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TOC Alert for Publication# 18 2018December 06<![CDATA[Table of contents]]>6412C1C4150<![CDATA[IEEE Transactions on Information Theory publication information]]>6412C2C2144<![CDATA[Monte Carlo Methods for the Ferromagnetic Potts Model Using Factor Graph Duality]]>6412744974641350<![CDATA[Codes on Graphs: Models for Elementary Algebraic Topology and Statistical Physics]]>$(n, k)$ group codes and their information sets; normal realizations of homology and cohomology spaces; dual and hybrid models; and connections with system-theoretic concepts, such as observability, controllability, and input/output realizations.]]>6412746574873027<![CDATA[A Factor-Graph Approach to Algebraic Topology, With Applications to Kramers–Wannier Duality]]>6412748875102281<![CDATA[Simultaneous Partial Inverses and Decoding Interleaved Reed–Solomon Codes]]>641275117528385<![CDATA[Centralized Repair of Multiple Node Failures With Applications to Communication Efficient Secret Sharing]]>6412752975501212<![CDATA[Binary Images of <inline-formula> <tex-math notation="LaTeX">${mathbb{Z}_2mathbb{Z}_4}$ </tex-math></inline-formula>-Additive Cyclic Codes]]>${mathbb {Z}}_{2}{mathbb {Z}}_{4}$ -additive code ${mathcal{ C}}subseteq {mathbb {Z}}_{2}^alpha times {mathbb {Z}}_{4}^beta $ is called cyclic if the set of coordinates can be partitioned into two subsets, the set of ${mathbb {Z}}_{2}$ and the set of ${mathbb {Z}}_{4}$ coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. We study the binary images of $mathbb {Z}_{2} mathbb {Z}_{4} $ -additive cyclic codes. We determine all ${mathbb {Z}_{2}mathbb {Z}_{4}}$ -additive cyclic codes with odd $beta $ whose Gray images are linear binary codes. In this case, it is shown that such binary codes are permutation equivalent (by the Nechaev permutation) to $mathbb {Z}_{2}$ -double cyclic codes. Finally, the generator polynomials of these binary codes are given.]]>641275517556485<![CDATA[Communication Cost for Updating Linear Functions When Message Updates are Sparse: Connections to Maximally Recoverable Codes]]>difference vector, but only know the amount of sparsity that is present in the difference vector. Under this setting, we are interested in devising linear encoding and decoding schemes that minimize the communication cost involved. We show that the optimal solution to this problem is closely related to the notion of maximally recoverable codes (MRCs), which were originally introduced in the context of coding for storage systems. In the context of storage, MRCs guarantee optimal erasure protection when the system is partially constrained to have local parity relations among the storage nodes. In our problem, we show that optimal solutions exist if and only if MRCs of certain kind (identified by the desired linear functions) exist. We consider point-to-point and broadcast versions of the problem and identify connections to MRCs under both these settings. For the point-to-point setting, we show that our linear-encoder-based achievable scheme is optimal even when non-linear encoding is permitted. The theory is illustrated in the context of updating erasure coded storage nodes. We present examples based on modern storage codes, such as the minimum bandwidth regenerating codes.]]>641275577576593<![CDATA[Bounds on Separating Redundancy of Linear Codes and Rates of X-Codes]]>641275777593896<![CDATA[A Statistical Model for Motifs Detection]]>$n$ vertices and edge probability $q_{0}$ . We ask whether the resulting graph can be distinguished reliably from a pure Erdős–Renyi random graph, and we present two types of result. First we investigate the question from a purely statistical perspective, and ask whether there is any test that can distinguish between the two graph models. We provide necessary and sufficient conditions that are essentially tight for small enough subgraphs. Next we study two polynomial-time algorithms for solving the same problem: a spectral algorithm and a semidefinite programming (SDP) relaxation. For the spectral algorithm, we establish sufficient conditions under which it distinguishes the two graph models with high probability. Under the same conditions the spectral algorithm indeed identifies the hidden subgraph. The spectral algorithm is substantially sub-optimal with respect to the optimal test. We show that a similar gap is present for the more sophisticated SDP approach.]]>641275947612448<![CDATA[Extreme Compressive Sampling for Covariance Estimation]]>$m^{2}/d^{2}$ , where $m$ is the compression dimension and $d$ is the ambient dimension. Applications to subspace learning (principal components analysis) and learning over distributed sensor networks are also discussed.]]>641276137635601<![CDATA[Lower Bounds on Exponential Moments of the Quadratic Error in Parameter Estimation]]>641276367648516<![CDATA[Approximation by Combinations of ReLU and Squared ReLU Ridge Functions With <inline-formula> <tex-math notation="LaTeX">$ell^1$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$ell^0$ </tex-math></inline-formula> Controls]]>$L^{infty } $ and $L^{2} $ error bounds for functions of many variables that are approximated by linear combinations of rectified linear unit (ReLU) and squared ReLU ridge functions with $ell ^{1} $ and $ell ^{0} $ controls on their inner and outer parameters. With the squared ReLU ridge function, we show that the $L^{2} $ approximation error is inversely proportional to the inner layer $ell ^{0} $ sparsity and it need only be sublinear in the outer layer $ell ^{0} $ sparsity. Our constructions are obtained using a variant of the Maurey–Jones–Barron probabilistic method, which can be interpreted as either stratified sampling with proportionate allocation or two-stage cluster sampling. We also provide companion error lower bounds that reveal near optimality of our constructions. Despite the sparsity assumptions, we showcase the richness and flexibility of these ridge combinations by defining a large family of functions, in terms of certain spectral conditions, that are particularly well approximated by them.]]