<![CDATA[ IEEE Transactions on Information Theory - new TOC ]]>
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TOC Alert for Publication# 18 2016August 22<![CDATA[Table of contents]]>629C1C4176<![CDATA[IEEE Transactions on Information Theory publication information]]>629C2C21477<![CDATA[Design of Spatially Coupled LDPC Codes Over GF<inline-formula> <tex-math notation="LaTeX">$(q)$ </tex-math></inline-formula> for Windowed Decoding]]> , , and develop design rules for -ary SC-LDPC code ensembles based on their iterative belief propagation decoding thresholds, with particular emphasis on low-latency windowed decoding (WD). We consider transmission over both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise channel (BIAWGNC) and present results for a variety of -regular SC-LDPC code ensembles constructed over GF using protographs. Thresholds are calculated using the protograph versions of -ary density evolution (for the BEC) and the -ary extrinsic information transfer analysis (for the BIAWGNC). We show that the WD of -ary SC-LDPC codes provides significant threshold gains compared with corresponding (uncoupled) -ary LDPC block code (LDPC-BC) ensembles when the window size is large enough and that these gains increase as the finite-field size increases. Moreover, we demonstrate that the new design rules provide WD thresholds that are close to capacity, even when both $m$ and are relatively small (thereby reducing decoding complexity and latency). The analysis further shows that, compared with standard flooding-schedule decoding, the WD of -ary SC-LDPC code ensembles results in significant reductions in both the decoding complexity and the decoding latency and that these reductions increase as increases. For the applications with a near-threshold performance requirement and a constraint on decoding latency, we show that using -ary SC-LDPC code ensembles, with moderate , instead of their binary counterparts results in reduced decoding complexity.]]>629478148002002<![CDATA[Information-Theoretic Sneak-Path Mitigation in Memristor Crossbar Arrays]]>62948014813977<![CDATA[Snake-in-the-Box Codes for Rank Modulation under Kendall’s <inline-formula> <tex-math notation="LaTeX">$tau $ </tex-math></inline-formula>-Metric in <inline-formula> <tex-math notation="LaTeX">$S_{2n+2}$ </tex-math></inline-formula>]]> -metric are studied in the rank modulation scheme for flash memories, where codewords are a subset of permutations in with minimal Kendall’s -distance two, and two cyclically consecutive codewords are connected via a push-to-the-top operation. Studies so far restrict the push-to-the-top operations only on odd indices, resulting in a snake consisting of permutations with the same parity, and thus, the minimal distance constraint is easily satisfied. Asymptotically optimal snake codes have been constructed this way in . As for , this framework keeps the last element fixed, and thus, a snake in is equivalent to a snake in , which is rather trivial. If one wants to do better, then it is inevitable to have some push-to-the-top operations on even indices, resulting in a combination of odd and even permutations in the snake, which increases the difficulty to guarantee the minimal Kendall’s -distance constraint. Thus, Horovitz and Etzion pose the open problem to prove or disprove that the size of the largest snake in is not larger than the size of the largest snake in . A first step toward this problem is a n-
gative answer by Wang and Fu, who construct a snake in with exactly one more permutation than an optimal snake in . In this paper, we give an explicit construction of a snake in with size asymptotically approaching .]]>62948144818461<![CDATA[Restricted Composition Deletion Correcting Codes]]>62948194832430<![CDATA[Multilevel Diversity Coding With Regeneration]]>629483348471570<![CDATA[Optimal Exact Repair Strategy for the Parity Nodes of the <inline-formula> <tex-math notation="LaTeX">$(k+2,k)$ </tex-math></inline-formula> Zigzag Code]]> zigzag code in coding matrix and then propose an optimal exact repair strategy for its parity nodes, whose repair disk I/O approaches a lower bound derived in this paper.]]>62948484856461<![CDATA[Further Exploration of Convolutional Encoders for Unequal Error Protection and New UEP Convolutional Codes]]>629485748662136<![CDATA[One- and Two-Point Codes Over Kummer Extensions]]> , where is a separable polynomial over . In addition, we compute the Weierstrass semigroup at two certain totally ramified places. We then apply our results to construct one- and two-point algebraic geometric codes with good parameters.]]>62948674872196<![CDATA[A Simple Proof of Polarization and Polarization for Non-Stationary Memoryless Channels]]>62948734878252<![CDATA[Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations]]>629487949091280<![CDATA[Two-User Erasure Interference Channels With Local Delayed CSIT]]>629491049231423<![CDATA[Projection Theorems for the Rényi Divergence on <inline-formula> <tex-math notation="LaTeX">$alpha $ </tex-math></inline-formula>-Convex Sets]]> on -convex sets. The forward projection on such a set is motivated by some works of Tsallis et al. in statistical physics, and the reverse projection is motivated by robust statistics. In a recent work, van Erven and Harremoës proved a Pythagorean inequality for Rényi divergences on -convex sets under the assumption that the forward projection exists. Continuing this study, a sufficient condition for the existence of a forward projection is proved for probability measures on a general alphabet. For , the proof relies on a new Apollonius theorem for the Hellinger divergence, and for , the proof relies on the Banach–Alaoglu theorem from the functional analysis. Further projection results are then obtained in the finite alphabet setting. These include a projection theorem on a specific -convex set, which is termed an -linear family, generalizing a result by Csiszár to . The solution to this problem yields a parametric family of probability measures, which turns out to be an extension of the exponential family, and it is termed an -exponen-
