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TOC Alert for Publication# 18 2019February 14<![CDATA[Table of contents]]>653C1C4152<![CDATA[IEEE Transactions on Information Theory publication information]]>653C2C2112<![CDATA[Asymptotic Coupling and Its Applications in Information Theory]]>$P_{X}$ and $P_{Y}$ is a joint distribution $P_{XY}$ with marginal distributions equal to $P_{X}$ and $P_{Y}$ . Given marginals $P_{X}$ and $P_{Y}$ and a real-valued function $f$ of the joint distribution $P_{XY}$ , what is its minimum over all couplings $P_{XY}$ of $P_{X}$ and $P_{Y}$ ? We study the asymptotics of such coupling problems with different $f$ ’s and with $X$ and $Y$ replaced by $X^{n}=(X_{1},ldots ,X_{n})$ and $Y^{n}=(Y_{1},ldots ,Y_{n})$ where $X_{i}$ and $Y_{i}$ are i.i.d. copies of random variables $Y$ with distributions $P_{X}$ and $P_{Y}$ , respectively. These include the maximal coupling, minimum distance coupling, maximal guessing coupling, and minimum entropy coupling problems. We characterize the limiting values of these coupling problems as $n$ tends to infinity. We show that they typically converge at least exponentially fast to their limits. Moreover, for the problems of maximal coupling and minimum excess-distance probability coupling, we also characterize (or bound) the optimal convergence rates (exponents). Furthermore, for the maximal guessing coupling problem, we show that it is equivalent to the distribution approximation problem. Therefore, some existing results for the latter problem can be used to derive the asymptotics of the maximal guessing coupling problem. We also study the asymptotics of the maximal guessing coupling problem for two general sources and a generalization of this problem, named the maximal guessing coupling through a channel problem. We apply the preceding results to several new information-theoretic problems, including exact intrinsic randomness, exact resolvability, channel capacity with input distribution constraint, and perfect stealth and secrecy communication.]]>65313211344587<![CDATA[Intrinsic Capacity]]>65313451360701<![CDATA[On the Evaluation of Marton’s Inner Bound for Two-Receiver Broadcast Channels]]>65313611371271<![CDATA[Invariance of the Han–Kobayashi Region With Respect to Temporally-Correlated Gaussian Inputs]]>65313721374176<![CDATA[Combinatorial Entropy Power Inequalities: A Preliminary Study of the Stam Region]]>${R}^{2^{n}-1}$ that arises from considering the entropy powers of subset sums of $n$ independent random vectors in a Euclidean space of finite dimension. We show that the class of fractionally superadditive set functions provides an outer bound to the Stam region, resolving a conjecture of Barron and Madiman. On the other hand, the entropy power of a sum of independent random vectors is not supermodular in any dimension. We also develop some qualitative properties of the Stam region, showing for instance that its closure is a logarithmically convex cone.]]>65313751386299<![CDATA[On the Entropy Power Inequality for the Rényi Entropy of Order [0, 1]]]>65313871396256<![CDATA[Quickest Change Detection Under Transient Dynamics: Theory and Asymptotic Analysis]]>65313971412687<![CDATA[Asymptotic Optimality of Mixture Rules for Detecting Changes in General Stochastic Models]]>65314131429504<![CDATA[Learning Mixtures of Sparse Linear Regressions Using Sparse Graph Codes]]>mixture of sparse linear regressions model. Let $boldsymbol {beta }^{(1)},ldots, boldsymbol {beta }^{(L)}in mathbb {C} ^{n}$ be $L $ unknown sparse parameter vectors with a total of $K $ non-zero elements. Noisy linear measurements are obtained in the form $y_{i} = boldsymbol {x}_{i} ^{mathrm{ H}} boldsymbol {beta }^{(ell _{i})} + w_{i}$ , each of which is generated randomly from one of the sparse vectors with the label $ell _{i} $ unknown. The goal is to estimate the parameter vectors efficiently with low sample and computational costs. This problem presents significant challenges as one needs to simultaneously solve the demixing problem of recovering the labels $ell _{i} $ as well as the estimation problem of recovering the sparse vectors $boldsymbol {beta }^{(ell)} $ . Our solution to the problem leverages the connection between modern coding theory and statistical inference. We introduce a new algorithm, Mixed-Coloring, which samples the mixture strategically using query vectors $boldsymbol {x}_{i} $ constructed based on ideas from sparse graph codes. Our novel code design allows for both efficient demixing and parameter estimation. To find $K$ non-zero elements, it is clear that we need at least $Theta (K)$ measurements, and thus the time complexity is at least $Theta (K)$ . In the noiseless setting, for a constant number of sparse parameter vectors, our algorithm achieves the order-optimal sample and time complexities of $Theta (K)$ . In the presence of Gaussian noise,^{1} for the problem with two parameter vectors (i.e., $L = 2$ ), we show that the Robust Mixed-Coloring algorithm achieves near-optimal $Theta (K mathop {mathrm {polylog}}nolimits (n))$ sample and time complexities. When $K = mathcal {O}(n^{alpha })$ for some constant $alpha in (0,1)$ (i.e., $K$ is sublinear in $n$ ), we can achieve sample and time complexities both sublinear in the ambient dimension. In one of our experiments, to recover a mixture of two regressions with dimension $n = 500$ and sparsity $K = 50$ , our algorithm is more than 300 times faster than EM algorithm, with about one third of its sample cost.

The proposed algorithm works even when the noise is non-Gaussian in nature, but the guarantees on sample and time complexities are difficult to obtain.

]]>653143014511880<![CDATA[Sharp Oracle Inequalities for Stationary Points of Nonconvex Penalized M-Estimators]]>65314521472380<![CDATA[Non-Parametric Sparse Additive Auto-Regressive Network Models]]>${(X_{t})}_{t=0}^{T}$ , where $X_{t} in mathbb {R}^{d}$ which may represent spike train responses for multiple neurons in a brain, crime event data across multiple regions, and many others. An important challenge associated with these time series models is to estimate an influence network between the $d$ variables, especially when $d$ is large, meaning we are in the high-dimensional setting. Prior work has focused on parametric vector auto-regressive models. However, parametric approaches are somewhat restrictive in practice. In this paper, we use the non-parametric sparse additive model (SpAM) framework to address this challenge. Using a combination of $beta $ and $phi $ -mixing properties of Markov chains and empirical process techniques for reproducing kernel Hilbert spaces (RKHSs), we provide upper bounds on mean-squared error in terms of the sparsity $s$ , the logarithm of the dimension $log ~d$ , the number of time points $T$ , and the smoothness of the RKHSs. Our rates are sharp up to logarithm factors in many cases. We also provide numerical experiments that support our theoretical results and display the potential advantages of using our non-parametric SpAM framework for a Chicago crime data set.]]>653147314921452<![CDATA[On Information-Theoretic Characterizations of Markov Random Fields and Subfields]]>$X_{i}, i~in V$ 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 (Kawabata and Yeung in 1992). We prove that Markov chain is essentially the only MRF such that the $I$ -Measure is always nonnegative. By applying our characterization of the smallest graph representation of a subfield of an MRF, we develop a recursive approach for constructing information diagrams for MRFs. Our work is built on the set-theoretic characterization of an MRF (Yeung et al. in 2002).]]>653149315111192<![CDATA[Estimation Efficiency Under Privacy Constraints]]>$Y$ under a privacy constraint dictated by another correlated random variable $X$ . When $X$ and $Y$ are discrete, we express the underlying privacy-utility tradeoff in terms of the privacy-constrained guessing probability ${mathcal {h}}(P_{XY}, varepsilon)$ , and the maximum probability $mathsf {P}_{mathsf {c}}(Y|Z)$ of correctly guessing $Y$ given an auxiliary random variable $Z$ , where the maximization is taken over all $P_{Z|Y}$ ensuring that $mathsf {P}_{mathsf {c}}(X|Z)leq varepsilon $ for a given privacy threshold $varepsilon geq 0$ . We prove that ${mathcal {h}}(P_{XY}, cdot)$ is concave and piecewise linear, which allows us to derive its expression in closed form for any $varepsilon $ when $X$ and $Y$ are binary. In the non-binary case, we derive ${mathcal {h}}(P_{XY}, -
