding Problem
Alon Kipnis (Stanford University, USA); Stefano Rini (National Chiao Tung University, Taiwan); Andrea Goldsmith (Stanford University, USA)
We consider the remote source coding setting in which a source realization is estimated from a lossy compressed sequence of noisy observations. Unlike in the optimal remote source coding problem, however, the encoder is bound to use good codes with respect to the observation sequence, i.e., codes that are optimal for the lossy reconstruction of the observation, rather than the remote source. This encoding strategy is denoted as the compress-and-estimate (CE) scheme. For the case of an i.i.d source observed through a memoryless channel, we show that the distortion in the CE scheme is characterized by a single-letter expression, referred to as the CE distortion-rate function (CE-DRF). In particular, we show that the CE-DRF can be attained by estimating the source from the output of a remote encoder employing any sequence of good codes with respect to the observation sequence. In addition, we show that the limiting distortion in estimating any finite sub-block of the source realization from the output of a remote encoder employing good codes, averaged over all sub-blocks, is also bounded by the CE-DRF.
pp. 2573-2577
17:20 Row-centric lossless compression of Markov images
Matthew G. Reyes and David L Neuhoff (University of Michigan, USA)
Motivated by the question of whether the recently introduced Reduced Cutset Coding (RCC) offers rate-complexity performance benefits over conventional context-based conditional coding for sources with two-dimensional Markov structure, this paper compares several row-centric coding strategies that vary in the amount of conditioning as well as whether a model or an empirical table is used in the encoding of blocks of rows. The conclusion is that, at least for sources exhibiting low-order correlations, 1-sided model-based conditional coding is superior to the method of RCC for a given constraint on complexity, and conventional context-based conditional coding is nearly as good as the 1-sided model-based coding.
pp. 2578-2582
17:40 A Practical Approach for Successive Omniscience
Ni Ding, Rodney Andrew Kennedy and Parastoo Sadeghi (The Australian National University, Australia)
The system that we study in this paper contains a set of users that observe a discrete memoryless multiple source and communicate via noise-free channels with the aim of attaining omniscience, the state that all users recover the entire multiple source. We adopt the concept of successive omniscience (SO), i.e., letting the local omniscience in some user subset be attained before the global omniscience in the entire system, and consider the problem of how to efficiently attain omniscience in a successive manner. Based on the existing results on SO, we propose a CompSetSO algorithm for determining a complimentary set, a user subset in which the local omniscience can be attained first without increasing the sum-rate, the total number of communications, for the global omniscience. We also derive a sufficient condition for a user subset to be complimentary so that running the CompSetSO algorithm only requires a lower bound, instead of the exact value, of the minimum sum-rate for attaining global omniscience. The CompSetSO algorithm returns a complimentary user subset in polynomial time. We show by example how to recursively apply the CompSetSO algorithm so that the global omniscience can be attained by multi-stages of SO.
pp. 2583-2587

Room: Europa

## Friday, June 30

### Friday, June 30, 08:30 - 09:30

#### FrP: Plenary Talk: Information Theory Out of its Box - Cédric Villani

Cédric Villani
Room: Europa
Chair: Stephan ten Brink (University of Stuttgart, Germany)

### Friday, June 30, 09:50 - 11:10

#### Fr1-1: Lattice Codes 2

Room: Europa
Chair: Robert F.H. Fischer (Ulm University, Germany)
09:50 On the Universality of Lattice Codes for a Class of Ergodic Fading Channels
Ahmed Hindy (University of Texas at Dallas, USA); Aria Nosratinia (University of Texas, Dallas, USA)
One of the main challenges of communication in the absence of transmitter channel knowledge is codebook universality, i.e., the existence of a single codebook that guarantees a given rate for all channel states. We address this problem for a class of ergodic fading multiple-input multiple-output (MIMO) channels, whose fading distribution is not necessarily isotropic. It is shown that a universal codebook drawn from a nested lattice code achieves the ergodic capacity to within a constant gap. Interestingly, the gap vanishes in some scenarios.
pp. 2588-2592
10:10 Index Mapping for Bit-error Resilient Multiple Description Lattice Vector Quantizer
This work addresses the construction of bit-error resilient multiple description lattice vector quantizers (MDLVQ) by proposing the design of a structured mapping $\gamma$ of side lattice points to binary indexes. We assume that the first description is correct while the second description may carry bit errors. To design the mapping $\gamma$ the set of side lattice points is first partitioned into Voronoi regions of an appropriate coarse lattice. Next a good channel code $C$ is selected, each Voronoi region is assigned a coset of this channel code and the side lattice points within each Voronoi region are mapped to binary sequences in the corresponding coset. We derive a lower bound on the error correction performance of the mapping $\gamma$ in terms of the performance of the code $C$ and we show that, as the rate of the MDLVQ grows to $\infty$, the mapping $\gamma$ becomes as good as the code $C$. Simulation results show the significant superiority of the proposed mapping versus random mappings.
pp. 2593-2597
10:30 On Shaping Complex Lattice Constellations from Multi-level Constructions
Perathorn Pooksombat (Mahidol University, Thailand); J Harshan (Advanced Digital Sciences Center, Singapore); Wittawat Kositwattanarerk (Mahidol University, Thailand)
Construction of lattices is known to have a strong connection to the study of classical linear codes over $\mathbb{F}_{2}$; one such celebrated construction is that of Barnes-Wall (BW) lattices over $\mathbb{Z}[i]$, with $i = \sqrt{-1}$, wherein a set of nested Reed-Muller codes when weighed over powers of the base $1+i$ results in the famous multi-level construction of BW lattices. Although such a construction facilitates simple encoding and decoding of information bits, the resulting set of codewords needs to be mapped onto their representatives in order to reduce the average energy of the lattice code. Drawing inspiration from the case of BW lattices, in this work, we address a general question of how to arrive at representatives of the codewords of a lattice code over $\mathbb{Z}[\theta]$, where $\theta$ is a quadratic integer, that is generated via a multi-level construction over linear codes over $\mathbb{F}_{q}$, for $q \neq 2$. In particular, we introduce a novel shaping function $\tau: \mathbb{Z}[\theta] \longmapsto \mathbb{Z}[\theta]$ on the components of lattice codewords, and prove that the natural constellation of lattices from multi-level constructions can be rearranged into a multi-dimensional cubic- or parallelepiped-shape under such a map. We show that our mapping results in a reduction of upto 29.82\% in average energy of lattice constellations. Our proposed mapping has applications in communications, particularly in encoding and decoding of lattice codes from multi-level constructions over $q$-ary linear codes for $q > 2$.
pp. 2598-2602
10:50 On the Design of Multi-Dimensional Irregular Repeat-Accumulate Lattice Codes
Min Qiu, Lei Yang, Yixuan Xie and Jinhong Yuan (University of New South Wales, Australia)
We propose and design the lattice codes with finite lattice constellations based on multi-dimensional (more than two dimensions) lattice partitions. The codes are constructed from non-binary irregular repeat-accumulate (IRA) codes. Most notably, we propose a novel encoding structure to ensure that the decoder's messages exhibit permutation-invariance and symmetry properties. With these two properties, the densities of the messages in our iterative decoder can be well modeled by Gaussian distributions described by a single parameter. Under the Gaussian approximation, extrinsic information transfer charts for our multi-dimensional IRA lattice codes are developed and used for analysing the convergence behaviour and optimising the decoding threshold. Simulation results show that our proposed lattice codes outperform the previously designed lattice codes with two-dimensional lattice partitions.
pp. 2603-2607

#### Fr1-2: Polar Codes 3

Room: Brussels
Chair: Peter Trifonov (Saint-Petersburg State Polytechnic University, Russia)
09:50 Performance Bounds of Concatenated Polar Coding Schemes
Dina Goldin and David Burshtein (Tel Aviv University, Israel)
A concatenated coding scheme using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first bound is obtained using outer codes which are typical linear codes from the ensemble of parity check matrices whose elements are chosen independently and uniformly. As a byproduct of this bound, it determines the required rate split of the total rate to the rates of the outer codes. A lower bound on the error exponent that holds for all BMS channels with a given capacity is then derived. Improved bounds and approximations for small blocklength codes are also obtained. The bounds are compared to actual simulation results from the literature.
pp. 2608-2612
Haewon Jeong (Carnegie Mellon University, USA); Christopher Blake (University of Toronto, USA); Pulkit Grover (Carnegie Mellon University, USA)
It is now well known that using a long and complicated error correcting code (ECC) designed for the worst-case error probability requirement wastes excessive total system energy (transmit + circuit energy) when the error probability requirement is much higher than the worst case. We propose a novel adaptive polar coding strategy that adjusts the decoder circuit to consume minimal decoding circuit energy at each given target error requirement. By combining Thompson's VLSI theory and scaling analysis of polar codes, we provide upper bounds on energy, area, and time complexity of polar decoding circuits in terms of target block error probability. The upper bounds are derived from an explicit construction of decoder circuit based on mesh-network structure. Comparison of the upper bounds for non-adaptive polar coding and our proposed adaptive polar coding showed that the adaptive coding strategy has a scaling-sense gain in decoding energy with little circuit area overhead when there is a large gap between the worst-case and typical target error rate requirements.
pp. 2613-2617
10:30 Polar codes with a stepped boundary
Ilya Dumer (University of California at Riverside, USA)
We design polar codes of blocklength $n\rightarrow\infty$ and code rate $R\rightarrow1$ that achieve the vanishing output error rates on the binary symmetric channels with transition error probability $p\rightarrow0$. These codes have a substantially smaller redundancy order $(1-R)n$ than do other known high-rate codes, such as Reed-Muller (RM) or BCH codes. The construction is explicit and has complexity of order $n\log n$. We also design asymptotically optimal low-rate codes that achieve the vanishing output error rates if $\ p\rightarrow1/2.$
pp. 2618-2622
10:50 Permuted Successive Cancellation Decoding for Polar Codes
Sarit Buzaglo (UCSD, USA); Arman Fazeli, Veeresh Taranalli and Paul H. Siegel (University of California, San Diego, USA); Alexander Vardy (University of California San Diego, USA)
Defined through a certain $2\times 2$ matrix called Arikan's kernel, polar codes are known to achieve the symmetric capacity of binary-input discrete memoryless channels under the successive cancellation (SC) decoder. Yet, for short block-lengths, polar codes fail to deliver a compelling performance under the low complexity SC decoding scheme. Recent studies provide evidence for improved performance when Arikan's kernel is replaced with larger kernels that have smaller scaling exponents. However, for $\ell\times \ell$ kernels the time complexity of the SC decoding increases by a factor of $2^{\ell}$. In this paper we study a special type of kernels called \emph{permuted kernels}. The advantage of these kernels is that the SC decoder for the corresponding polar codes can be viewed as a permuted version of the SC decoder for the conventional polar codes that are defined through Arikan's kernel. This permuted successive cancellation (PSC) decoder outputs its decisions on the input bits according to a permuted order of their indices. We introduce an efficient PSC decoding algorithm and show simulations for two $16\times 16$ permuted kernels that have better scaling exponents than Arikan's kernel.
pp. 2623-2627

#### Fr1-3: Multiple Access 3

Room: K2
Chair: Young-Han Kim (UCSD, USA)
09:50 On the Degrees of Freedom of Wide-Band Multi-Cell Multiple Access Channels With No CSIT
Yo-Seb Jeon and Namyoon Lee (POSTECH, Korea); Ravi Tandon (University of Arizona, USA)
This paper considers a K-cell multiple access channel with inter-symbol interference (ISI). The primary finding of this paper is that, without instantaneous channel state information at a transmitter, the interference-free sum degrees of freedom of K is asymptotically achievable when the number of users per cell is sufficiently large, and also when the number of channel-impulse-response taps of desired links is greater than that of interfering links. This achievability is shown by a blind interference management method that exploits the relativity in delay spreads between desired and interfering links.
pp. 2628-2632
10:10 Low-Density Code-Domain NOMA: Better Be Regular
Ori Shental (Bell Labs, USA); Benjamin M. Zaidel (Bar-Ilan University, Israel); Shlomo (Shitz) Shamai (The Technion, Israel)
A closed-form analytical expression is derived for the limiting empirical squared singular value density of a channel transfer matrix corresponding to sparse low-density code-domain (LDCD) non-orthogonal multiple-access (NOMA) with regular random user-resource allocation. The derivation relies on associating the channel transfer matrix with the adjacency matrix of a large semiregular bipartite graph. For a simple repetition-based sparse spreading scheme, the result directly follows from a rigorous analysis of spectral measures of infinite graphs. Turning to random (sparse) binary spreading, we harness the cavity method from statistical physics, and show that the limiting spectral density coincides in both cases. This result is then used to compute the normalized input-output mutual information of the underlying vector channel in the large-system limit. The latter may be interpreted as the achievable total throughput per dimension with optimum processing in a corresponding multiple-access channel setting or, alternatively, in a fully-symmetric broadcast channel setting with full decoding capabilities at each receiver. Surprisingly, the total throughput of regular LDCD-NOMA is found to be not only superior to that achieved with irregular user-resource allocation, but also to the total throughput of dense randomly-spread NOMA, for which optimum processing is computationally intractable. In contrast, the superior performance of regular LDCD-NOMA can be potentially achieved with a feasible message-passing algorithm. This observation may advocate employing regular, rather than irregular, LDCD-NOMA in 5G cellular physical layer design.
pp. 2633-2637
10:30 Capacity Region of a One-Bit Quantized Gaussian Multiple Access Channel
Borzoo Rassouli and Deniz Gündüz (Imperial College London, United Kingdom (Great Britain)); Morteza Varasteh (Imperial College, United Kingdom (Great Britain))
The capacity region of a two-transmitter Gaussian multiple access channel (MAC) under average input power constraints is studied, when the receiver employs a zero-threshold one-bit analog-to-digital converter (ADC). It is proved that the input distributions that achieve the boundary points of the capacity region are discrete. Based on the position of a boundary point, upper bounds on the number of the mass points of the corresponding distributions are derived. Finally, a conjecture on the sufficiency of $K$ mass points in a point-to-point real AWGN with a $K$-bin ADC front end (no matter symmetric or asymmetric) is settled.
pp. 2638-2642
10:50 On OR Many-Access Channels
Wenyi Zhang and Lingyan Huang (University of Science and Technology of China, P.R. China)
OR multi-access channel is a simple model where the channel output is the Boolean OR among the Boolean channel inputs. We revisit this model, showing that employing Bloom filter, a randomized data structure, as channel inputs achieves its capacity region with joint decoding and the symmetric sum rate of $\ln 2$ bits per channel use without joint decoding. We then proceed to the many-access'' regime where the number of potential users grows without bound, treating both activity recognition and message transmission problems, establishing scaling laws which are optimal within a constant factor, based on Bloom filter channel inputs.
pp. 2643-2647