>641276497656274<![CDATA[A Joint Typicality Approach to Compute–Forward]]>$K$ senders.]]>6412765776851246<![CDATA[Common-Message Broadcast Channels With Feedback in the Nonasymptotic Regime: Stop Feedback]]>$K$ -user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiy et al. (2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e., zero dispersion. In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message $K$ -user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaard et al. (2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case.]]>641276867718919<![CDATA[Common-Message Broadcast Channels With Feedback in the Nonasymptotic Regime: Full Feedback]]>641277197741690<![CDATA[Universal Sampling Rate Distortion]]>641277427758454<![CDATA[Spatiotemporal Information Coupling in Network Navigation]]>information coupling may result in poor performance: algorithms that discard information coupling are often inaccurate, and algorithms that keep track of all the neighbors’ interactions are often inefficient. In this paper, we develop a principled framework to characterize the information coupling present in network navigation. Specifically, we derive the equivalent Fisher information matrix for individual agents as the sum of effective information from each neighbor and the coupled information induced by the neighbors’ interaction. We further characterize how coupled information decays with the network distance in representative case studies. The results of this paper can offer guidelines for the development of distributed techniques that adequately account for information coupling, and hence enable accurate and efficient network navigation.]]>6412775977791199<![CDATA[Network Coherence Time Matters—Aligned Image Sets and the Degrees of Freedom of Interference Networks With Finite Precision CSIT and Perfect CSIR]]>network coherence time, i.e., coherence time in an interference network, where all channels experience the same coherence patterns. This is accomplished by a novel adaptation of the aligned image sets bound and settles various open problems noted previously by Naderi and Avestimehr and by Gou et al. For example, a necessary and sufficient condition is obtained for the optimality of 1/2 DoF per user in a partially connected interference network, where the channel state information at the receivers (CSIRs) is perfect, the channel state information at the transmitters (CSITs) is instantaneous but limited to finite precision, and the network coherence time is $T_{c}=1$ . The surprising insight that emerges is that even with perfect CSIR and instantaneous finite precision CSIT, the network coherence time matters, i.e., it has a DoF impact.]]>641277807791622<![CDATA[On Privacy Amplification, Lossy Compression, and Their Duality to Channel Coding]]>[7] and turns out to be equivalent to a recent formulation in terms of the $E_gamma $ divergence by Yang et al.[9]. In the latter, we show that the protocols for privacy amplification based on linear codes can be easily repurposed for channel simulation. Combined with the known relations between channel simulation and lossy source coding, this implies that the privacy amplification can be understood as a basic primitive for both channel simulation and lossy compression. Applied to symmetric channels or lossy compression settings, our construction leads to protocols of the optimal rate in the asymptotic i.i.d. limit. Finally, appealing to the notion of channel duality recently detailed by us in [15], we show that the linear error-correcting codes for symmetric channels with quantum output can be transformed into linear lossy source coding schemes for classical variables arising from the dual channel. This explains a “curious duality” in these problems for the (self-dual) erasure channel observed by Martinian and Yedidia [16] and partly anticipates recent results on optimal lossy compression by polar and low-density generator matrix codes.]]>641277927801469<![CDATA[Energy-Constrained Private and Quantum Capacities of Quantum Channels]]>641278027827717<![CDATA[On the Capacity of a Class of Signal-Dependent Noise Channels]]>641278287846608<![CDATA[Universal Lattice Codes for MIMO Channels]]>641278477865560<![CDATA[State-Dependent Gaussian Multiple Access Channels: New Outer Bounds and Capacity Results]]>641278667882828<![CDATA[Plausible Deniability Over Broadcast Channels]]>641278837902869<![CDATA[Polar Coding for the Multiple Access Wiretap Channel via Rate-Splitting and Cooperative Jamming]]>explicit and low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting, which introduces two virtual transmitters, and cooperative jamming strategies implemented by these virtual transmitters. Specifically, our coding scheme combines point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on block Markov encoding to be able to deal with an arbitrary channel and strong secrecy. Consequently, our coding scheme is the combination of inter-dependent block Markov constructions. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.]]>6412790379211343<![CDATA[Blank page]]>6412B7922B79223<![CDATA[IEEE Transactions on Information Theory information for authors]]>6412C3C366