arepsilon)$ in the high-utility regime (i.e., for sufficiently large, but nontrivial, values of $varepsilon $ ) under the assumption that $Y$ and $Z$ have the same alphabets. We also analyze the privacy-constrained guessing probability for two scenarios in which $X$ , $Y$ , and $Z$ are binary vectors. When $X$ and $Y$ are continuous random variables, we formulate the corresponding privacy-utility tradeoff in terms of ${mathsf {sENSR}}(P_{XY}, varepsilon)$ , the smallest normalized minimum mean squared-error (mmse) incurred in estimating $Y$ from a Gaussian perturbation $Z$ . Here, the minimization is taken over a family of Gaussian perturbations $Z$ for which the mmse of $f(X)$ given $Z$ is within a factor $1- varepsilon $ from the variance of $f(X)$ for any non-constant real-valued function ]]>65315121534931<![CDATA[Estimation of a Density From an Imperfect Simulation Model]]>653153515461003<![CDATA[Provable Dynamic Robust PCA or Robust Subspace Tracking]]>653154715774593<![CDATA[Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices]]>65315781588800<![CDATA[A Data-Dependent Weighted LASSO Under Poisson Noise]]>data-dependent weights are based on Poisson concentration inequalities. Unlike previous analyses of the weighted LASSO, the proposed analysis depends on conditions which can be checked or shown to hold in general settings with high probability. 2000 Math Subject Classification: 60E15, 62G05, 62G08, and 94A12.]]>65315891613719<![CDATA[Finite-Field Matrix Channels for Network Coding]]>et al. studied certain classes of finite-field matrix channels in order to model random linear network coding where exactly $t$ random errors are introduced. In this paper, we consider a generalization of these matrix channels where the number of errors is not required to be constant, indeed the number of errors may follow any distribution. We show that a capacity-achieving input distribution can always be taken to have a very restricted form (the distribution should be uniform given the rank of the input matrix). This result complements, and is inspired by a paper of Nobrega et al., which establishes a similar result for a class of matrix channels that model network coding with link erasures. Our result shows that the capacity of our channels can be expressed as maximization over probability distributions on the set of possible ranks of input matrices: a set of linear rather than exponential size.]]>65316141625570<![CDATA[Joint Crosstalk-Avoidance and Error-Correction Coding for Parallel Data Buses]]>65316261638694<![CDATA[Cooperative Repair: Constructions of Optimal MDS Codes for All Admissible Parameters]]>centralized repair and cooperative repair. The centralized model assumes that all the failed nodes are recreated in one location, while the cooperative one stipulates that the failed nodes may communicate but are distinct, and the amount of data exchanged between them is included in the repair bandwidth. As our first result, we prove a lower bound on the minimum bandwidth of cooperative repair. We also show that the cooperative model is stronger than the centralized one, in the sense that any maximum distance separable (MDS) code with optimal repair bandwidth under the former model also has optimal bandwidth under the latter one. These results were previously known under the additional “uniform download” assumption, which is removed in our proofs. As our main result, we give explicit constructions of MDS codes with optimal cooperative repair for all possible parameters. More precisely, given any $n,k,h,d$ such that $2le h le n-dle n-k$ we construct $(n,k)$ MDS codes over the field $F$ of size $|F|ge (d+1-k)n$ that can optimally repair any $h$ erasures from any $d$ helper nodes. The repair scheme of our codes involves two rounds of communication. In the first round, each failed node downloads information from the helper nodes, and in the second one, each failed node downloads additional information from the-