#### Fr1-4: Information Retrieval

Room: K3
Chair: Eitan Yaakobi (Technion, Israel)
09:50 Improved Codes for List Decoding in the Levenshtein's channel and Information Retrieval
Tero K Laihonen and Tuomo Lehtilä (University of Turku, Finland)
In this paper, we consider $t$-revealing codes in the binary Hamming space. Let $C$ be a code and denote by $I_t(C;x)$ the set of elements of $C$ which are within (Hamming) distance $t$ from a word $x$. A code $C$ is called $t$-revealing if the majority voting on the coordinates of the words in $I_t(C;\boldsymbol{x})$ gives unambiguously $\boldsymbol{x}$. These codes have applications, for instance, to the list decoding problem of the Levenshtein's channel model, which is relevant for recent advanced storage technologies, and to the information retrieval problem of the Yaakobi-Bruck model of associative memories. We give $t$-revealing codes which improve some of the key parameters for these applications compared to earlier code constructions, namely, the length of the output list of the decoder and the maximal number of input clues needed for information retrieval.
pp. 2648-2652
10:10 Binary, Shortened Projective Reed Muller Codes for Coded Private Information Retrieval
Myna Vajha and Vinayak Ramkumar (Indian Institute of Science, India); P Vijay Kumar (Indian Institute of Science & University of Southern California, India)
The notion of a Private Information Retrieval (PIR) code was recently introduced by Fazeli, Vardy and Yaakobi who showed that this class of codes permit PIR at reduced levels of storage overhead in comparison with replicated-server PIR. In the present paper, the construction of an $(n,k)$ $\tau$-server binary, linear PIR code having parameters $n = \sum\limits_{i = 0}^{\ell} {m \choose i}$, $k = {m \choose \ell}$ and $\tau = 2^{\ell}$ is presented. These codes are obtained through homogeneous-polynomial evaluation and correspond to the binary, Projective Reed Muller (PRM) code. The construction can be extended to yield PIR codes for any $\tau$ of the form $2^{\ell}$, $2^{\ell}-1$ and any value of $k$, through a combination of single-symbol puncturing and shortening of the PRM code. Each of these code constructions above, have smaller storage overhead in comparison with other PIR codes appearing in the literature. For the particular case of $\tau=3,4$, we show that the codes constructed here are optimal, systematic PIR codes by providing an improved lower bound on the block length $n(k, \tau)$ of a systematic PIR code. It follows from a result by Vardy and Yaakobi, that these codes also yield optimal, systematic primitive multiset $(n, k, \tau)_B$ batch codes for $\tau=3,4$. The PIR code constructions presented here also yield upper bounds on the generalized Hamming weights of binary PRM codes.
pp. 2653-2657
10:30 Sparse Ternary Codes for similarity search have higher coding gain than dense binary codes
Sohrab Ferdowsi, Sviatoslav Voloshynovskiy, Dimche Kostadinov and Taras Holotyak (University of Geneva, Switzerland)
This paper addresses the problem of Approximate Nearest Neighbor (ANN) search in pattern recognition where feature vectors in a database are encoded as compact codes in order to speed-up the similarity search in large-scale databases. Considering the ANN problem from an information-theoretic perspective, we interpret it as an encoding, which maps the original feature vectors to a less entropic sparse representation while requiring them to be as informative as possible. We then define the coding gain for ANN search using information-theoretic measures. We next show that the classical approach to this problem, which consists of binarization of the projected vectors is sub-optimal. Instead, a properly designed ternary encoding achieves higher coding gains and lower complexity.
pp. 2658-2662
10:50 PIR Array Codes with Optimal PIR Rates
Tuvi Etzion (Technion-Israel Institute of Technology, Israel); Simon R Blackburn (Royal Holloway University of London, United Kingdom (Great Britain))
There has been much recent interest in Private information Retrieval (PIR) in models where a database is stored across several servers using coding techniques from distributed storage, rather than being simply replicated. In particular, a recent breakthrough result of Fazelli, Vardy and Yaakobi introduces the notion of a PIR code and a PIR array code, and uses this notion to produce efficient protocols. In this paper we are interested in designing PIR array codes. We consider the case when we have $m$ servers, with each server storing a fraction $(1/s)$ of the bits of the database; here $s$ is a fixed rational number with $s > 1$. We study the maximum PIR rate of a PIR array code with the $k$-PIR property (which enables a $k$-server PIR protocol to be emulated on the $m$ servers), where the PIR rate is defined to be $k/m$. We present upper bounds on the achievable rate, some constructions, and ideas how to obtain PIR array codes with the highest possible PIR rate. In particular, we present constructions that asymptotically meet our upper bounds, and the exact largest PIR rate is obtained when $1 < s \leq 2$.
pp. 2663-2667

#### Fr1-5: Information Dynamics

Room: K4
Chair: Anant Sahai (UC Berkeley, USA)
09:50 The Capacity of Unstable Dynamical Systems-Interaction of Control and Information Transmission
Ioannis Tzortzis, Charalambos D Charalambous and Christos K Kourtellaris (University of Cyprus, Cyprus); Sergey Loyka (University of Ottawa, Canada)
The extremum problem of maximizing directed information from inputs to outputs of dynamical systems, not necessarily stationary or ergodic, which may correspond to unstable control systems or unstable communication channels, over conditional distributions with feedback, subject to an average cost constraint of total power $\kappa \in [0,\infty)$ is investigated. It is shown that optimal conditional distributions, which for communication channels correspond to channel input distributions, and for control systems correspond to randomized control strategies, have a dual role, to simultaneously control the output process and to encode information. The dual role is due to the interaction of control and information transmission; it states that encoders in communication channels operate as encoders-controllers, while controllers in control systems operate as a controllers-encoders. Through the analysis of Gaussian linear control systems with randomized strategies, which are equivalent to Additive Gaussian Noise channels, {\it Stable or Unstable}, with arbitrary memory on past outputs, with an average constraint of quadratic form, it is shown that unstable dynamical systems have {\it Control-Coding Capacity} which is operational, precisely as in Shannon's operational definition. However, the control-coding capacity is zero, unless the power $\kappa$ allocated to the system, exceeds a threshold $\kappa_{min}$, where $\kappa_{min}$ is the minimum cost of ensuring asymptotic stability and ergodicity. The excess power $\kappa-\kappa_{min}$ is turned into an achievable rate of information transmission over the dynamical system.
pp. 2668-2672
10:10 Optimal Quantizations of B-DMCs Maximizing $\alpha$-Mutual Information with Monge Property
Yuta Sakai and Ken-ichi Iwata (University of Fukui, Japan)
This study examines quantizations for outputs of binary-input discrete memoryless channels (B-DMCs) by concatenating its output with another DMC, so-called a quantizer. As an objective function of channel quantizations, we employ the $\alpha$-mutual information of a B-DMC, which connects to more powerful coding theorem than the ordinary mutual information. Showing a Monge property of the $\alpha$-mutual information, we propose an optimal quantizer design algorithm for given B-DMC in polynomial time complexity with respect to the output alphabet size and the quantized level. Since the proposed method employs the SMAWK algorithm due to the Monge property, our algorithm is faster than a naive dynamic programming.
pp. 2673-2677
10:30 Information and estimation in Fokker-Planck channels
Andre Wibisono (University of Wisconsin-Madison, USA); Varun Jog (University of Wisconsin - Madison, USA); Po-Ling Loh (University of Wisconsin-Madison, USA)
We study the relationship between information- and estimation-theoretic quantities in time-evolving systems. We focus on the Fokker-Planck channel defined by a general stochastic differential equation, and show that the time derivatives of entropy, KL divergence, and mutual information are characterized by estimation-theoretic quantities involving an appropriate generalization of the Fisher information. Our results vastly extend De Bruijn's identity and the classical I-MMSE relation.
pp. 2678-2682
10:50 Dynamical Systems, Ergodicity, and Posterior Matching
Todd Coleman (UCSD, USA)
The Posterior Matching (PM) scheme is a mutual information maximizing scheme for efficiently communicating a message point in a continuum over a noisy channel, by utilizing the feedback after each channel use. It was originally developed when the message point was on a subset of the real line, and more recently we have generalized the framework to arbitrary dimensions. We consider a wide class of encoder dynamical systems and demonstrate a necessary condition for reliability, the measurability of the message point with respect to the infinite sequence of observations, to involve invertibility of a dynamical system. This justifies the use of optimal transport theory to construct diffeomorphism based encoders that allow for this. Next, we show that the ergodicity of the aforementioned dynamical system state variable is a necessary and sufficient condition for posterior matching to be reliable. Lastly, we show a surprising all or nothing'' result: this same condition is necessary and sufficient to achieve capacity.
pp. 2683-2687

#### Fr1-6: Coding for Insertion and Deletion Channels 2

Room: K5
Chair: Vahid Aref (Nokia Bell Labs, Germany)
09:50 Asymptotically Optimal Sticky-Insertion-Correcting Codes with Efficient Encoding and Decoding
Hessam Mahdavifar (University of Michigan, USA); Alexander Vardy (University of California San Diego, USA)
The problem of constructing sticky-insertion-correcting codes with efficient encoding and decoding is considered. An $(n,M,r)$ sticky-insertion-correcting code consists of $M$ codewords of length $n$ such that any pattern of up to $r$ sticky insertions can be corrected. We utilize BCH codes and their analogous in the Lee space to construct explicit and systematic codes that are immune to up to $r$ sticky insertions. It is shown that the ratio of the number of constructed redundancy bits in the construction to a certain upper bound approaches one as the block length grows large, which implies the optimality of the construction.
pp. 2688-2692
10:10 Permutation Codes Correcting a Single Burst Deletion II: Stable Deletions
Yeow Meng Chee (Nanyang Technological University, Singapore); San Ling (NTU, Singapore); Tuan Thanh Nguyen, Van Khu Vu and Hengjia Wei (Nanyang Technological University, Singapore)
We construct permutation codes capable of correcting bursts of stable deletions. For correcting a single burst of exactly $s$ stable deletions, our code has size $\dfrac{sn!}{((2s)!n)^2}$, while the upper bound is $\dfrac{n!}{s!(n-s+1)}$.We also construct permutation codes for the cases of single burst of up to $s$ stable deletions, and up to $b$ bursts of at most $s$ stable deletions each.
pp. 2693-2697
10:30 Guess & Check Codes for Deletions and Synchronization
Serge Kas Hanna and Salim El Rouayheb (Illinois Institute of Technology, USA)
We consider the problem of constructing codes that can correct $\delta$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions $(\delta=1)$ with an asymptotically optimal redundancy. Finding similar codes for $\delta \geq 2$ deletions is an open problem. We propose a new family of codes, that we call Guess \& Check (GC) codes, that can correct, with high probability, a constant number of deletions $\delta$ occurring at uniformly random positions within an arbitrary string. The GC codes are based on MDS codes and have an asymptotically optimal redundancy that is $\Theta(\delta \log n)$. We provide deterministic polynomial time encoding and decoding schemes for these codes. We also describe the applications of GC codes to file synchronization.
pp. 2698-2702
10:50 On Unique Decoding from Insertion Errors
Kayvon Mazooji (UCLA, USA)
For any code, the set of received words generated by insertion errors is infinitely large. We prove that infinitely many of these words are uniquely decodable. We proceed to analyze how often unique decoding from insertions occurs for arbitrary codes. These questions are relevant because insertion errors frequently occur in synchronization and DNA, a medium which is beginning to be used for long term data storage. For a codeword $c$ of length $n,$ we are interested in two particular measures. The first is the probability of uniquely decoding when $t$ insertions occur, if each distinct length $n+t$ received word is output with equal probability. The second is the probability of uniquely decoding when $t$ sequential insertions occur, and each insertion position and element are selected uniformly at random. This paper attempts to better understand the behavior of the measures for arbitrary codewords, placing a particular emphasis on limiting behavior as $t$ or $n$ increases. Our most substantial contribution is the derivation of upper bounds on both measures, which are mathematically related to Levenshtein's reconstruction problem.
pp. 2703-2707

#### Fr1-7: Security 6

Room: K6
Chair: Oliver Kosut (Arizona State University, USA)
09:50 Characterizing Optimal Security and Round-Complexity for Secure OR Evaluation
Amisha Jhanji, Hemanta K Maji and Raphael Meyer (Purdue University, USA)
Secure multi-party computation allows mutually distrusting parties to compute securely over their private data. However, even in the semi-honest two-party setting, most interesting functions cannot be computed securely in the information-theoretic plain model. Intuitively, the objective of accurately evaluating the output of such functions is inherently inimical to the privacy concerns of the parties. Securely evaluating OR of the input bits of two parties is the simplest example, and this result captures the essence of the hardness in securely evaluating most functions. This work studies the interplay between accuracy and privacy of secure 2-party function evaluation in the information-theoretic plain model. We provide an optimal accuracy versus privacy tradeoff for computing OR(x,y), where x and y are, respectively, the private input bits of Alice and Bob. In particular, we construct a round-optimal two-party protocol for OR that has maximum semi-honest security in the information-theoretic plain model. Prior results exhibit only weak tradeoffs that are far from the optimal. We generalize our techniques to obtain a tight accuracy-versus-privacy tradeoff characterization for a stronger notion of security, namely differentially-private semi-honest security. The technical heart of our result is a new technique to derive inequalities for distributions of transcripts generated by protocols. This approach reduces the domain of the optimization problem from an unbounded number of transcripts to a constant size while preserving the optimal solution to the original problem. We believe that these techniques for analyzing protocols in the information-theoretic plain model will be of independent interest.
pp. 2708-2712
10:10 Learning Adversary's Actions for Secret Communication
Mehrdad Tahmasbi and Matthieu Bloch (Georgia Institute of Technology, USA); Aylin Yener (Pennsylvania State University, USA)
We analyze the problem of secure communication over a wiretap channel with an active adversary, in which the legitimate transmitter has the opportunity to sense and learn the adversary's actions. Specifically, the adversary has the ability to switch between two channels and to observe the corresponding output at every channel use; the encoder, however, has causal access to a degraded and noisy version of the attacker's observations. We develop a joint learning/transmission coding scheme that allows the legitimate users to exploit their ability to learn to adapt to the adversary's actions. For some channel models, we show that the achievable rates, which we define precisely, are arbitrarily close to those obtained with hindsight if the transmitter had known the actions ahead of time. This suggests that there is much to exploit and gain in physical-layer security by monitoring the environment.
pp. 2713-2717
10:30 On the Equivalency of Reliability and Security Metrics for Wireline Networks
Mohammad mahdi Mojahedian and Amin Gohari (Sharif University of Technology, Iran); Mohammad Reza Aref (Sharif University of Tech., Iran)
In this paper, we show the equivalency of weak and strong secrecy conditions for a large class of secure network coding problems. When we restrict to linear operations, we show the equivalency of "perfect secrecy with zero-error constraint" and "weak secrecy with $\epsilon$-error constraint".
pp. 2718-2722
10:50 A code-based blind signature
Olivier Blazy (University of Limoges, France); Philippe Gaborit (Universite de Limoges, France); Julien Schrek (Limoges University, France); Nicolas Sendrier (INRIA, France)
In this paper we give the first blind signature protocol for code-based cryptography. Our approach is different from the classical original RSA based blind signature scheme, it is done in the spirit of the Fischlin approach [7] which is based on proofs of knowledge. To achieve our goal we consider a new tool for zero-knowledge (ZK) proofs, the Concatenated Stern ZK protocol, which permits to obtain an authentication protocol for concatenated matrices. A signature is then obtained from the usual Fiat-Shamir heuristic. We describe our blind signature protocol for cryptography based on Hamming metric and show how it can be extended to rank based cryptography. The security of our blind protocol is based on the security of a trapdoor function for the syndrome decoding problem: the CFS signature scheme for Hamming distance and on the more recent RankSign protocol for rank metric. We give proofs in the random oracle model (ROM) for our blind signature scheme, which rely on the Syndrome Decoding problem. The parameters we obtain for our protocol are practical for rank metric (200kBytes) for the signature length and 15kBytes for public key size) and a little less practical for Hamming distance.
pp. 2723-2727