ial family. An orthogonality relationship between the -exponential and -linear families is established, and it is used to turn the reverse projection on an -exponential family into a forward projection on an -linear family. This paper also proves a convergence result of an iterative procedure used to calculate the forward projection on an intersection of a finite number of -linear families.]]>62949244935285<![CDATA[Multicoding Schemes for Interference Channels]]>629493649521055<![CDATA[Strong Converse Theorems for Classes of Multimessage Multicast Networks: A Rényi Divergence Approach]]>62949534967307<![CDATA[Capacity Results for Multicasting Nested Message Sets Over Combination Networks]]>629496849921641<![CDATA[The Two-User Causal Cognitive Interference Channel: Novel Outer Bounds and Constant Gap Result for the Symmetric Gaussian Noise Channel in Weak Interference]]> and are derived for the class of injective semideterministic CCICs, where the noises at the different source-destination pairs are independent. These outer bounds, as well as an achievable rate region based on Gelfand-Pinsker binning, superposition coding, and simultaneous decoding at the receivers, are then specialized to the Gaussian noise case. It is shown that the novel outer bounds are necessary to characterize the capacity within a constant gap when the cooperation link is weaker than the direct links, that is, in this regime unilateral cooperation leaves some system resources underutilized.]]>629499350171495<![CDATA[On the Relation Between Identifiability, Differential Privacy, and Mutual-Information Privacy]]>$D$ , we define the privacy-distortion functions $epsilon _{mathrm{ i}}^{*}(D)$ , $epsilon _{mathrm{ d}}^{*}(D)$ , and $epsilon _{mathrm{ m}}^{*}(D)$ to be the smallest (most private/best) identifiability level, differential privacy level, and mutual information between the input and the output, respectively. We characterize $epsilon _{mathrm{ i}}^{*}(D)$ and $epsilon _{mathrm{ d}}^{*}(D)$ , and prove that $epsilon _{mathrm{ i}}^{*}(D)-epsilon _{X}le epsilon _{mathrm{ d}}^{*}(D)le epsilon _{mathrm{ i}}^{*}(D)$ for $D$ within certain range, where $epsilon _{X}$ is a constant determined by the prior distribution of the original database $X$ , and diminishes to zero when $X$ is uniformly distributed. Furthermore, we show that $epsilon _{mathrm{ i}}^{*}(D)$ and $epsilon _{mathrm{ m}}^{*}(D)$ can be achieved by the same mechanism for $D$ within certain range, i.e., there is a mechanism that simultaneously minimizes the identifiability level and achieves the best mutual-information privacy. Based on these two connections, we prove that this mutual-information optimal mechanism satisfies $epsilon $ -differential privacy with $epsilon _{mathrm{ d}}^{*}(D)le epsilon le epsilon _{mathrm{ d}}^{*}(D)+2epsilon _{X}$ . The results in this paper reveal some consistency between two worst case notions of privacy, namely, identifiability and differential privacy, and an average notion of privacy, mutual-information privacy.]]>62950185029632<![CDATA[Power Optimization in Random Wireless Networks]]> -dimensional lattice of transmit-receive pairs. In this model, which has the important feature of a minimum distance between transmitter nodes, we find that when the network is infinite, power control is always feasible below a positive critical value of the users’ signal-to-interference-plus-noise ratio (SINR) target. Drawing on tools and ideas from statistical physics, we show how this problem can be mapped to the Anderson impurity model for diffusion in random media. In this way, by employing the so-called coherent potential approximation method, we calculate the average power in the system (and its variance) for 1-D and 2-D networks. This approach is equivalent to traditional techniques from random matrix theory and is in excellent agreement with the numerical simulations; however, it fails to predict when power control becomes infeasible. In this regard, even though infinitely large systems are always unstable beyond a critical value of the users’ SINR target, finite systems remain stable with high probability even beyond this critical SINR threshold. We calculate this probability by analyzing the density of low lying eigenvalues of an associated random Schrödinger operator, and we show that the network can exceed this critical SINR threshold by at least before undergoing a phase transition to the unstable regime. Finally, using the same techniques, we also calculate the tails of the distribution of transmit power in the system and the rate of convergence of the Foschini–Miljanic power-