other failed nodes. This implies that our codes achieve the optimal repair bandwidth using the smallest possible number of rounds.]]>65316391656511<![CDATA[List-Decodable Zero-Rate Codes]]>$tau in [{0,1}]$ for which there exists an arrangement of $M$ balls of relative Hamming radius $tau $ in the binary hypercube (of arbitrary dimension) with the property that no point of the latter is covered by $L$ or more of them. As $Mto infty $ the maximal $tau $ decreases to a well-known critical value $tau _{L}$ . In this paper, we prove several results on the rate of this convergence. For the binary case, we show that the rate is $Theta (M^{-1})$ when $L$ is even, thus extending the classical results of Plotkin and Levenshtein for $L=2$ . For $L=3$ , the rate is shown to be $Theta (M^{-({2}/{3})})$ . For the similar question about spherical codes, we prove the rate is $Omega (M^{-1})$ and $O(M^{-({2L}/{L^{2}-L+2})})$ .]]>65316571667298<![CDATA[Constructions of Linear Codes With One-Dimensional Hull]]>65316681676397<![CDATA[BP-LED Decoding Algorithm for LDPC Codes Over AWGN Channels]]>653167716931727<![CDATA[On <inline-formula> <tex-math notation="LaTeX">$sigma$ </tex-math></inline-formula>-LCD Codes]]>$sigma $ complementary dual ($sigma $ -LCD), which includes known Euclidean LCD codes, Hermitian LCD codes, and Galois LCD codes. Like Euclidean LCD codes, $sigma $ -LCD codes can also be used to construct LCP of codes. We show that for $q > 2$ , all $q$ -ary linear codes are $sigma $ -LCD, and for every binary linear code $mathcal C$ , the code ${0}times mathcal C$ is $sigma $ -LCD. Furthermore, we study deeply $sigma $ -LCD generalized quasi-cyclic (GQC) codes. In particular, we provide the characterizations of $sigma $ -LCD GQC codes, self-orthogonal GQC codes, and self-dual GQC codes, respectively. Moreover, we provide the constructions of asymptotically good $sigma $ -LCD GQC codes. Finally, we focus on $sigma $ <-
tex-math>-LCD abelian codes and prove that all abelian codes in a semi-simple group algebra are $sigma $ -LCD. The results derived in this paper extend those on the classical LCD codes and show that $sigma $ -LCD codes allow the construction of LCP of codes more easily and with more flexibility.]]>65316941704302<![CDATA[Local Rank Modulation for Flash Memories]]>$0 < sleq tleq n$ with $s$ dividing $n$ , an $(s,t,n)$ -LRM scheme is a LRM scheme where the $n$ cells are locally viewed cyclically through a sliding window of size $t$ resulting in a sequence of small permutations, which requires less comparisons and less distinct values. The gap between two such windows equals to $s$ . In this paper, encoding, decoding, and asymptotic enumeration of the $(1,t,n)$ -LRM scheme are studied.]]>65317051713393<![CDATA[Cache-Aided Interference Channels]]>65317141724647<![CDATA[Cooperative Multi-Sender Index Coding]]>et al. and identify its limitations in the implementation of multi-sender composite coding and in the strategy of sender partitioning. We then propose two new coding components to overcome these limitations and develop a multi-sender cooperative composite coding (CCC). We show that CCC can strictly improve upon partitioned DCC, and is the key to achieve optimality for a number of index-coding instances. The usefulness of CCC and its special cases is illuminated via non-trivial examples, and the capacity region is established for each example. Comparisons between CCC and other non-cooperative schemes in recent works are also provided to further demonstrate the advantage of CCC.]]>653172517391461<![CDATA[Factorizations of Binomial Polynomials and Enumerations of LCD and Self-Dual Constacyclic Codes]]>${mathbb {F}}_{q}$ be a finite field with order $q$ , where $q$ is a positive power of a prime $p$ . Suppose that $n$ is a positive integer and the product of distinct prime factors of $n$ divides $q-1$ , i.e., $rad(n)mid (q-1)$ . In this paper, we explicitly factorize the polynomial $x^{n}-lambda $ for each $lambda in {mathbb {F}}_{q}^{*}$ . As applications, first, we obtain all repeated-root $lambda $ -constacyclic codes and their dual codes of length $np^{s}$ over ${mathbb {F}}_{q}$ ; second, we determine all simple-root LCD cyclic codes and LCD negacyclic codes of length $n$ over ${mathbb {F}}_{q}$ ; third, we list all self-dual repeated-root negacyclic codes of l-