#### Fr1-8: Multiple Access

Room: K7+8
Chair: Richard Wesel (University of California, Los Angeles, USA)
09:50 Asymptotic Analysis of Tone Reservation Method for the PAPR Reduction of CDMA Systems
Holger Boche (Technical University Munich, Germany); Ezra Tampubolon (Technische Universität München, Germany)
The high peak value of the transmission signal of wireless communication systems lead to wasteful energy consumption and degradation of several transmission performances. We continue the theoretical contributions made in [1], [2] towards the understanding of tone reservation method for orthogonal transmission schemes. There it was shown that the combinatorial object called arithmetic progression plays an important role in setting limitations for the applicability of the tone reservation method for OFDM system. In this work, we introduce the combinatorial object called perfect Walsh sum (PWS), playing a similar role for CDMA systems as arithmetic progression for OFDM systems. We show that for a given $m,n\in\mathbb{N}$ and $\delta\in (0,1)$, every subset $\mathcal{I}$ of the set $[N]$ of the first $N=2^n$ numbers, which fulfills $|\mathcal{I}|/N\geq\delta$ and $|\mathcal{I}|\geq 2(2/\delta)^{2^{m}-1}$, contains a PWS of size $2^{m}$. Consequences of the latter are results analogous to the famous Szemer\'edi Theorem on arithmetic progressions, Conlon-Gower's Theorem on probabilistic construction of "sparse" sets containing an arithmetic progression, and even a solution of Erdős' conjecture on arithmetic progressions. Those results give in particular an insight into the asymptotic behaviour of tone reservation method for CDMA systems.
pp. 2728-2732
10:10 Spatial random multiple access with multiple departure
Serguei Foss (Heriot-Watt University, United Kingdom (Great Britain)); Andrey Turlikov (Saint-Petersburg State University of Aerospace Instrumentation, Russia); Maxim Grankin (Saint Petersburg State University of Aerospace Instrumentation & Quantenna Communications, Russia)
We introduce a new model of spatial random multiple access systems with a non-standard departure policy: all arriving messages are distributed uniformly on a finite sphere in the space, and when a successful transmission of a single message occurs, the transmitted message leaves the system together with all its neighbours within a ball of a given radius centred at the message's location. We consider three classes of protocols: centralised protocols and decentralised protocols with either ternary or binary feedback; and analyse their stability. Further, we discuss some asymptotic properties of stable protocols
pp. 2733-2736
10:30 Coded Random Access Design for Constrained Outage
MohammadReza Ebrahimi (University of Tehran, Iran); Farshad Lahouti (Caltech Institute of Techlonogy, USA); Victoria Kostina (California Institute of Technology, USA)
The emergence of networks of many devices in the context of cyber-physical systems motivates novel solutions for communication over random access channels. Currently deployed random access protocols attempt to avoid collisions, and target the performance of a scheduled multiple access system (a strategy known to be only suboptimal from the information-theoretic perspective). In contrast, in this paper, we allow collisions among the transmissions of different users. We consider code design for random access channels with erasures in which the number of users in each frame is unknown at the transmitters but known at the receiver, and we present a two-layer coding architecture for joint contention resolution and erasure correction.For random LDPC codes based on this scheme, the density evolution is asymptotically analyzed, which enables optimized code design for maximized throughput with constrained outage. The results demonstrate that the proposed low-complexity scheme approaches the outage capacity of the random access channel with erasures when the average number of active users is small.
pp. 2737-2741

#### Fr1-9: Channel Identification

Room: K9
Chair: Kenta Kasai (Tokyo Institute of Technology, Japan)
09:50 On Optimal Error Exponents in Noiseless Channel Identification
Marat V Burnashev (Institute for Information Transmission Problems, Russian Academy of Sciences, Russia); Hirosuke Yamamoto (The University of Tokyo, Japan)
Recently Yamamoto and Ueda proposed multiple object identification (MOID) codes to identify multiple objects via a channel at once, which is an extension of identification (ID) codes. They gave the explicit construction of MOID codes and derived the achievable triplet of coding rate $R$, the error exponents $E_1$ and $E_2$ of type I and type II decoding error probabilities. However, they did not treat the converse problem of the coding theorem. In this paper, we consider the coding rate of multiple objects $R_K$ in addition to $R$, $E_1$, and $E_2$, and derive a condition that $(R, R_K, E_1, E_2)$ must satisfy for any MOID codes of noiseless channels.
pp. 2742-2745
10:10 Channel Resolvability Theorems for General Sources and Channels
Hideki Yagi (University of Electro-Communications, Japan)
In the problem of channel resolvability, where a given output probability distribution via a channel is approximated by transforming the uniform random numbers, characterizing the asymptotically minimum rate of the size of the random numbers, called the channel resolvability, has been open. In this paper, we derive a general formula for the channel resolvability for a given general source and channel pair. We also investigate the channel resolvability in an optimistic sense. It is demonstrated that the derived general formulas recapture a single-letter formula for the stationary memoryless source and channel. The established formulas reduce to an alternative form of sup-spectral entropy rates which often appear in the information spectrum methods when the channel is the identity mapping.
pp. 2746-2750
10:30 Hierarchical Identification with Pre-processing
Minh Thanh Vu and Tobias J. Oechtering (KTH Royal Institute of Technology); Mikael Skoglund (KTH Royal Institute of Technology, Sweden)
We study a two-stage identification problem with pre-processing to enable efficient data retrieval and reconstruction. The first stage outputs a list of compatible users to the second stage which uses it to return the exact user identity with a corresponding reconstruction sequence. The rate- distortion region is characterized. A connection to a two observer identification problem is also studied.
pp. 2751-2755
10:50 Mismatched Identification via Channels
Anelia Somekh-Baruch (Bar-Ilan University, Israel)
The problem of identification via channels concerns a decoder that needs to provide a reliable answer to the question of whether or not a specific message (unknown in advance) was transmitted. The achievability result of Ahlswede and Dueck who introduced this problem, relied on a {\it universal} identification decoder. This decoder assigns a channel output vector $y^n$ to a decision region ${\cal D}_m$ if the empirical mutual information between $y^n$ and an input vector that could have been transmitted given message $m$ exceeds a certain threshold. We study a generalized class of identification decoders that determine the decision regions by comparing a type-dependent metric" to a threshold. We introduce the notion of identification capacity with respect to a given decoding metric as the supremum of achievable normalized iterated logarithm of the number of messages that can be identified reliably using these metrics. We characterize achievable identification rates and error exponents using a type-dependent metric. In the case of an additive metric we show that the random coding achievable rate for classical mismatched decoding is an achievable identification rate.
pp. 2756-2760

### Friday, June 30, 11:30 - 12:50

#### Fr2-1: Rank Metric Codes

Room: Europa
Chair: Sven Puchinger (Ulm University, Germany)
11:30 On Decoding Rank-Metric Codes over Large Fields
Ron M. Roth (Technion, Israel)
A decoding algorithm is presented for rank-metric array codes that are based on diagonal interleaving of MDS codes. W.r.t. this metric, such array codes are known to be optimal when the underlying field is algebraically closed. It is also shown that for any list decoding radius that is smaller than the minimum rank distance, the list size can be bounded from above by an expression that is independent of the field.
pp. 2761-2765
11:50 Universal secure rank-metric coding schemes with optimal communication overheads
Umberto Martínez-Peñas (Aalborg University, Denmark)
We study the problem of reducing the communication overhead from a wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to universal secure linear network coding and secure distributed storage with crisscross erasures. Our main contribution is a method to transform coding schemes based on linear rank-metric codes, with certain properties, to schemes with lower communication overheads. By applying this method to pairs of Gabidulin codes, we obtain coding schemes with optimal information rate with respect to their security and rank error correction capability, and with universally optimal communication overheads, when $n \leq m$, being $n$ and $m$ the number of columns and number of rows, respectively. Moreover, our method can be applied to other families of maximum rank distance codes when $n > m$. The downside of the method is generally expanding the packet length, but some practical instances come at no cost.
pp. 2766-2770
12:10 MRD Rank Metric Convolutional Codes
Diego Napp and Raquel Pinto (University of Aveiro, Portugal); Joachim Rosenthal (University of Zurich, Switzerland); Paolo Vettori (University of Aveiro, Portugal)
So far, in the area of Random Linear Network Coding, attention has been given to the so-called one-shot network coding, meaning that the network is used just once to propagate the information. In contrast, one can use the network more than once to spread redundancy over different shots. In this paper, we propose rank metric convolutional codes for this purpose. The framework we present is slightly more general than the one which can be found in the literature. We introduce a rank distance, which is suitable for convolutional codes, and derive a new Singleton-like upper bound. Codes achieving this bound are called Maximum Rank Distance (MRD) convolutional codes. Finally, we prove that this bound is optimal by showing a concrete construction of a family of MRD convolutional codes.
pp. 2771-2775
12:30 A decoding algorithm for Twisted Gabidulin codes
Tovohery Randrianarisoa and Joachim Rosenthal (University of Zurich, Switzerland)
In this work, we modify the decoding algorithm for subspace codes by Kötter and Kschischang to get a decoding algorithm for (generalized) twisted Gabidulin codes. The decoding algorithm we present applies to cases where the code is linear over the base field $\mathbb{F}_q$ but not linear over $\mathbb{F}_{q^n}$.
pp. 2776-2779

#### Fr2-2: Iterative Decoding 2

Room: Brussels
Chair: Yuval Cassuto (Technion, Israel)
11:30 An Iterative Soft-decision Decoding Algorithm for Reed-Solomon Codes
Huang Chang Lee (Chang Gung University, Taiwan); Jyun-Han Wu and Yeong-Luh Ueng (National Tsing Hua University, Taiwan); Chung-Hsuan Wang (National Chiao Tung University, Taiwan)
This paper proposes an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes. The proposed decoding algorithm combines the concepts of adapting the parity-check matrix and informed dynamic scheduling decoding. The parity-check matrix is re-arranged before each iteration, where the systematic part is mapped to the least reliable bits, consequently reducing their influence on the other bits. Using dynamic scheduling, the more important decoding messages are updated to these least reliable bits, meaning that the majority of the error bits with low reliability can be corrected. When the proposed integrated decoding is applied to (255, 239) RS code, the difference between its frame error rate performance (FER) and the maximum-likelihood (ML) bound can be reduced to 0.8 dB, and a gain of about 0.1 dB is achieved compared to all the previously recorded soft-decision decoding for RS codes.
pp. 2780-2784
11:50 Decoding from Pooled Data: Phase Transitions of Message Passing
Ahmed El Alaoui (UC Berkeley, USA); Aaditya Ramdas (University of California, Berkeley, USA); Florent Krzakala (Ecole Normale Superieure, France); Lenka Zdeborova (Institut de Physique Theorique IPhT, CEA Saclay and CNRS, France); Michael Jordan (UC Berkeley, USA)
We consider the problem of decoding a discrete signal of categorical variables from the observation of several histograms of pooled subsets of it. We present an Approximate Message Passing (AMP) algorithm for recovering the signal in the \emph{random dense} setting where each observed histogram involves a random subset of size proportional to $n$ of entries. We characterize the performance of the algorithm in the asymptotic regime where the number of observations $m$ tends to infinity proportionally to $n$, by deriving the corresponding State Evolution (SE) equations and studying their dynamics. We initiate the analysis of the multi-dimensional SE dynamics by proving their convergence to a fixed point, along with some further properties of the iterates. The analysis reveals sharp phase transition phenomena where the behavior of AMP changes from exact recovery to weak correlation with the signal as $m/n$ crosses a threshold. We derive formulae for the threshold in some special cases and show that they accurately match experimental behavior.
pp. 2785-2789
12:10 Topological Interference Management with Decoded Message Passing: A Polyhedral Approach
Xinping Yi and Giuseppe Caire (Technische Universität Berlin, Germany)
We consider the topological interference management problem with decoded message passing (TIM-MP) using a polyhedral approach. The TIM-MP problem studies partially-connected interference networks with no channel state information except for the network topology (i.e., connectivity graph) at the transmitters, while the decoded messages at the receivers can be routed to other receivers via backhaul links to help cancel interference. With the aid of polyhedral combinatorics, we identify the structural properties of certain classes of network topologies where orthogonal access achieves the optimal degrees-of-freedom (DoF) region in the information-theoretic sense. We are also able to prove the linear optimality of orthogonal access in terms of symmetric DoF for the networks up to four users with all possible network topologies (218 instances).
pp. 2790-2794

#### Fr2-3: Coded Caching 2

Room: K2
Chair: Petros Elia (EURECOM, France)
11:30 Decentralized Caching and Coded Delivery over Gaussian Broadcast Channels
Mohammad Mohammadi Amiri and Deniz Gündüz (Imperial College London, United Kingdom (Great Britain))
A cache-aided $K$-user Gaussian broadcast channel (BC) is considered. The transmitter has a library of $N$ equal-rate files, from which each user demands one. The impact of the equal-capacity receiver cache memories on the minimum required transmit power to satisfy all user demands is studied. Decentralized caching with uniformly random demands is considered, and both the minimum average power (averaged over all demand combinations) and the minimum peak power (minimum power required to satisfy the worst-case demand combination) are studied. Upper and lower bounds are presented on the minimum required average and peak transmit power as a function of the cache capacity, assuming uncoded cache placement. The gaps between the upper and lower bounds on both the minimum peak and average power values are shown to be relatively small through numerical results, particularly for large cache capacities.
pp. 2795-2799
11:50 Low Subpacketization Schemes for Coded Caching
Li Tang and Aditya Ramamoorthy (Iowa State University, USA)
Coded caching is a technique that generalizes conventional caching and promises significant reductions in traffic over caching networks. However, the basic coded caching scheme requires that each file hosted in the server be partitioned into a large number (called the subpacketization level) of non-overlapping subfiles. From a practical perspective, this is problematic as it means that prior schemes are only applicable when the size of the files is extremely large. In this work, we propose coded caching schemes based on combinatorial structures called resolvable designs. These structures can be obtained in a natural manner from linear block codes whose generator matrices possess certain rank properties. We demonstrate that several schemes with subpacketization levels that are exponentially smaller than the basic scheme can be obtained.
pp. 2800-2804
Enrico Piovano, Hamdi Joudeh and Bruno Clerckx (Imperial College London, United Kingdom (Great Britain))
This work investigates the interplay of coded caching and spatial multiplexing in an overloaded Multiple-Input-Single-Output (MISO) Broadcast Channel (BC), i.e. a system where the number of users is greater than the number of transmitting antennas. On one hand, coded-caching uses the aggregate global cache memory of the users to create multicasting opportunities. On the other hand, the multiple antennas at the transmitter leverages the available CSIT to transmit multiple streams simultaneously. In this paper, we introduce a novel scheme which combines both the gain derived from coded caching and spatial multiplexing and outperforms existing schemes in terms of delivery time and CSIT requirement.
pp. 2805-2809

#### Fr2-4: Channel Capacity 4

Room: K3
Chair: Hideki Yagi (University of Electro-Communications, Japan)
11:30 The Arbitrarily Varying Channel Under Constraints with Causal Side Information at the Encoder
Uzi Pereg (Technion); Yossef Steinberg (Technion, Israel)
We study the arbitrarily varying channel (AVC) with input and state constraints, when the encoder has state information in a causal manner. Lower and upper bounds on the random code capacity are developed. A lower bound on the deterministic code capacity is established in the case of a message-averaged input constraint. In the setting where a state constraint is imposed on the jammer, while the user is under no constraints, the random code bounds coincide, and the random code capacity is determined. Furthermore, for this scenario, a generalized non-symmetrizability condition is stated, under which the deterministic code capacity coincides with the random code capacity.
pp. 2815-2819
11:50 Storage Capacity as an Information-Theoretic Analogue of Vertex Cover
Arya Mazumdar (University of Massachusetts Amherst, USA); Andrew McGregor (University of Massachusetts, Amherst, USA); Sofya Vorotnikova (University of Massachusetts, USA)
Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be recovered from the information stored at the neighboring vertices. Computing the storage capacity is a fundamental problem in network coding and is related, or equivalent, to some well-studied problems such as index coding with side information and generalized guessing games. In this paper, we consider storage capacity as a natural information-theoretic analogue of the minimum vertex cover of a graph. Indeed, while it was known that storage capacity is upper bounded by minimum vertex cover, we show that by treating it as such we can get a $3/2$ approximation for planar graphs, and a $4/3$ approximation for triangle-free planar graphs. Since the storage capacity is intimately related to the index coding rate, we get a $1.923$ approximation of index coding for planar graphs and $3/2$ approximation for triangle-free planar graphs. Previously only a trivial $4$ approximation of the index coding rate was known for planar graphs. We then develop a general method of gadget covering'' to upper bound the storage capacity in terms of the average of a set of vertex covers. This method is intuitive and leads to the exact characterization of storage capacity for various families of graphs, such as cycles with chords. Finally, we generalize the storage capacity notion to include recovery from partial failures in distributed storage. We show tight upper and lower bounds on this partial recovery capacity that scales nicely with the fraction of failure in a vertex.
pp. 2820-2824
12:10 Gaussian ISI Channels with Mismatch
Wasim Huleihel (MIT, USA); Salman Salamatian (Massachusetts Institute of Technology, USA); Neri Merhav (Technion, Israel); Muriel Médard (MIT, USA)
This paper considers the problem of channel coding over Gaussian intersymbol interference (ISI) channels with a given (possibly suboptimal) metric decoding rule. Specifically, it is assumed that the mismatched decoder has incorrect knowledge of the ISI coefficients (or, the impulse response function). The mismatch capacity is the highest achievable rate for a given decoding rule. Unfortunately, existing lower bounds to the mismatch capacity for multi-letter channels and decoding metrics (or, channels and decoding metrics with memory), as in our model, are presented only in the form of multi-letter expressions, and thus cannot be calculated in practice. Consequently, they provide little insight on the mismatch problem. In this paper, we derive a computable single-letter lower bound to the mismatch capacity, and discuss some implications of our results.
pp. 2825-2829
12:30 Characterization of Super-Additivity and Discontinuity Behavior of the Capacity of Arbitrarily Varying Channels under List Decoding
Holger Boche (Technical University Munich, Germany); Rafael F. Schaefer (Technische Universität Berlin, Germany); H. Vincent Poor (Princeton University, USA)
The arbitrarily varying channel (AVC) models communication over a channel that varies in an arbitrary and unknown manner from channel use to channel use. This paper considers the AVC under list decoding and studies the corresponding list capacity. In particular, the list capacity function is shown to be discontinuous and the corresponding discontinuity points are characterized for all possible list sizes. For orthogonal AVCs it is then shown that the list capacity is super-additive, implying that joint encoding and decoding for two orthogonal AVCs can yield a larger list capacity than independent processing of both channels. This discrepancy is shown to be arbitrary large.
pp. 2830-2834