control algorithm in the presence of random erasures.]]>629503050581615<![CDATA[A Framework for Joint Design of Pilot Sequence and Linear Precoder]]>629505950791337<![CDATA[Rate-Distortion Function for a Heegard-Berger Problem With Two Sources and Degraded Reconstruction Sets]]>62950805092662<![CDATA[Multi-Class Source-Channel Coding]]>62950935104848<![CDATA[Volume of Metric Balls in High-Dimensional Complex Grassmann Manifolds]]>62951055116827<![CDATA[From Denoising to Compressed Sensing]]>629511751442750<![CDATA[Unknown Sparsity in Compressed Sensing: Denoising and Inference]]> can be accurately recovered from an underdetermined set of linear measurements with provided that is sufficiently sparse. However, in applications, the degree of sparsity is typically unknown, and the problem of directly estimating has been a longstanding gap between theory and practice. A closely related issue is that is a highly idealized measure of sparsity, and for real signals with entries not equal to 0, the value is not a useful description of compressibility. In our previous conference paper [1] that examined these problems, we considered an alternative measure of soft sparsity, , and designed a procedure to estimate that does not rely on sparsity assumptions. This paper offers a new deconvolution-based method for estimating unknown sparsity, which has wider applicability and sharper theoretical guarantees. In particular, we introduce a family of entropy-based sparsity measures . This family interpolates between and as ranges over [0, 2]. For any , we propose an estimator whose relative error converges at the dimension-free rate of , even when . Our main results also describe the limiting distribution of , as well as some connections to basis pursuit denosing, the Lasso, deterministic measurement matrices, and inference problems in CS.]]>629514551661027<![CDATA[Representer Theorems for Sparsity-Promoting <inline-formula> <tex-math notation="LaTeX">$ell _{1}$ </tex-math></inline-formula> Regularization]]>$ell _{1}$ versus $ell _{2}$ regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the solution is specified as the minimizer of a convex cost functional. We derive a series of representer theorems that give the generic form of the solution depending on the type of regularization. We start with the analysis of the problem in finite dimensions and then extend our results to the infinite-dimensional spaces $ell _{2}( mathbb {Z})$ and $ell _{1}( mathbb {Z})$ . We also consider the use of linear transformations in the form of dictionaries or regularization operators. In particular, we show that the $ell _{2}$ solution is forced to live in a predefined subspace that is intrinsically smooth and tied to the measurement operator. The $ell _{1}$ solution, on the other hand, is formed by adaptively selecting a subset of atoms in a dictionary that is specified by the regularization operator. Beside the proof that $ell _{1}$ solutions are intrinsically sparse, the main outcome of our investigation is that the use of $ell _{1}$ regularization is much more favorable for injecting prior knowledge: it results in a functional form that is independent of the system matrix, while this is not so in the $ell _{2}$ scenario.]]>62951675180395<![CDATA[Estimation for Models Defined by Conditions on Their L-Moments]]>629518151981134<![CDATA[Recent Results on Balanced Symmetric Boolean Functions]]> , the -variable elementary symmetric Boolean function of degree . As an application of this result to elementary symmetric Boolean functions, we show that all the trivially balanced elementary symmetric Boolean functions are of the form , where and are any positive integers. It implies that Cusick et al.’s conjecture, which claims that is the only nonlinear balanced elementary symmetric Boolean functions, is equivalent to the conjecture that all the balanced elementary symmetric Boolean functions are trivially balanced.]]>62951995203171<![CDATA[There Are Infinitely Many Bent Functions for Which the Dual Is Not Bent]]>et al. yields bent functions for which the dual is also bent. In this paper, the first construction of non-weakly regular bent functions for which the dual is not bent is presented. We call such functions non-dual-bent functions. Until now, only sporadic examples found via computer search were known. We then show that with the direct sum of bent functions and with the construction by Çeşmelioğlu et al., one can obtain infinitely many non-dual-bent functions once one example of a non-dual-bent function is known.]]>62952045208178<![CDATA[New Families of Optimal Frequency Hopping Sequence Sets]]>62952095224803<![CDATA[Equiangular Tight Frames From Hyperovals]]>62952255236384<![CDATA[Aperiodic Crosscorrelation of Sequences Derived From Characters]]> -sequences) typically have mean square aperiodic crosscorrelation on par with that of random sequences, but that if one takes a pair of -sequences where one is the reverse of the other, and shifts them appropriately, one can get significantly lower mean square aperiodic crosscorrelation. Sequence pairs with even lower mean square aperiodic crosscorrelation are constructed by taking a Legendre sequence, cyclically shifting it, and then cutting it (approximately) in half and using the halves as the sequences of the pair. In some of these constructions, the mean square aperiodic crosscorrelation can be lowered further if one truncates or periodically extends (appends) the sequences. Exact asymptotic formulas for mean squared aperiodic crosscorrelation are proved for sequences derived from additive characters (including -sequences and modified versions thereof) and multiplicative characters (including Legendre sequences and their relatives). Data are presented that show that the sequences of modest length have performance that closely approximates the asymptotic formulas.]]>629523752591223<![CDATA[On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback]]>62952605277463<![CDATA[Blank page]]>629B5278B52784<![CDATA[Blank page]]>629B5279B52804<![CDATA[IEEE Transactions on Information Theory information for authors]]>629C3C3194