ngth $np^{s}$ over ${mathbb {F}}_{q}$ . In contrast to known results, the lengths of constacyclic codes in this paper have more flexible parameters.]]>65317401751302<![CDATA[From ds-Bounds for Cyclic Codes to True Minimum Distance for Abelian Codes]]>${mathbb B}$ -apparent distance. We also study conditions for an Abelian code to verify that its ${mathbb B}$ -apparent distance reaches its (true) minimum distance. Then, we construct some codes as an application.]]>65317521763307<![CDATA[Lattice-Based Robust Distributed Source Coding]]>65317641781601<![CDATA[Monotonicity of Step Sizes of MSE-Optimal Symmetric Uniform Scalar Quantizers]]>$N$ increases by two, and that for any generalized gamma density and all sufficiently large $N$ , optimal step size again decreases when $N$ increases by two. Also, it is shown that for a Laplacian density and sufficiently large $N$ , optimal step size decreases when $N$ increases by just one.]]>653178217921325<![CDATA[Asymptotically Tight Bounds on the Depth of Estimated Context Trees]]>$x$ of length $n$ over a finite alphabet of size $alpha $ , for popular estimators of tree models, where the estimated order is determined by the depth of a context tree estimate, and in the special case of plain Markov models, where the tree is constrained to be perfect (with all leaves at the same depth). First, we consider penalized maximum likelihood estimators where a context tree $hat {T}$ is obtained by minimizing a cost of the form $-log hat {P}_{T}(x) + f(n)|S_{T}|$ , where $hat {P}_{T}(x)$ is the ML of $x$ under a model with context tree $T$ , $S_{T}$ is the set of leaves of $T$ , and $f(n)$ is an increasing (penalization) function of $n$ (the popular BIC estimator is a special case with $f(n)=frac {alpha -1}{2}log n$ ). For plain Markov models, a simple argument yields a known upper bound $overline {k}(n) = O(log n)$ on the maximum order that can be es-
imated for $x$ , and we show that, in fact, this simple bound is not far from tight. For general context trees, we derive an asymptotic upper bound, $n^{1/2 - o(1)}$ , on the estimated depth, and we exhibit explicit input sequences that asymptotically attain the bound up to a multiplicative constant factor. We show that a similar upper bound applies also to MDL estimators based on the KT probability assignment and, moreover, the same example sequences asymptotically approach the upper bound also in this case.]]>65317931806373<![CDATA[The Age of Information: Real-Time Status Updating by Multiple Sources]]>653180718271244<![CDATA[A New Method to Construct Strictly Optimal Frequency Hopping Sequences With New Parameters]]>$M$ and sequence length $N$ over a frequency slot set of size $q$ with respect to the partial Hamming correlation bound derived by Niu et al. when $N>{q^{2}}/{M}$ and $qgeq 2$ , and that by Cai et al. when $N>{q^{2}}/{M}$ and $qgeq {2N}/({N-2})$ . Furthermore, we define a special partition-type difference packing (DP) called $[N,nabla,H_{a}^{l}]$ PDP and give several classes of $[N,nabla,H_{a}^{l}]$ PDPs. Then, we present a new construction of strictly optimal FH sequences. By choosing different PDPs, the FH sequences constructed can give new and flexible parameters. By utilizing this -