#### Fr2-5: Communications 4

Room: K4
Chair: Remi A Chou (Pennsylvania State University, USA)
11:30 Optimal Covert Communications using Pulse-Position Modulation
Matthieu Bloch (Georgia Institute of Technology, USA); Saikat Guha (Raytheon BBN Technologies, USA)
This paper shows the optimality of Pulse-Position Modulation (PPM) for covert communications over discrete- memoryless channels. Specifically, the concatenation of an m-ary outer code of length O(m) and an inner code consisting of PPM of order m achieves the information-theoretic limits of covert communications. This suggests alternative code constructions for covert communications, in which the sparsity of the PPM symbols ensures covertness and an appropriate choice of the blocklength results in the square root law.
pp. 2835-2839
11:50 Covert Communication with Noncausal Channel-State Information at the Transmitter
Si-Hyeon Lee (POSTECH, Korea); Ligong Wang (ETIS & CNRS, France); Ashish Khisti (University of Toronto, Canada); Gregory Wornell (MIT, USA)
We consider the problem of covert communication over a state-dependent channel, where the transmitter has noncausal knowledge of the channel states. Here, covert'' means that the probability that a warden on the channel can detect the communication must be small. In contrast with traditional models without noncausal channel-state information at the transmitter, we show that covert communication can be possible with positive rate. We derive closed-form formulas for the maximum achievable covert communication rate (covert capacity'') in this setting for discrete memoryless channels as well as additive white Gaussian noise channels. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.
pp. 2840-2844
12:10 Strong Coordination of Signals and Actions over Noisy Channels
Giulia Cervia (ETIS/ ENSEA, University Cergy-Pontoise, CNRS, France); Laura Luzzi (ENSEA & CNRS, Université de Cergy-Pontoise, France); Mael Le Treust (ETIS / ENSEA, Université Cergy-Pontoise, CNRS, France); Matthieu Bloch (Georgia Institute of Technology, USA)
We develop a random binning scheme for strong coordination in a network of two nodes separated by a noisy channel, in which the input and output signals have to be coordinated with the source and its reconstruction. In the case of non-causal encoding and decoding, we propose a joint source-channel coding scheme and develop inner and outer bounds for the strong coordination region. While the set of achievable target distributions is the same as for empirical coordination, we show that a positive rate of common randomness is required for strong coordination.
pp. 2845-2849
12:30 Strong Coordination over Noisy Channels: Is Separation Sufficient?
Sarah Obead, Badri N Vellambi and Joerg Kliewer (New Jersey Institute of Technology, USA)
We study the problem of strong coordination in which agents X and Y communicate over a noisy communication channel to ensure that their actions follow a behavior specified by a joint probability distribution. We propose two novel coding schemes for this noisy coordination scenario and derive inner bounds for the respective strong capacity region. The first scheme is a joint coordination-channel coding scheme that utilizes the randomness provided by the communication channel to reduce the local randomness required in generating the action sequence at Node Y. The second scheme exploits separate coordination and channel coding where local randomness is extracted from the channel after decoding. Finally we present a example in which the joint scheme is able to outperform the separate case in terms of coordination rate.
pp. 2850-2854

#### Fr2-6: Coding and Decoding

Room: K5
Chair: Hessam Mahdavifar (University of Michigan, USA)
11:30 Universal Decoding Using a Noisy Codebook
Neri Merhav (Technion, Israel)
We consider the topic of universal decoding with a decoder that does not have direct access to the codebook, but only to noisy versions of the various randomly generated codewords, a problem motivated by biometrical identification systems. Both the source that generates the original (clean) codewords, and the channel that corrupts them in generating the noisy codewords, as well as the main channel for communicating the messages, are all modeled by non-unifilar, finite-state systems (hidden Markov models). As in previous works on universal decoding, here too, the average error probability of our proposed universal decoder is shown to be as small as that of the optimal maximum likelihood (ML) decoder, up to a multiplicative factor that is a sub-exponential function of the block length. It therefore has the same error exponent, whenever the ML decoder has a positive error exponent. The universal decoding metric is based on Lempel-Ziv (LZ) incremental parsing of each noisy codeword jointly with the given channel output vector, but this metric is somewhat different from the one proposed in earlier works on universal decoding for finite-state channels, by Ziv (1985) and by Lapidoth and Ziv (1998). The reason for the difference is that here, unlike in those earlier works, the probability distribution that governs the (noisy) codewords is, in general, not uniform across its support. This non-uniformity of the codeword distribution also makes our derivation more challenging. Another reason for the more challenging analysis is the fact that the effective induced channel between the noisy codeword of the transmitted message and the main channel output is not a finite-state channel in general.
pp. 2855-2859
11:50 Variable-to-Fixed Length Homophonic Coding Suitable for Asymmetric Channel Coding
Junya Honda and Hirosuke Yamamoto (The University of Tokyo, Japan)
In the communication through asymmetric channels the capacity-achieving input distribution is not uniform in general. Homophonic coding is a framework to invertibly convert a (usually uniform) message into a sequence with some target distribution, and is a promising candidate to generate codewords with the target nonuniform distribution for asymmetric channels. In particular, a Variable-to-Fixed length (VF) homophonic code is suitable as a component of channel codes to avoid decoding error propagation. However, the existing VF homophonic code requires to know the maximum relative gap of probabilities between two adjacent sequences beforehand, which is unrealistic for long block codes. In this paper we propose a new VF homophonic code without such requirement by allowing one-symbol decoding delay. We evaluate this code theoretically and experimentally to verify its asymptotic optimality.
pp. 2860-2864
12:10 Optimality of the recursive data exchange protocol
Himanshu Tyagi (Indian Institute of Science, India); Shun Watanabe (Tokyo University of Agriculture and Technology, Japan)
Multiple parties observe correlated data generated independent and identically (in time) from a known joint distribution. Parties communicate with each other interactively to enable each party to recover the data observed by all the other parties and attain omniscience. We characterize the asymptotic growth of the number of bits of interactive communication required by the parties to attain omniscience up to the second-order term. For the converse, we provide a single-shot lower bound for the required number of bits of communication, which yields the asymptotic result as a special case. It is shown that the knowledge of the distribution can be used to modify the recently proposed recursive universal data exchange protocol to render it optimal up to the second-order term. As a corollary, we provide a precise characterization of the reduction in communication for omniscience due to interaction.
pp. 2865-2869
12:30 Explicit Constructions of Finite-Length WOM Codes
Yeow Meng Chee and Han Mao Kiah (Nanyang Technological University, Singapore); Alexander Vardy (University of California San Diego, USA); Eitan Yaakobi (Technion, Israel)
Write-once memory (WOM) is a storage device consisting of binary cells which can only increase their levels. A $t$-write WOM code is a coding scheme which allows to write $t$ times to the WOM without decreasing the levels of the cells. The sum-rate of a WOM code is the ratio between the total number of bits written to the memory and the number of cells. It is known that the maximum sum-rate of a $t$-write WOM code is $\log(t+1)$. This is also an achievable upper bound both by information theory arguments and explicit WOM code constructions. While existing constructions of WOM codes were targeted to increase the sum-rate, we consider here two more figures of merit in evaluating the constructions. The first one is the complexity of the encoding and decoding maps of the code. The second one is called the convergence rate, and is defined to be the minimum code length $n(\epsilon)$ in order to reach $\epsilon$ close to a point in the capacity region. One of our main results in the paper is a specific capacity achieving construction for two-write WOM codes which has polynomial complexity and relatively short block length to be $\epsilon$ close to the capacity. Using these two-write WOM codes, we obtain three-write WOM codes that approach sum-rate 1.809 with relatively short block lengths. Finally, we provide another construction of three-write WOM that achieves sum-rate 1.71 by using only 100 cells.
pp. 2870-2874

#### Fr2-7: Privacy and Security

Room: K6
Chair: Philippe Gaborit (Universite de Limoges, France)
11:30 On Information-Theoretic Privacy with General Distortion Cost Functions
Kousha Kalantari, Lalitha Sankar and Oliver Kosut (Arizona State University, USA)
The privacy-utility tradeoff problem is formulated as determining the privacy mechanism (random mapping) that minimizes the mutual information (a metric for privacy leakage) between the private features of the original dataset and a released version. The minimization is subject to a constraint on the average distortion cost defined as a function $f$ evaluated for every distortion $d$ between the public features and the released version of dataset. The asymptotic optimal leakage is derived both for general and stationary memoryless privacy mechanisms. It is shown that for convex cost functions there is no asymptotic loss in using stationary memoryless mechanisms. Of independent interest are the proof techniques developed here for arbitrary cost functions.
pp. 2875-2879
11:50 Impact of the Communication Channel on Information Theoretical Privacy
Mehmet Özgün Demir (Boğaziçi University, Turkey); Gunes Karabulut Kurt (Istanbul Technical University, Turkey); Guido Dartmann (University of Applied Sciences Trier, Germany); Volker Lücken (RWTH Aachen University & Chair for Integrated Signal Processing Systems, Germany); Gerd H. Ascheid (RWTH Aachen University, Germany)
As private information of individuals become more accessible, data privacy evolved to be an important aspect of communication technologies. Among existing privacy definitions, the utility privacy trade-off model is suitable for the assessment of privacy due to its relation with information theory and rate distortion theory. In this paper, the effects of the wireless channel errors are studied with respect to the utility privacy trade-off in a wireless communication network. First, the transmission error probability is embedded to the existing trade-off definitions. Then, it is shown via numerical examples, in which binary and normally distributed sources satisfy the updated rate distortion equivocation and equivocation distortion functions.
pp. 2880-2884
12:10 Constructive Interference Based Secure Precoding
Muhammad R. A. Khandaker, Christos Masouros and Kai Kit Wong (University College London, United Kingdom (Great Britain))
Recent advances in interference exploitation showed that exploiting knowledge of interference constructively can improve the receive signal-to-interference and noise ratio (SINR) at the destination. This paper exploits this concept to design artificial noise (AN) beamformers constructive to the intended receiver (IR) yet keeping AN disruptive to possible eavesdroppers (Eves). A multiple-input single-output (MISO) wiretap channel with multiple eavesdroppers scenario has been investigated taking both perfect and imperfect channel information into consideration. The main objective is to improve the receive SINR at the IR through exploitation of AN power in an attempt to minimize the total transmit power, while confusing the Eves.
pp. 2885-2889
12:30 Secure and reliable connectivity in heterogeneous wireless sensor networks
Rashad Eletreby (Carnegie Mellon University, USA); Osman Yağan (Carnegie Mellon University & CyLab, USA)
We consider a wireless sensor network secured by the heterogeneous random key predistribution scheme and investigate its reliability against both link and node failures. The heterogeneous random key predistribution scheme is a lightweight security mechanism proposed to secure sensor networks that include nodes with varying levels of resources, features, or connectivity requirements; e.g., regular nodes vs. cluster heads. To capture the reliability of the network against both link and node failure, we consider the case when each link fails independently with probability $1-\alpha$ and present conditions (in the form of zero-one laws) on how to scale the parameters of the resulting network so that it is $k$-connected with high probability, i.e., the network remains connected even if any $k − 1$ nodes fail or leave the network. Collectively, we obtain a network that is reliable against the probabilistic failure of each link and against the failure of any $k−1$ nodes. We present numerical results to support these conditions in the finite-node regime.
pp. 2890-2894

#### Fr2-8: Computation

Room: K7+8
Chair: Anelia Somekh-Baruch (Bar-Ilan University, Israel)
11:30 Communication-Aware Computing for Edge Processing
Songze Li (University of Southern California, USA); Mohammad Ali Maddah-Ali (Bell Labs, Alcatel Lucent, USA); Salman Avestimehr (University of Southern California, USA)
We consider a mobile edge computing problem, in which mobile users offload their computation tasks to computing nodes (e.g., base stations) at the network edge. The edge nodes compute the requested functions and communicate the computed results to the users via wireless links. For this problem, we propose a Universal Coded Edge Computing (UCEC) scheme for linear functions to simultaneously minimize the load of computation at the edge nodes, and maximize the physical-layer communication efficiency towards the mobile users. In the proposed UCEC scheme, edge nodes create coded inputs of the users, from which they compute coded output results. Then, the edge nodes utilize the computed coded results to create communication messages that zero-force all the interference signals over the air at each user. Specifically, the proposed scheme is universal since the coded computations performed at the edge nodes are oblivious of the channel states during the communication process from the edge nodes to the users.
pp. 2895-2899
11:50 Encoded Distributed Optimization
Can Karakus (University of California, Los Angeles, USA); Yifan Sun (Technicolor Corporation, USA); Suhas Diggavi (University of California Los Angeles, USA)
Today, many real-world machine learning and data analytics problems are of a scale that requires distributed optimization; unlike in centralized computing, these systems are vulnerable to network and node failures. Recently, coding-theoretic ideas have been applied to mitigate node failures in such distributed computing networks. Relaxing the exact recovery requirement of such techniques, we propose a novel approach for adding redundancy in large-scale convex optimization problems, making solvers more robust against sudden and persistent node failures and loss of data. This is done by linearly encoding the data variables; all other aspects the computation operate as usual. We show that under moderate amounts of redundancy, it is possible to recover a close approximation to the solution under node failures. In particular, we show that encoding with (equiangular) tight frames result in bounded objective error, and obtain an explicit error bound for a specific construction that uses Paley graphs. We also demonstrate the performance of the proposed technique for three specific machine learning problems, (two using real world datasets) namely ridge regression, binary support vector machine, and low-rank approximation.
pp. 2900-2904
12:10 Fundamental Estimation Limits in Autoregressive Processes with Compressive Measurements
Milind Rao (Stanford University, USA); Tara Javidi (UCSD, USA); Yonina C. Eldar (Technion-Israel Institute of Technology, Israel); Andrea Goldsmith (Stanford University, USA)
We consider the problem of estimating the parameters of a vector autoregressive (VAR) process from low-dimensional random projections of the observations. This setting covers the cases where we make compressive measurements of the observations or have limits in the data acquisition process associated with the measurement system and are only able to subsample. We first present fundamental bounds for the convergence of any estimator for the covariance or state-transition matrices with and without considering structural constraints of sparsity and low-rankness. We then construct an estimator for these matrices or the parameters of the VAR process and show that it is optimal in an order sense.
pp. 2905-2909
12:30 Minimizing Latency for Secure Distributed Computing
Rawad Bitar (Illinois Institute of Technology, USA); Parimal Parag (Indian Institute of Science, India); Salim El Rouayheb (Illinois Institute of Technology, USA)
We consider the setting of a master server who possesses confidential data (genomic, medical data, etc.) and wants to run intensive computations on it, as part of a machine learning algorithm for example. The master wants to distribute these computations to untrusted workers who have volunteered or are incentivized to help with this task. However, the data must be kept private (in an information theoretic sense) and not revealed to the individual workers. The workers may be busy, or even unresponsive, and will take a random time to finish the task assigned to them. We are interested in reducing the aggregate delay experienced by the master. We focus on linear computations as an essential operation in many iterative algorithms. A known solution is to use a linear secret sharing scheme to divide the data into secret shares on which the workers can compute. We propose to use instead new secure codes, called Staircase codes, introduced previously by two of the authors. We study the delay induced by Staircase codes which is always less than that of secret sharing. The reason is that secret sharing schemes need\ to wait for the responses of a fixed fraction of the workers, whereas Staircase codes offer more flexibility in this respect. For instance, for codes with rate $R=1/2$ Staircase code can lead to up to $40\%$ reduction in delay compared to secret sharing.
pp. 2910-2914

### Friday, June 30, 14:40 - 16:20

#### Fr3-1: Codes and Graphs

Room: Europa
Chair: Norbert Goertz (Vienna University of Technology (TU Wien), Austria)
14:40 On sparse graph coding for coherent and noncoherent demodulation
Charles-Ugo Piat-Durozoi (INPT/IRIT, France); Charly Poulliat (INP - ENSEEIHT Toulouse, France); Nathalie Thomas (University of Toulouse, France); Marie-Laure Boucheret (University of Toulouse IRIT Enseeiht, France); Guy Lesthievent (CNES, France)
In this paper, we consider a bit-interleaved coded modulation scheme (BICM) composed of an error correcting code serially concatenated with a M-ary non linear modulation. We first compare demodulation strategies for both the coherent and the non coherent cases. Then, we perform an asymptotic analysis and try to show that the design of coding schemes performing well for both the coherent and the non coherent regimes should be done carefully when considering sparse graph based codes such as low-density parity-check (LDPC) codes. It will be shown that optimized coding schemes for the non coherent setting can perform fairly well when using coherent demodulation, while on the contrary, optimized coding schemes for the coherent setting may lead to "non stable" coding schemes in the non coherent setting.
pp. 2915-2919
15:00 The Number of Independent Sets In Hexagonal Graphs
Zhun Deng (Harvard University & Work, USA); Jie Ding, Kathryn Heal and Vahid Tarokh (Harvard University, USA)
We derive the tightest known bounds on η, the growth rate of the logarithm of the number of independent sets on a hexagonal lattice. To obtain these bounds, we generalize a method proposed by Calkin and Wilf. Their original strategy cannot immediately be used to derive bounds for η, due to the difference in symmetry between square and hexagonal lattices, so we propose a modified method and an algorithm to derive rigorous bounds on η. In particular, we prove that 1.546440708536001 ≤ η ≤ 1.5513, which improves upon the best known bounds of 1.5463 ≤ η ≤ 1.5527 given by Nagy and Zeger. Our lower bound matches the numerical estimate of Baxter up to 9 digits after the decimal point, and our upper bound can be further improved by following our method.
pp. 2920-2924
15:20 Density Evolution on a Class of Smeared Random Graphs
Kabir Chandrasekher and Orhan Ocal (University of California, Berkeley, USA); Kannan Ramchandran (University of California at Berkeley, USA)
We introduce a new ensemble of random bipartite graphs, which we term the smearing ensemble', where each left node is connected to some number of consecutive right nodes. Such graphs arise naturally in recovering sparse wavelet coefficients when signal acquisition is in the Fourier domain, such as in magnetic resonance imaging (MRI). Graphs from this ensemble exhibit small, structured cycles with high probability, rendering current techniques for determining iterative decoding thresholds inapplicable. In this paper, we develop a theoretical platform to analyze and evaluate the power of smearing-based structure. Despite the existence of these small cycles, we derive exact density evolution recurrences for iterative decoding on graphs with smear-length two. Furthermore, we give lower bounds on the performance of a much larger class from the smearing ensemble, and provide numerical experiments showing tight agreement between empirical thresholds and those determined by our bounds. We additionally detail a system architecture to recover sparse wavelet representations in the MRI setting, giving explicit oversampling thresholds for the one-stage Haar wavelet.
pp. 2925-2929
15:40 Connectivity of inhomogeneous random key graphs intersecting inhomogeneous Erdős-Rényi graphs
Rashad Eletreby (Carnegie Mellon University, USA); Osman Yağan (Carnegie Mellon University & CyLab, USA)
We study the connectivity of a random graph formed by the intersection of an inhomogeneous random key graph with an inhomogeneous Erdős-Rényi graph. The former graph is naturally induced by a heterogeneous random key predistribution scheme introduced for securing wireless sensor network communications. In this scheme, nodes are divided into r classes according to a probability distribution $\mu={\mu_1,...,\mu_r}$, and a class-$i$ sensor is assigned $K_i$ cryptographic keys that are selected uniformly at random from a common pool of $P$ keys. The latter graph represents a heterogeneous on/off channel model, where the wireless channel between a class-$i$ node and a class-$j$ node is on (resp. off) with probability $\alpha_{ij}$ (resp. $1 − \alpha_{ij}$) independently from others. We present conditions on how to scale the parameters of the intersection model so that it is connected with high probability as the number of nodes gets large. The result is given in the form of a zero-one law and supported by a numerical study in the finite-node regime.
pp. 2930-2934

#### Fr3-2: LDPC Codes 3

Room: Brussels
Chair: Boris D. Kudryashov (St. Petersburg University of Information Technologies, Mechanics and Optics, Russia)
14:40 Message Alignment for Discrete LDPC Decoders with Quadrature Amplitude Modulation
Jan Lewandowsky, Maximilian Stark and Gerhard Bauch (Hamburg University of Technology, Germany)
Recent works describe the design of discrete decoders for low-density parity-check codes by application of mutual information maximizing clustering algorithms in discrete density evolution. In the resulting discrete message passing decoders only integers are exchanged and node operations become simple lookup operations. Earlier works only describe discrete decoders for binary modulation schemes. This paper presents a new technique called message alignment which enables to design discrete decoders for higher-order modulation schemes. First, we design a channel output quantizer for quadrature amplitude modulation with the Information Bottleneck method. The quantizer attempts to preserve the relevant information on the modulation symbols. Afterwards, we illustrate that the assignment of several bits to one modulation symbol does not allow straightforward decoder design with the available discrete density evolution technique. The proposed message alignment solves this problem. The resulting discrete decoder is compared with state-of-the-art decoders using bit error rate simulations.
pp. 2935-2939
15:00 Rate-Loss Reduction of SC-LDPC Codes by Optimizing Reliable Variable Nodes via Expected Graph Evolution
Heeyoul Kwak, Jaewha Kim and Jong-Seon No (Seoul National University, Korea)
The outstanding decoding performance of spatially-coupled low-density parity-check (SC-LDPC) codes comes from wave-like propagation of reliable messages. The reliable messages are triggered by shortened (known) variable nodes in some consecutive reliable positions. However, at the cost of the improvement, shortened variable nodes cause rate-loss of SC-LDPC codes. To reduce the rate-loss, additional variable nodes (so called reliable variable nodes) can be added to the reliable positions instead of shortened variable nodes. Density evolution (DE) is an efficient method to design degree distribution of the reliable variable nodes. However, degree distributions obtained by DE show degraded performance in finite-length code performance. In this paper, we generalize the expected graph evolution and use the analysis tool in optimizing degree distribution which shows the minimum rate-loss without finite-length performance degradation. From the well designed degree distribution, rate-loss reduction by 60\% can be achieved without finite-length performance degradation.
pp. 2940-2944
15:20 Compute-Forward Multiple Access (CFMA) with Nested LDPC Codes
Erixhen Sula (École Polytechnique Fédérale de Lausanne, Switzerland); Jingge Zhu (UC Berkeley, USA); Adriano Pastore (Centre Tecnològic de Telecomunicacions de Catalunya (CTTC), Spain); Sung Hoon Lim (Korea Institute of Ocean Science and Technology, Korea); Michael Gastpar (EPFL & University of California, Berkeley, Switzerland)
Inspired by the compute-and-forward scheme from Nazer and Gastpar, a novel multiple-access scheme introduced by Zhu and Gastpar makes use of nested lattice codes and sequential decoding of linear combinations of codewords to recover the individual messages. This strategy, coined compute-forward multiple access (CFMA), provably achieves points on the dominant face of the multiple-access capacity region while circumventing the need of time sharing or rate splitting. For a two-user multiple-access channel (MAC), we propose a practical procedure to design suitable codes from off-the-shelf LDPC codes and present a sequential belief propagation decoder with complexity comparable with that of point-to-point decoders. We demonstrate the potential of our strategy by comparing several numerical evaluations with theoretical limits.
pp. 2945-2949
15:40 Edge Spreading Design of High Rate Array-Based SC-LDPC Codes
David G. M. Mitchell (New Mexico State University, USA); Eirik Rosnes (University of Bergen, Norway)
Absorbing sets (ASs) are combinatorially defined objects existing in the Tanner graph of a low-density parity-check (LDPC) code that have been shown to cause failures in the iterative message-passing decoder when transmission occurs over the additive white Gaussian noise channel. In this paper, we propose an edge spreading approach to construct high rate array-based spatially-coupled LDPC codes by jointly optimizing the AS spectrum and the minimum distance. By considering general edge spreadings and by considering a larger memory, we show that strictly better codes can be constructed, both in terms of achievable minimum distance for small-to-moderate block lengths and in terms of the number of small ASs.
pp. 2950-2954
16:00 LDPC Code Design for Correlated Sources using EXIT Charts
Mohamad. Khas and Hamid Saeedi (Tarbiat Modares University, Iran); Reza Asvadi (Shahid Beheshti University, Iran)
This paper is concerned with the design of capacity approaching ensembles of Low-Density Parity-Check (LDPC) codes for correlated sources. We consider correlated binary sources where the data is encoded independently at each source through a systematic LDPC encoder and sent over two independent Gaussian channels. At the receiver, a joint iterative decoder consisting of two component LDPC decoders is considered where the encoded bits at the output of each component decoder are used at the other decoder as the a priori information. We first provide asymptotic performance analysis using the concept of extrinsic information transfer (EXIT) charts. Compared to the conventional EXIT charts devised to analyze LDPC codes for point to point communication, the proposed EXIT charts have been completely modified to able to accommodate the systematic nature of the codes as well as the iterative behavior between the two component decoders. Then the developed modified EXIT charts are deployed to design ensembles for different levels of correlation. Our results show that as the average degree of the designed ensembles grow, the thresholds corresponding to the designed ensembles approach the capacity. In particular, for ensembles with average degree of around 9, the gap to capacity is reduced to about 0.2 dB.
pp. 2955-2959

#### Fr3-3: Caching 3

Room: K2
Chair: Aditya Ramamoorthy (Iowa State University, USA)
14:40 Fundamental Limits of Distributed Caching in Multihop D2D Wireless Networks
Mingyue Ji and Rong-Rong Chen (University of Utah, USA); Giuseppe Caire (Technische Universität Berlin, Germany); Andreas Molisch (University of Southern California, USA)
We consider a wireless Device-to-Device (D2D) caching network, where users make arbitrary requests from a library of files and have pre-fetched (cached) information on their devices, subject to a per-node storage capacity constraint. The network is assumed to obey the protocol model'', widely considered in the wireless network literature. Unlike other related works, which either restrict the communication to single-hop, or assume entire file caching, here we consider both multi-hop transmission and fully general caching strategies, including file subpacketization. We propose a caching strategy based on deterministic assignment of MDS-coded packets of the library files, and a coded multicast delivery strategy where the users send linearly coded messages to each other in order to collectively satisfy their demands. We show that our approach can achieve the information theoretic outer bound within a multiplicative constant factor in practical parameter regimes.
pp. 2960-2964
15:00 Fundamental Limits on Latency in Transceiver Cache-Aided HetNets
Jaber Kakar (Ruhr-Universitaet Bochum, Germany); Soheil Gherekhloo and Aydin Sezgin (RUB, Germany)
Stringent mobile usage characteristics force wireless networks to undergo a paradigm shift from conventional connection-centric to content-centric deployment. With respect to 5G, caching and heterogenous networks (HetNet) are key technologies that will facilitate the evolution of highly content-centric networks by facilitating unified quality of service in terms of low-latency communication. In this paper, we study the impact of transceiver caching on the latency for a HetNet consisting of a single user, a receiver and one cache-assisted transceiver. We define an information-theoretic metric, the delivery time per bit (DTB), that captures the delivery latency. We establish coinciding lower and upper bounds on the DTB as a function of cache size and wireless channel parameters; thus, enabling a complete characterization of the DTB optimality of the network under study. As a result, we identify cache beneficial and non-beneficial channel regimes.
pp. 2965-2969
15:20 Cache-Aided Cooperation with No CSIT
Eleftherios Lampiris, Jingjing Zhang and Petros Elia (EURECOM, France)
This work explores cache-aided interference management in the absence of channel state information at the transmitters (CSIT), focusing on the setting with $K$ transmitter/receiver pairs endowed with caches, where each receiver $k$ is connected to transmitter $k$ via a direct link with normalized capacity 1, and to any other transmitter via a cross link with normalized capacity $\tau \le 1$. In this setting, we explore how a combination of pre-caching at transmitters and receivers, together with interference enhancement techniques, can a) partially counter the lack of CSIT, and b) render the network self-sufficient, in the sense that the transmitters need not receive additional data after pre-caching. Toward this we present new schemes that blindly harness topology and transmitter-and-receiver caching, to create separate streams, each serving many receivers at a time. Key to our approach is a combination of three impactful techniques, Rate-splitting, Interference Enhancement and Coded Caching.
pp. 2970-2974

#### Fr3-4: Entropy 3

Room: K3
Chair: Peter Harremoës (Niels Brock, Copenhagen Business College, Denmark)
14:40 Arimoto-Renyi Conditional Entropy and Bayesian Hypothesis Testing
Igal Sason (Technion - Israel Institute of Technology, Israel); Sergio Verdú (Princeton University, USA)
This paper gives upper and lower bounds on the minimum error probability of Bayesian M-ary hypothesis testing in terms of the Arimoto-Renyi conditional entropy of an arbitrary order $\alpha$. The improved tightness of these bounds over their specialized versions with the Shannon conditional entropy ($\alpha=1$) is demonstrated. In particular, in the case where $M$ is finite, we show how to generalize Fano's inequality under both the conventional and list-decision settings. As a counterpart to the generalized Fano's inequality, allowing $M$ to be infinite, a lower bound on the Arimoto-Renyi conditional entropy is derived as a function of the minimum error probability. Explicit upper and lower bounds on the minimum error probability are obtained as a function of the Arimoto-Renyi conditional entropy.
pp. 2975-2979
15:00 Rényi Entropy Rate of Hidden Markov Processes
Chengyu Wu (The University of Hong Kong, Hong Kong); Easton Li Xu (Texas A&M University, USA); Guangyue Han (The University of Hong Kong, Hong Kong)
In this paper, we focus our attention on the Rényi entropy rate of hidden Markov processes under certain positivity assumptions. The existence of the Rényi entropy rate for such processes is established. Furthermore, we show that, with some extra fast-forgetting'' assumptions, the Rényi entropy rate of the approximating Markov processes exponentially converges to that of the original hidden Markov process, as the Markov order goes to infinity.
pp. 2980-2984
15:20 Sharp Bounds on Arimoto's Conditional Rényi Entropies Between Two Distinct Orders
Yuta Sakai and Ken-ichi Iwata (University of Fukui, Japan)
This study examines sharp bounds on Arimoto's conditional Rényi entropy of order $\beta$ with a fixed another one of distinct order $\alpha \neq \beta$. Arimoto inspired the relation between the Rényi entropy and the $\ell_{r}$-norm of probability distributions, and he introduced a conditional version of the Rényi entropy. From this perspective, we analyze the $\ell_{r}$-norms of particular distributions. As results, we identify specific probability distributions whose achieve our sharp bounds on the conditional Rényi entropy. The sharp bounds derived in this study can be applicable to other information measures, e.g., the minimum average probability of error, the Bhattacharyya parameter, Gallager's reliability function $E_{0}$, and Sibson's $\alpha$-mutual information, whose are strictly monotone functions of the conditional Rényi entropy.
pp. 2985-2989
15:40 Minimax Rényi Redundancy
Semih Yagli, Yücel Altuğ and Sergio Verdú (Princeton University, USA)
The redundancy for universal lossless compression in Campbell's setting is characterized as a minimax R\'enyi divergence, which is shown to be equal to the maximal $\alpha$-mutual information via a generalized redundancy-capacity theorem. Special attention is placed on the analysis of the asymptotics of minimax R\'enyi divergence, which is determined up to a term vanishing in blocklength.
pp. 2990-2994
16:00 Infinity-Rényi entropy power inequalities
Peng Xu, James Melbourne and Mokshay Madiman (University of Delaware, USA)
An optimal $\infty$-R\'enyi entropy power inequality is derived for $d$-dimensional random vectors. In fact, the authors establish a matrix $\infty$-EPI analogous to the generalization of the classical EPI established by Zamir and Feder. The result is achieved by demonstrating uniform distributions as extremizers of a certain class of $\infty$-R\'enyi entropy inequalities, and then putting forth a new rearrangement inequality for the $\infty$-R\'enyi entropy. Quantitative results are then derived as consequences of a new geometric inequality for uniform distributions on Euclidean balls
pp. 2995-2999

#### Fr3-5: Machine Learning 2

Room: K4
Chair: Parimal Parag (Indian Institute of Science, India)
14:40 Noisy Inductive Matrix Completion Under Sparse Factor Models
Akshay Soni (Yahoo Research, USA); Troy Chevalier (Yahoo, USA); Swayambhoo Jain (University of Minnesota, USA)
Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a general class of noisy matrix completion tasks where the underlying matrix is following an IMC model, i.e., it is formed by a mixing matrix (a priori unknown) sandwiched between two known feature matrices. The mixing matrix here is assumed to be well approximated by the product of two sparse matrices -- referred here to as sparse factor models''. We extend an existing result to provide theoretical error bounds for the sparsity-regularized maximum likelihood estimators for the class of problems discussed in this paper. The main result is general in the sense that it can be used to derive error bounds for various noise models. In this paper, we instantiate our main result for the case of Gaussian noise and provide corresponding error bounds in terms of squared loss.
pp. 3000-3004
15:00 On the Problem of On-line Learning with Log-Loss
Yaniv Fogel and Meir Feder (Tel-Aviv University, Israel)
In this paper we consider the problem of on-line learning with respect to the logarithmic loss, where the learner provides a probability assignment for the next label given the past and current data samples and the past labels. We consider the problem in the individual and the stochastic settings. Our first result is a class of new universal on-line probability assignment schemes based on the mixture approach. Now, in classical learning, it is well known that there are model classes that can be learned in batch, but cannot be learned sequentially for all data samples sequences. We show that for these model classes the proposed mixture schemes lead to a vanishing regret in the individual setting when the adversary is somewhat constrained. In the stochastic setting we show that any on-line solution for the log-loss may be used to obtain a solution for a wide variety of loss functions.
pp. 3005-3009
15:20 Multiclass MinMax Rank Aggregation
Pan Li (University of Illinois Urbana-Champaign, USA); Olgica Milenkovic (University of Illinois at Urbana-Champaign (UIUC), USA)
We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on the Mallows model and genomic data.
pp. 3010-3014
15:40 Adiabatic Persistent Contrastive Divergence Learning
Hyeryung Jang, Hyungwon Choi, Yung Yi and Jinwoo Shin (KAIST, Korea)
This paper studies the problem of parameter learning in graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps. However, both E and M steps are computationally intractable for high dimensional data, while the substitution of one step to a faster surrogate for combating against intractability can often cause failure in convergence. To tackle the issue, the Contrastive Divergence (CD) learning scheme has been popularly used in the deep learning community, where it runs the mean-field approximation in E step and a few cycles of Markov Chains (MC) in M step. In this paper, we analyze a variant of CD, called Adiabatic Persistent Contrastive Divergence (APCD), which runs a few cycles of MCs in both E and M steps. Using multi-time-scale stochastic approximation theory, we prove that APCD converges to a correct optimum, where the standard CD is impossible to have such a guarantee due to the mean-field approximation gap in E step. Despite of such stronger theoretical guarantee of APCD, its possible drawback is on slow mixing on E step for practical purposes. To address the issue, we also design a hybrid approach applying both mean-field and MC approximations in E step, where it outperforms the standard mean-field-based CD in our experiments on real-world datasets.
pp. 3015-3019
16:00 Online Nonparametric Anomaly Detection based on Geometric Entropy Minimization
Yasin Yilmaz (University of South Florida, USA)
We consider the online and nonparametric detection of abrupt and persistent anomalies, such as a change in the regular system dynamics at a time instance due to an anomalous event (e.g., a failure, a malicious activity). Combining the simplicity of the nonparametric Geometric Entropy Minimization (GEM) method with the timely detection capability of the Cumulative Sum (CUSUM) algorithm we propose a computationally efficient online anomaly detection method that is applicable to high-dimensional datasets, and at the same time achieve a near-optimum average detection delay performance for a given false alarm constraint. We provide new insights to both GEM and CUSUM, including new asymptotic analysis for GEM, which enables soft decisions for outlier detection, and a novel interpretation of CUSUM in terms of the discrepancy theory, which helps us generalize it to the nonparametric GEM statistic. We numerically show, using both simulated and real datasets, that the proposed nonparametric algorithm attains a close performance to the clairvoyant parametric CUSUM test.
pp. 3020-3024

#### Fr3-6: Estimation 2

Room: K5
Chair: Laura Cottatellucci (EURECOM, France)
14:40 Spectral Initialization for Nonconvex Estimation: High-Dimensional Limit and Phase Transitions
Yue M. Lu (Harvard University, USA); Gen Li (Tsinghua University, P.R. China)
We study a simple spectral method that serves as a key ingredient in a growing line of work using efficient iterative algorithms for estimating signals in nonconvex settings. Unlike previous work, which focuses on the phase retrieval setting and provides only bounds on the performance, we consider arbitrary generalized linear sensing models and provide an exact characterization of the performance of the spectral method in the high-dimensional regime. Our analysis reveals a phase transition phenomenon that depends on the sampling ratio. When the ratio is below a critical threshold, the estimates given by the spectral method are no better than random guesses drawn uniformly from the hypersphere; above the threshold, however, the estimates become increasingly aligned with the underlying signal. Worked examples and numerical simulations are provided to illustrate and verify the analytical predictions.
pp. 3025-3029
15:00 Jackknife estimation for Markov processes with no mixing constraints
Kevin Oshiro, Changlong Wu and Narayana Prasad Santhanam (University of Hawaii at Manoa, USA)
The jackknife resampling procedure is widely used to reduce the bias of a statistic. As with other resampling techniques,the jackknife procedure is motivated by and is well understood in the i.i.d. regime. However, its analysis when samples have memory is limited, and predominantly restricted to cases with strong mixing or memory constraints. In this paper, we analyze a natural jackknife resampling procedure for Markov sources with no mixing assumptions. For the problem to be well posed, we instead adopt a physically motivated continuity condition that ensures that the information a bit in the past provides about the current bit, conditioned on all bits in between, diminishes with the amount of history we have. We compute the jackknife procedure for variance of transition probability estimates given arbitrary contexts. We show that the bias of this jackknife procedure can be bounded close to the true variance.
pp. 3030-3034
15:20 Minimax Risk for Missing Mass Estimation
Nikhilesh Rajaraman and Andrew Thangaraj (IIT Madras, India); Ananda Theertha Suresh (University of California, San Diego, USA)
The problem of estimating the missing mass or total probability of unseen elements in a sequence of $n$ random samples is considered under the squared error loss function. The worst-case risk of the popular Good-Turing estimator is shown to be between $0.6080/n$ and $0.6179/n$. The minimax risk is shown to be lower bounded by $0.25/n$. This appears to be the first such published result on minimax risk for estimation of missing mass, which has several practical and theoretical applications.
pp. 3035-3039

#### Fr3-7: Information Theory and Statistics 2

Room: K6
Chair: Himanshu Tyagi (Indian Institute of Science, India)
14:40 Ensemble Estimation of Mutual Information
Kevin Moon (Yale University); Kumar Sricharan (Xerox PARC); Alfred Hero III (University of Michigan, USA)
We derive the mean squared error convergence rates of kernel density-based plug-in estimators of mutual information measures between two multidimensional random variables $\mathbf{X}$ and $\mathbf{Y}$ for two cases: 1) $\mathbf{X}$ and $\mathbf{Y}$ are both continuous; 2) $\mathbf{X}$ is continuous and $\mathbf{Y}$ is discrete. Using the derived rates, we propose an ensemble estimator of these information measures for the second case by taking a weighted sum of the plug-in estimators with varied bandwidths. The resulting ensemble estimator achieves the $1/N$ parametric convergence rate when the conditional densities of the continuous variables are sufficiently smooth. To the best of our knowledge, this is the first nonparametric mutual information estimator known to achieve the parametric convergence rate for this case, which frequently arises in applications (e.g. variable selection in classification). The estimator is simple to implement as it uses the solution to an offline convex optimization problem and simple plug-in estimators. Ensemble estimators that achieve the parametric rate are also derived for the first case ($\mathbf{X}$ and $\mathbf{Y}$ are both continuous) and another case: 3) $\mathbf{X}$ and $\mathbf{Y}$ may have any mixture of discrete and continuous components.
pp. 3040-3044
15:00 Minimum Rates of Approximate Sufficient Statistics
Masahito Hayashi (Nagoya University, Japan); Vincent Y. F. Tan (National University of Singapore, Singapore)
Given a sufficient statistic for a parametric family of distributions, one can estimate the parameter without access to the data itself. However, the memory or code size for storing the sufficient statistic may nonetheless still be prohibitive. Indeed, for $n$ independent data samples drawn from a $k$-nomial distribution with $d=k-1$ degrees of freedom, the length of the code scales as $d\log n+O(1)$. In many applications though, we may not have a useful notion of sufficient statistics and also may not need to reconstruct the generating distribution exactly. By adopting a Shannon-theoretic approach in which we consider allow a small error in estimating the generating distribution, we construct various notions of approximate sufficient statistics and show that the code length can be reduced to $\frac{d}{2}\log n+O(1)$. We consider errors measured according to the relative entropy and variational distance criteria. For the code construction parts, we leverage Rissanen's minimum description length (MDL) principle, which yields a non-vanishing error measured using the relative entropy. For the converse parts, we use Clarke and Barron's asymptotic expansion for the relative entropy of a parametrized distribution and the corresponding mixture distribution. The limitation of this method is that only a weak converse for the variational distance can be shown. We develop new techniques to achieve vanishing errors and we also prove strong converses for all our statements. The latter means that even if the code is allowed to have a non-vanishing error, its length must still be at least $\frac{d}{2}\log n$.
pp. 3045-3049
15:20 Information-theoretic characterizations of Markov random fields and subfields
Raymond W. Yeung (The Chinese University of Hong Kong, Hong Kong); Ali Al-Bashabsheh (Beijing Advanced Innovation Center for Big Data and Brain Computing (BDBC), Beihang University, P.R. China); Chao Chen (Xi'dian, P.R. China); Qi Chen (The Chinese University of Hong Kong, Hong Kong); Pierre Moulin (University of Illinois at Urbana-Champaign, USA)
Let $X_i, i \in V$ form a Markov random field (MRF) represented by an undirected graph $G = (V,E)$, and $V'$ be a subset of $V$. We determine the smallest graph that can always represent the subfield $X_i, i \in V'$ as an MRF. Based on this result, we obtain a necessary and sufficient condition for a subfield of a Markov tree to be also a Markov tree. When $G$ is a path so that $X_i, i \in V$ form a Markov chain, it is known that the $I$-Measure is always nonnegative [2]. We prove that Markov chain is essentially the only MRF that possesses this property. Our work is built on the set-theoretic characterization of an MRF in [4]. Unlike most works in the literature, we do not make the standard assumption that the underlying probability distribution is factorizable with respect to the graph representing the MRF.
pp. 3050-3054
15:40 Conditional Central Limit Theorems for Gaussian Projections
Galen Reeves (Duke University, USA)
This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on low-dimensional projections of high-dimensional point clouds. The focus of this paper is on the typical behavior when the projections are generated by an i.i.d. Gaussian projection matrix. The main results are bounds on the deviation between the conditional distribution of the projections and a Gaussian approximation, where the conditioning is on the projection matrix. The bounds are given in terms of the quadratic Wasserstein distance and relative entropy and are stated explicitly as a function of the number of projections and certain key properties of the random vector. The proof uses Talagrand's transportation inequality and a general integral-moment inequality for mutual information. Applications to random linear estimation and compressed sensing are discussed.
pp. 3055-3059
16:00 An Information Theoretic Analysis of Sequential Decision-Making
Meik Dörpinghaus (TU Dresden, Germany); Édgar Roldán and Izaak Neri (Max-Planck-Institute for the Physics of Complex Systems, Germany); Heinrich Meyr (RWTH Aachen University, Germany); Frank Jülicher (Max Planck Institute for the Physics of Complex Systems, Germany)
We provide a novel analysis of Wald's sequential probability ratio test based on information theoretic measures for symmetric thresholds, symmetric noise, and equally likely hypotheses. This test is optimal in the sense that it yields the minimum mean decision time. To analyze the decision-making process we consider information densities, which represent the stochastic information content of the observations yielding a stochastic termination time of the test. Based on this, we show that the conditional probability to decide for hypothesis $H_1$ (or the counter-hypothesis $H_0$) given that the test terminates at time instant $k$ is independent of time $k$. An analogous property has been found for a continuous-time first passage problem with two absorbing boundaries in the contexts of non-equilibrium statistical physics and communication theory. Moreover, we study the evolution of the mutual information between the binary variable to be tested and the output of the Wald test. Notably, we show that the decision time of the Wald test contains no information on which hypothesis is true beyond the decision outcome.
pp. 3060-3064

#### Fr3-8: Index Coding 2

Room: K7+8
Chair: Guido Montorsi (Politecnico di Torino, Italy)
14:40 On the Capacity for Distributed Index Coding
Yucheng Liu (Australian National University, Australia); Parastoo Sadeghi (The Australian National University, Australia); Fatemeh Arbabjolfaei (University of California, San Diego, USA); Young-Han Kim (UCSD, USA)
The distributed index coding problem is studied, whereby multiple messages are stored at different servers to be broadcast to receivers with side information. First, the existing composite coding scheme is enhanced for the centralized (single-server) index coding problem, which is then merged with fractional partitioning of servers to yield a new coding scheme for distributed index coding. New outer bounds on the capacity region are also established. For 213 out of 218 non-isomorphic distributed index coding problems with four messages the achievable sum-rate of the proposed distributed composite coding scheme matches the outer bound, thus establishing the sum-capacity for these problems.
pp. 3065-3069
15:00 Improved Bounds for Multi-Sender Index Coding
Min Li and Lawrence Ong (The University of Newcastle, Australia); Sarah J Johnson (University of Newcastle, Australia)
We establish new capacity bounds for the multi-sender unicast index-coding problem. We first revisit existing bounds proposed by Sadeghi et al. and identify the suboptimality of their inner bounds in general. We then present a simplified version of the existing multi-sender maximal-acyclic-induced-subgraph outer bound. For the inner bound, we propose joint link-and-sender partitioning to replace sender partitioning in partitioned Distributed Composite Coding (DCC). This leads to a modified DCC (mDCC) that outperforms partitioned DCC and suffices to achieve optimality for some index-coding instances. We also propose cooperative compression of composite messages in composite coding to exploit messages common to different senders to support larger composite rates than those by point-to-point compression in the existing schemes. We then develop a new multi-sender Cooperative Composite Coding (CCC) scheme. CCC further improves upon mDCC in general, and is instrumental to achieve optimality for a number of index-coding instances.
pp. 3070-3074
15:20 Uniprior Index Coding
Vijaya Kumar Mareedu (International Institute of Information Technology, Hyderabad (IIIT H), India); Prasad Krishnan (IIIT Hyderabad, India)
The index coding problem is a problem of efficient broadcasting with side-information. We look at the uniprior index coding problem, in which the receivers have disjoint side-information symbols and arbitrary demand sets. Previous work has addressed single uniprior index coding, in which each receiver has a single unique side-information symbol. Modeling the uniprior index coding problem as a \textit{supergraph}, we focus on a class of uniprior problems defined on \textit{generalized cycle} supergraphs. For such problems, we prove upper and lower bounds on the optimal broadcast rate. Using a connection with Eulerian directed graphs, we also show that the upper and lower bounds are equal for a subclass of uniprior problems. We show the NP-hardness of finding the lower bound for uniprior problems on generalized cycles. Finally, we look at a simple extension of the generalized cycle uniprior class for which we give bounds on the optimal rate and show an explicit scheme which achieves the upper bound.
pp. 3075-3079
15:40 Rate $\frac{1}{3}$ Index Coding: Forbidden and Feasible Configurations
Linear index coding can be formulated as an interference alignment problem, in which precoding vectors of the minimum possible length are to be assigned to the messages in such a way that the precoding vector of a demand (at some receiver) is independent of the space of the interference (non side-information) precoding vectors. An index code has rate $\frac{1}{l}$ if the assigned vectors are of length $l$. In this paper, we introduce the notion of strictly rate $\frac{1}{L}$ message subsets which must necessarily be allocated precoding vectors from a strictly $L$-dimensional space ($L=1,2,3$) in any rate $\frac{1}{3}$ code. We develop a general necessary condition for rate $\frac{1}{3}$ feasibility using intersections of strictly rate $\frac{1}{L}$ message subsets. We apply the necessary condition to show that the presence of certain interference configurations makes the index coding problem rate $\frac{1}{3}$ infeasible. We also obtain a class of index coding problems, containing certain interference configurations, which are rate $\frac{1}{3}$ feasible based on the idea of \textit{contractions} of an index coding problem. Our necessary conditions for rate $\frac{1}{3}$ feasibility and the class of rate $\frac{1}{3}$ feasible problems obtained subsume all such known results for rate $\frac{1}{3}$ index coding.
pp. 3080-3084

#### Fr3-9: Statistics 2

Room: K9
Chair: Raymond W. Yeung (The Chinese University of Hong Kong, Hong Kong)
14:40 Divergence Scaling of Fixed-Length, Binary-Output, One-to-one Distribution Matching
Patrick Schulte (Technische Universität München, Germany); Bernhard C. Geiger (Technical University of Munich, Germany)
Distribution matching is the process of invertibly mapping a uniformly distributed input sequence onto sequences that approximate the output of a desired discrete memoryless source. The special case of a binary output alphabet and one-to-one mapping is studied. A fixed-length distribution matcher is proposed that is optimal in the sense of minimizing the unnormalized informational divergence between its output distribution and a binary memoryless target distribution. Upper and lower bounds on the unnormalized divergence are computed that increase logarithmically in the output block length $n$. It follows that a recently proposed constant composition distribution matcher performs within a constant gap of the minimal achievable informational divergence.
pp. 3085-3089
15:00 Lower Bounds on the Minimax Risk for the Source Localization Problem
Praveen Venkatesh and Pulkit Grover (Carnegie Mellon University, USA)
The `source localization'' problem is one in which we estimate the location of a point source observed through a diffusive medium using an array of sensors. We give lower bounds on the minimax risk (mean squared-error in location) in estimating the location of the source, which apply to all estimators, for certain classes of diffusive media, when using a uniformly distributed sensor array. We show that for sensors of a fixed size, the lower bound decays with increasing numbers of sensors. We also analyze a more physical sensor model to understand the effect of shrinking the size of sensors as their number increases to infinity, wherein the bound saturates for large sensor numbers. In this scenario, it is seen that there is greater benefit to increasing the number of sensors as the signal-to-noise ratio increases. Our bounds are the first to give a scaling for the minimax risk in terms of the number of sensors used.
pp. 3090-3094
15:20 On the Optimality of Some Group Testing Algorithms
Matthew Aldridge (University of Bath & Heilbronn Institute for Mathematical Research, United Kingdom (Great Britain))
We consider Bernoulli nonadaptive group testing with $k = n^\theta$ defectives, for $\theta \in (0,1)$. The practical definite defectives (DD) detection algorithm is known to be optimal for $\theta > 1/2$. We give a new upper bound on the rate of DD, showing that DD is strictly suboptimal for $\theta < 0.41$. We also show that the SCOMP algorithm and algorithms based on linear programming achieve a rate at least as high as DD, so in particular are also optimal for $\theta > 1/2$.
pp. 3095-3099
15:40 Measurement Dependent Noisy Search: The Gaussian Case
Anusha Lalitha (University of California San Diego, USA); Nancy Ronquillo and Tara Javidi (UCSD, USA)
This paper considers the problem of searching for the unknown location of a target among a finite number of possible locations by probing multiple locations simultaneously. Outcome of each search measurement is corrupted by Gaussian noise whose intensity is proportional to the number of locations probed. We characterize a non-asymptotic lower bound on adaptivity gain; i.e. reduction in the expected number of measurements under an adaptive search strategies over the non-adaptive search strategies. Then we investigate the adaptivity gain in two complementary asymptotic regimes: one where the total search area is kept fixed but the location width is shrinking or the search resolution is increasing, and the other where each location width is fixed but the total search area is growing. Interestingly, adaptivity gain grows in distinctly different manner in these two regimes. In particular, adaptivity gains are significant in the later regime when the total search space grows; implying adaptivity is far more critical when either total search area or the noise intensity is large.
pp. 3100-3104
16:00 Scalable Multichannel Joint Sequential Change Detection and Isolation
Sourabh Banerjee and Georgios Fellouris (University of Illinois at Urbana-Champaign, USA)
The problem of joint sequential change detection and isolation in a multichannel system is considered. It is assumed that a disruption occurs at some unknown time, and changes the distributions of the observations in an unknown subset of channels. The problem is to quickly detect the change, and at the same time to reliably isolate the affected channels. A novel scheme is proposed for this task, which admits a recursive structure, is scalable with respect to the number of channels, and does not require any prior information about the change-point. Its performance is analyzed in the special case that the number of affected channels is known. Specifically, explicit critical values are obtained for the control of the false alarm rate and the conditional probability of wrong isolation below arbitrary levels to be prescribed by the practitioner. Finally, the asymptotic optimality of the average detection delay of the proposed scheme is established as the error probabilities go to 0 and the effect of the prior distribution for the change point vanishes in the limit.
pp. 3105-3109

### Friday, June 30, 16:40 - 18:00

#### Fr4-1: Coding Theory 4

Room: Europa
Chair: Hans-Andrea Loeliger (ETH Zurich, Switzerland)
16:40 A New Approach for Constructing and Decoding Maximum Rank Distance Codes
Hessam Mahdavifar (University of Michigan, USA)
A rank-metric code is a subset of $\mathbb{F}_q ^{n \times m}$, where $\mathbb{F}_q$ is a finite field. Gabidulin codes are a well-known class of algebraic rank-metric codes that meet the Singleton bound on the minimum rank distance of a code. The construction, encoding, and decoding of Gabidulin codes use the extension field $\mathbb{F}_{q^m}$, where the code is regarded as a linear block code of length $n$ over $\mathbb{F}_{q^m}$. However, the parameter $m$ can be large in certain applications and therefore, performing field operations over $\mathbb{F}_{q^m}$ can become very complex. In this paper, we investigate methods for constructing and decoding rank-metric codes by looking into linear codes of length $nm$ over the base field $\mathbb{F}_q$. Random coding bounds are derived on the minimum distance of such codes and an explicit structure is demonstrated to construct maximum rank distance codes. It is shown how to construct sparse parity-check matrices for these structures which enables low complexity parallelized decoders with complexity that scales linearly with $m$.
pp. 3110-3114
17:00 Individually-Secure Multi-Source Multicast
Alejandro Cohen (Ben-Gurion University, Israel); Asaf Cohen (Ben-Gurion University of the Negev, Israel); Omer Gurewitz (Ben-Gurion University Of The Negev, Israel); Muriel Médard (MIT, USA)
The principal mission of Multi-Source Multicast (MSM) is to disseminate all messages from all sources in a network to all destinations. MSM is utilized in numerous applications. In many of them, securing the messages disseminated is critical. A common secure model is to consider a network where there is an eavesdropper which is able to observe a subset of the network links, and seek a code which keeps the eavesdropper ignorant regarding all the messages. While this is solved when all messages are located at a single source, Secure MSM (SMSM) is an open problem, and the rates required are hard to characterize in general. In this paper, we consider Individual Security, which promises that the eavesdropper has zero mutual information with each message individually. We completely characterize the rate region for SMSM under individual security, and show that such a security level is achievable at the full capacity of the network, that is, the cut-set bound is the matching converse, similar to non-secure MSM. Moreover, we show that the field size is similar to non-secure MSM and does not have to be larger due to the security constraint.
pp. 3115-3119
Alex Karrila, Niko Väisänen, David Karpuk and Camilla Hollanti (Aalto University, Finland)
In this paper, we study lattice coding for Rician fading wireless channels. This is motivated in particular by preliminary studies suggesting the Rician fading model for millimeter-wavelength wireless communications. We restrict to lattice codes arising from rotations of $\mathbb{Z}^n$, and to a single-input single-output (SISO) channel. We observe that several lattice design criteria suggest the optimality of Hadamard rotations. For instance, we prove that Hadamard rotations maximize the diamond-packing density among all rotated $\mathbb{Z}^n$ lattices. Finally, we provide simulations to show that Hadamard rotations outperform optimal algebraic rotations and cross-packing lattices in the Rician channel.
pp. 3120-3124

#### Fr4-2: DNA and Coding

Room: Brussels
Chair: Olgica Milenkovic (University of Illinois at Urbana-Champaign (UIUC), USA)
16:40 Mutually Uncorrelated Codes for DNA Storage
Maya Levy (Technion - Israel Institute of Technology, Israel); Eitan Yaakobi (Technion, Israel)
Mutually Uncorrelated (MU) codes is a class of codes in which no proper prefix of one codeword is a suffix of another codeword. These codes were originally studied for synchronization purposes and recently, Yazdi et al. showed their applicability to enable random access in DNA storage. In this work we follow the research of Yazdi et al. and study MU codes along with their extensions to correct errors and balanced codes. We first study a well known construction of MU codes and show that its existing lower bound on the cardinality is tight. We also present efficient algorithm for MU codes with linear encoding and decoding. We then extend these results for $(d_h,d_m)$-MU codes that impose a minimum Hamming distance of $d_e$ between different codewords and $d_m$ between prefixes and suffixes. Particularly we show an efficient construction of these codes with nearly optimal redundancy. We provide similar results for the edit distance and balanced MU codes.
pp. 3125-3129
17:00 Noise and Uncertainty in String-Duplication Systems
Siddharth Jain and Farzad Farnoud (Hassanzadeh) (California Institute of Technology, USA); Moshe Schwartz (Ben-Gurion University of the Negev, Israel); Jehoshua Bruck (California Institute of Technology, USA)
Duplication mutations play a critical role in the generation of biological sequences. Simultaneously, they have a deleterious effect on data stored using in-vivo DNA data storage. While duplications have been studied both as a sequence-generation mechanism and in the context of error correction, for simplicity these studies have not taken into account the presence of other types of mutations. In this work, we consider the capacity of duplication mutations in the presence of point-mutation noise, and so quantify the generation power of these mutations. We show that if the number of point mutations is vanishingly small compared to the number of duplication mutations of a constant length, the generation capacity of these mutations is zero. However, if the number of point mutations increases to a constant fraction of the number of duplications, then the capacity is nonzero. Lower and upper bounds for this capacity are also presented. Another problem that we study is concerned with the mismatch between code design and channel in data storage in the DNA of living organisms with respect to duplication mutations. In this context, we consider the uncertainty of such a mismatched coding scheme measured as the maximum number of input codewords that can lead to the same output.
pp. 3130-3134
17:20 Rank Modulation Codes for DNA Storage
Netanel Raviv (Technion & Tel-Aviv University, Israel); Moshe Schwartz (Ben-Gurion University of the Negev, Israel); Eitan Yaakobi (Technion, Israel)
Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to maintain reliability in reading and writing, new coding schemes must be developed. In a reading technique called shotgun sequencing, a long DNA string is read in a sliding window fashion, and a profile vector is produced. It was recently suggested by Kiah et al. that such a vector can represent the permutation which is induced by its entries, and hence a rank modulation scheme arises. Although this interpretation suggests high error tolerance, it is unclear which permutations are feasible, and how to produce a DNA string whose profile vector induces a given permutation. In this paper, by observing some necessary conditions, an upper bound for the number of feasible permutations is given. Further, a technique for deciding the feasibility of a permutation is devised. By using this technique, an algorithm for producing a considerable number of feasible permutations is given, which applies to any alphabet size and any window length.
pp. 3135-3139
17:40 Fundamental Limits of DNA Storage Systems
Reinhard Heckel (University of California, Berkeley, USA); Ilan Shomorony (UC Berkeley, USA); Kannan Ramchandran (University of California at Berkeley, USA); David Tse (Stanford University, USA)
Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and tradeoffs of DNA-based storage systems under a simple model, motivated by current technological constraints on DNA synthesis and sequencing. Our model captures two key distinctive aspects of DNA storage systems: (1) the data is written onto many short DNA molecules that are stored in an unordered way and (2) the data is read by randomly sampling from this DNA pool. Under this model, we characterize the storage capacity, and show that a simple index-based coding scheme is optimal.
pp. 3140-3144

#### Fr4-3: Error Exponents

Room: K2
Chair: Meir Feder (Tel-Aviv University, Israel)
16:40 Distributed Identity Testing with Zero-Rate Compression
Wenwen Zhao and Lifeng Lai (University of California, Davis, USA)
In this paper, we consider the identity testing problems in the distributed setting, in which each terminal has data only relates to one random variable. Each terminal sends zero-rate message to the decision maker, and the decision maker decides the distribution of $(X^n; Y^n)$, which is indirectly revealed from the encoded messages, is the same as or $\lambda$-far from a given distribution. Interpreting this as a distributed composite hypothesis testing problem, we characterize the best error exponent of the type 2 error probability using a universal coding scheme under the exponential-type constraint on the type 1 error probability.
pp. 3145-3149
17:00 Exponential source/channel duality
Sergey Tridenski and Ram Zamir (Tel Aviv University, Israel)
We propose a source/channel duality in the exponential regime, where success/failure in source coding parallels error/correctness in channel coding, and a distortion constraint becomes a log-likelihood ratio (LLR) threshold. We establish this duality by first deriving exact exponents for lossy coding of a memoryless source P, at distortion D, for a general i.i.d. codebook distribution Q, for both encoding success (R<R(P,Q,D)) and failure (R>R(P,Q,D)). We then turn to maximum likelihood (ML) decoding over a memoryless channel P with an i.i.d. input Q, and show that if we substitute P=QP, Q=Q, and D=0 under the LLR distortion measure, then the exact exponents for decoding-error (R < I(Q, P)) and strict correct-decoding (R > I(Q, P)) follow as special cases of the exponents for source encoding success/failure, respectively. Moreover, by letting the threshold D take general values, the exact random-coding exponents for erasure (D>0) and list decoding (D<0) under the simplified Forney decoder are obtained. Finally, we derive the exact random-coding exponent for Forney's optimum tradeoff erasure/list decoder, and show that at the erasure regime it coincides with Forney's lower bound and with the simplified decoder exponent, settling a long standing conjecture.
pp. 3150-3154
17:20 Error Exponents for Sparse Communication
Lóránt Farkas and Tamás Kói (Budapest University of Technology and Economics, Hungary); Imre Csiszár (Renyi Institute, Hungarian Academy of Science, Hungary)
Communication over a discrete memoryless channel is addressed when codewords are transmitted in certain time intervals of arbitrary locations, at other times the channel outputs pure noise. The receiver has to locate and decode the codewords. Exponential error bounds are derived, jointly achievable via a semi-universal or universal decoder. Implications are discussed for the familiar model of communication under strong asynchronism when in exponentially long time only one codeword is transmitted.
pp. 3155-3159
17:40 Universal Random Access Error Exponents for Codebooks with Different Word-Lengths
Lóránt Farkas and Tamás Kói (Budapest University of Technology and Economics, Hungary)
Csiszár's channel coding theorem for multiple codebooks is generalized allowing the codeword lengths differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent for this codebook alone, in addition, the overload detection failure probability tends to 0. This is proved even for sender and receiver not knowing the channel. As a corollary, a substantial improvement is obtained when the sender knows the channel.
pp. 3160-3164

#### Fr4-4: Bounds 4

Room: K3
Chair: Itzhak Tamo (Tel Aviv University, Israel)
16:40 Bounds on the Rate and Minimum Distance of Codes with Availability
Balaji Srinivasan Babu (IISc, India); P Vijay Kumar (Indian Institute of Science & University of Southern California, India)
In this paper we investigate bounds on rate and minimum distance of codes with $t$ availability. We present bounds on minimum distance of a code with $t$ availability that are tighter than existing bounds. For bounds on rate of a code with $t$ availability, we restrict ourselves to a sub-class of codes with $t$ availability called codes with strict $t$ availability and derive a tighter rate bound. Codes with strict $t$ availability can be defined as the null space of an $(m \times n)$ parity-check matrix $H$, where each row has weight $(r+1)$ and each column has weight $t$, with intersection between support of any two rows at most one. We also present two general constructions for codes with $t$ availability.
pp. 3165-3169
17:00 Improved existence bounds on IPP codes using the Clique Lovász Local Lemma
Cástor Aranda and Marcel Fernández (Technical University of Catalonia, Spain)
Codes with the Identifying Parent Property constitute a powerful type of codes with many uses in fingerprinting. Thus, it is of great interest to find sharp existence bounds for that class of codes. By applying a specific variation of the Lovász Local Lemma, we get existence bounds on q-ary IPP codes that improve previously stated ones.
pp. 3170-3174
17:20 Explicit bounds on the length of optimal X-codes
Yu Tsunoda and Yuichiro Fujiwara (Chiba University, Japan)
X-codes are linear maps with a special combinatorial property that generalizes superimposed codes, disjunct matrices, and cover-free families. In the context of circuit testing, a $(t,n,d,x)$ X-code compresses $n$-bit output from the circuit under test into $t$ bits while allowing for detecting the existence of up to $d$ erroneous output bits even if up to $x$ bits of the correct behavior are unknowable. A simple counting argument shows that a $(t,n,d,x)$ X-code with $t = O(\log n)$ exists, where the coefficient of the logarithmic term when the base is $2$ is at most $2^{x+1}(d+x)\ln 2$ with $\ln$ being the natural logarithm to base $e$. While there are also known constructions that provide X-codes with smaller $t$ for given $n$ and some specific $d$ and $x$, no stronger general upper bounds on the smallest possible $t$ that work for any $d$ and $x$ are available in the literature. Here, we derive general upper bounds in closed form that reduce the coefficient of the basic general bound to $(x+1)(d+x-1)e\ln 2$. In terms of the highest achievable rate, our results exponentially improve the known asymptotic lower bound $1/(2^{x+1}(d+x)\ln 2)$ to $1/((x+1)(d+x-1)e\ln 2)$.
pp. 3175-3179
17:40 A convolution inequality for entropy over Z2
Varun Jog (University of Wisconsin - Madison, USA)
We prove an inequality for the entropy of a sum of two independent random variables taking values in the group $\mathbb Z_2$. Our inequality is very simply stated, and may be interpreted as a lower bound on the capacity of a cascade of two BSC channels in terms of the capacities of the component BSC channels. The inequality provides an upper bound on the entropy of a sum of two $\mathbb Z_2$-valued random variables, and thus it may also be thought of as a reverse entropy power inequality. One of the intriguing features of this inequality is that it only holds if entropy is measured in bits; i.e., the base with respect to which logarithms are taken matters crucially.
pp. 3180-3184

#### Fr4-5: Shannon Theory and Applications

Room: K4
Chair: Sergio Verdú (Princeton University, USA)
16:40 Topological Structures on DMC spaces
Rajai Nasser (École Polytechnique Fédérale de Lausanne, Switzerland)
Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet $\mathcal{X}$ and output alphabet $\mathcal{Y}$ can be naturally endowed with the quotient of the Euclidean topology by the equivalence relation. We show that this topology is compact, path-connected and metrizable. A topology on the space of equivalent channels with fixed input alphabet $\mathcal{X}$ and arbitrary but finite output alphabet is said to be natural if and only if it induces the quotient topology on the subspaces of equivalent channels sharing the same output alphabet. We show that every natural topology is $\sigma$-compact, separable and path-connected. On the other hand, if $|\mathcal{X}|\geq 2$, a Hausdorff natural topology is not Baire and it is not locally compact anywhere. This implies that no natural topology can be completely metrized if $|\mathcal{X}|\geq 2$. The finest natural topology, which we call the strong topology, is shown to be compactly generated, sequential and $T_4$. On the other hand, the strong topology is not first-countable anywhere, hence it is not metrizable. We show that in the strong topology, a subspace is compact if and only if it is rank-bounded and strongly-closed. We provide a necessary and sufficient condition for a sequence of channels to converge in the strong topology. We introduce a metric distance on the space of equivalent channels which compares the noise levels between channels. The induced metric topology, which we call the noisiness topology, is shown to be natural. We also study topologies that are inherited from the space of meta-probability measures by identifying channels with their Blackwell measures. We show that the weak-$\ast$ topology is exactly the same as the noisiness topology and hence it is natural. We prove that if $|\mathcal{X}|\geq 2$, the total variation topology is not natural nor Baire, hence it is not completely metrizable. Moreover, it is not locally compact anywhere. Finally, we show that the Borel $\sigma$-algebra is the same for all Hausdorff natural topologies.
pp. 3185-3189
17:00 A Strong Data Processing Inequality for Thinning Poisson Processes and Some Applications
Ligong Wang (ETIS & CNRS, France)
This paper derives a simple strong data processing inequality (DPI) for Poisson processes: after a Poisson process is passed through $p$-thinning---in which every arrival remains in the process with probability $p$ and is erased otherwise, independently of the other points---the mutual information between the Poisson process and any other random variable is reduced to no more than $p$ times its original value. This strong DPI is applied to prove tight converse bounds in several problems: hypothesis testing with communication constraints, a mutual information game, and a CEO problem.
pp. 3190-3194
17:20 Continuity of Channel Parameters and Operations under Various DMC Topologies
Rajai Nasser (École Polytechnique Fédérale de Lausanne, Switzerland)
We study the continuity of several channel parameters and operations under various topologies on the space of equivalent discrete memoryless channels (DMC). We show that mutual information, channel capacity, Bhattacharyya parameter, probability of error of a fixed code, and optimal probability of error for a given code rate and blocklength, are continuous under various DMC topologies. We also show that channel operations such as sums, products, interpolations, and Ar{\i}kan-style transformations are continuous.
pp. 3195-3199
17:40 SCW Codes for Optimal CSI-Free Detection in Diffusive Molecular Communications
Vahid Jamali (Friedrich-Alexander-University Erlangen-N¨urnberg, Germany); Arman Ahmadzadeh (University of Erlangen-Nuremberg, Germany); Nariman Farsad (Stanford University, USA); Robert Schober (University of British Columbia, Canada)
Instantaneous or statistical channel state information (CSI) is needed for most detection schemes developed in the molecular communication (MC) literature. Since the MC channel changes, e.g., due to variations in the velocity of flow, the temperature, or the distance between transmitter and receiver, CSI acquisition has to be conducted repeatedly to keep track of CSI variations. Frequent CSI acquisition may entail a large overhead whereas infrequent CSI acquisition may result in a low CSI estimation quality. To cope with these issues, we design codes which facilitate maximum likelihood sequence detection at the receiver without instantaneous or statistical CSI. In particular, assuming concentration shift keying modulation, we show that a class of codes, referred to as strongly constant-weight (SCW) codes, enables optimal CSI-free sequence detection at the cost of decreasing the data rate. For the proposed SCW codes, we analyze the code rate and the error rate. Simulation results verify our analytical derivations and reveal that the proposed CSI-free detector for SCW codes outperforms the baseline coherent and non-coherent detectors for uncoded transmission.
pp. 3200-3204

#### Fr4-6: Quantum IT 5

Room: K5
Chair: Masahito Hayashi (Nagoya University, Japan)
16:40 Pretty good measures in quantum information theory
Raban Iten, Joseph M. Renes and David Sutter (ETH Zurich, Switzerland)
Quantum generalizations of Rényi's entropies are a useful tool to describe a variety of operational tasks in quantum information processing. Two families of such generalizations turn out to be particularly useful: the Petz quantum Rényi divergence $\bar D_\alpha(\rho||\sigma)$ and the minimal quantum Rényi divergence $\tilde D_\alpha(\rho||\sigma)$. In this paper, we prove a reverse Araki-Lieb-Thirring inequality that implies a new relation between these two families of divergences, namely that $\alpha \bar D_\alpha(\rho||\sigma) \leq \tilde D_\alpha(\rho||\sigma)$ for $\alpha \in [0,1]$ and where $\rho$ and $\sigma$ are density operators. This bound suggests defining a "pretty good fidelity", whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction.
pp. 3205-3209
17:00 Linear Programming Bounds for Entanglement-Assisted Quantum Codes
Ching-Yi Lai (Academia Sinica, Taiwan); Alexei Ashikhmin (Nokia Bell Labs, USA)
In this paper, we define two split weight enumerators for general quantum codes with entanglement assistance, including nonadditive codes. We show that they obey a MacWilliams identity, which allows us to prove algebraic linear programming bounds, such as the Singleton bound, the Hamming bound, and the first linear programming bound. On the other hand, we derive additional constraints on the size of Pauli subgroups for quantum codes, which helps to improve the linear programming bounds on the minimum distance of quantum codes of small length.
pp. 3210-3214
17:20 Estimating the Information Rate of a Channel with Classical Input and Output and a Quantum State
Michael Cao and Pascal Vontobel (The Chinese University of Hong Kong, Hong Kong)
We consider the problem of transmitting classical information over a time-invariant channel with memory. A popular class of time-invariant channels with memory are finite-state-machine channels, where a classical state evolves over time and governs the relationship between the classical input and the classical output of the channel. For such channels, various techniques have been developed for estimating and bounding the information rate. In this paper we consider a class of time-invariant channels where a quantum state evolves over time and governs the relationship between the classical input and the classical output of the channel. We propose algorithms for estimating and bounding the information rate of such channels. In particular, we discuss suitable graphical models for doing the relevant computations.
pp. 3215-3219
17:40 Fundamental limits of quantum-secure covert optical sensing
Boulat Bash (Raytheon BBN Technologies, USA); Christos Gagatsos and Animesh Datta (University of Warwick, United Kingdom (Great Britain)); Saikat Guha (Raytheon BBN Technologies, USA)
We present a square root law for active sensing of phase $\theta$ of a single pixel using optical probes that pass through a single-mode lossy thermal-noise bosonic channel. Specifically, we show that, when the sensor uses an n-mode covert optical probe, the mean squared error (MSE) of the resulting estimator $\hat{\theta}_n$ scales as $\langle(\theta-\hat{\theta}_n)^2\rangle=\mathcal{O}(1/\sqrt{n})$; improving the scaling necessarily leads to detection by the adversary with high probability. We fully characterize this limit and show that it is achievable using laser light illumination and a heterodyne receiver, even when the adversary captures every photon that does not return to the sensor and performs arbitrarily complex measurement as permitted by the laws of quantum mechanics.
pp. 3220-3224

#### Fr4-7: Source Coding 5

Room: K6
Chair: Galen Reeves (Duke University, USA)
16:40 Source Coding with Distortion Profile Constraints
Pierre Moulin (University of Illinois at Urbana-Champaign, USA)
In rate-distortion theory, three main types of distortion constraints have been popular: average, pointwise, and excess probability (aka $\epsilon$-fidelity). A new setup is proposed here, which is suitable for fixed-length codes and constrains the distribution (profile) of distortions. This is accomplished by imposing multiple constraints on excess-distortion probabilities as well as an optional constraint on average distortion. We show that coding redundancy for compressing discrete memoryless sources is upper-bounded by $R_2/\sqrt{n} + \frac{\log n}{2n} + O(\frac{\log\log n}{n}) + \overline{R}_4 + o(1)$ where $n$ is the block length, $R_2$ the second-order coding rate, and $\overline{R}_4$ a constant. For the special case of coding with a single $\epsilon$-fidelity constraint, $R_2 = \sqrt{V} \,\mathcal{Q}^{-1}(\epsilon)$ where $V$ is the source rate-dispersion function, and $\mathcal{Q}$ is the tail probability of a normal random variable. The upper bound is proved using a random coding scheme and deriving exact asymptotics for the probability of distortion balls with input type dependent radius.
pp. 3225-3229
17:00 Lower Bounds on Rate of Fixed-Length Source Codes under Average- and $\epsilon$-Fidelity Constraints
Pierre Moulin (University of Illinois at Urbana-Champaign, USA)
This paper studies lossy coding of discrete memoryless sources and derives new asymptotic lower bounds on the rate of optimal fixed-length codes. Both average and excess-probability distortion constraints are studied. We show that in each case the rate of optimal codes is lower bounded by $R(D) + R_2/\sqrt{n} + (\log n)/(2n) + \underline{R}_4/n + o(1)$ where $n$ is the block length, $R(D)$ is Shannon's rate-distortion function, $R_2$ is the second-order coding rate, and $\underline{R}_4$ a constant that is explicitly identified.
pp. 3230-3234
17:20 Enhanced MDL with Application to Atypicality
Elyas Sabeti and Anders Høst-Madsen (University of Hawaii, USA)
With the enormous amount of data generated through the internet and sensors, Internet of Things, it becomes too overwhelming for humans to examine it all. One solution is to reduce the data to a set of statistics. The perspective in this paper is the opposite, namely that most of this data is just background noise, and the interesting parts are those that deviate from background noise, the parts that are atypical. In order to find such "interesting" parts of data, universal approaches are required, since it is not known in advance what we are looking for. Our approach is to use Rissanen's minimum description length (MDL) as a tool for that. We would like to be able to find both short and long atypical sequences of data, and we therefore need accurate expressions of MDL, without prior assumptions. In this paper we develop a modified predictive MDL method that works better for short sequences.
pp. 3235-3239
17:40 Distributed Coding of Multispectral Images
Maxim Goukhshtein (University of Toronto, Canada); Petros T Boufounos (Mitsubishi Electric Research Laboratories & Rice University, USA); Toshiaki Koike-Akino (Mitsubishi Electric Research Laboratories (MERL), USA); Stark Draper (University of Toronto, Canada)
The acquisition and compression of multispectal images is often performed in an environment where resources such as computational power and memory are scarce. To that end, we propose a new extremely low-complexity encoding approach for compression of multispectral images, that shifts the complexity to the decoding. Our method combines principles from compressed sensing and distributed source coding. Specifically, the encoder compressively measures blocks of the band of interest and uses syndrome coding to encode the bitplanes of the measurements. The decoder has access to side information, which is used to predict the bitplanes and to decode them. The side information is also used to guide the reconstruction of the image from the decoded measurements. Our experimental results demonstrate significant improvement in the rate-distortion trade-off when compared to similar low-complexity coding schemes.
pp. 3240-3244