onstruction method recursively, we can obtain new $[N,nabla,H_{a}^{l}]$ PDPs, which lead to infinitely many classes of strictly optimal FH sequences with new parameters. Moreover, based upon an $[N,nabla,H_{a}^{l}]$ PDP, we present a construction of strictly optimal FH sequence sets. By preceding construction method and recursive construction, we can also obtain infinite classes of strictly optimal FH sequence sets which can give new and flexible parameters.]]>65318281844946<![CDATA[A Key Recovery Reaction Attack on QC-MDPC]]>653184518611175<![CDATA[Rényi Resolvability and Its Applications to the Wiretap Channel]]>$[{0,2}]cup {infty }$ ) to measure the level of approximation. We also provide asymptotic expressions for normalized Rényi divergence when the Rényi parameter is larger than or equal to 1 as well as (lower and upper) bounds for the case when the same parameter is smaller than 1. We characterize the Rényi resolvability, which is defined as the minimum rate required to ensure that the Rényi divergence vanishes asymptotically. The Rényi resolvabilities are the same for both the normalized and unnormalized divergence cases. In addition, when the Rényi parameter smaller than 1, consistent with the traditional case where the Rényi parameter is equal to 1, the Rényi resolvability equals the minimum mutual information over all input distributions that induce the target output distribution. When the Rényi parameter is larger than 1 the Rényi resolvability is, in general, larger than the mutual information. The optimal Rényi divergence is proven to vanish at least exponentially fast for both of these two cases, as long as the code rate is larger than the Rényi resolvability. The optimal exponential rate of decay for i.i.d. random codes is also characterized exactly. We apply these results to the wiretap channel, and completely characterize the optimal tradeof-
between the rates of the secret and non-secret messages when the leakage measure is given by the (unnormalized) Rényi divergence. This tradeoff differs from the conventional setting when the leakage is measured by the traditional mutual information.]]>653186218971043<![CDATA[A Unified Theory of Multiple-Access and Interference Channels via Approximate Capacity Regions for the MAC-IC-MAC]]>et al. For the semi-deterministic MAC-IC-MAC, it is shown that single-user coding at the non-interfering transmitters and superposition coding at the interfering transmitter of each MAC achieves a rate region that is within a quantifiable gap of the capacity region, thereby extending such a result for the two-user semi-deterministic IC by Telatar and Tse. For the Gaussian MAC-IC-MAC, an approximate capacity region that is within a constant gap of the capacity region is obtained, generalizing such a result for the two-user Gaussian IC by Etkin et al. On contrary to the aforementioned approximate capacity results for the two-user IC, whose achievability requires the union of all admissible input distributions, our gap results on the semi-deterministic and the Gaussian MAC-IC-MAC are achievable by only a subset and one of all admissible coding distributions, respectively. The symmetric generalized degrees of freedom (GDoFs) of the symmetric Gaussian MAC-IC-MAC with more than one user per cell, which is a function of the interference strength (the ratio of INR to SNR at high SNR, both expressed in dB) and the numbers of users in each cell, are V-shaped with flat shoulders. An analysis based on signal-level partitions shows that the non-interfering transmitters utilize the signal-level partitions at the receiver where they are intended that cannot be accessed by the interfering transmitters (due to the restriction of superpositio-
coding), thereby improving the sum symmetric GDoF of up to one degree of freedom per cell under a range of SINR exponent levels, which in turn becomes wider as the number of transmitters in each cell increases. Consequently, time-sharing between interfering and non-interfering transmitters is GDoF-suboptimal in general, as is time-sharing between the two embedded MAC-Z-MACs.]]>653189819201211<![CDATA[On the KZ Reduction]]>polynomially smaller than the existing sharpest one. We also propose upper bounds on the lengths of the columns of KZ reduced matrices, and an upper bound on the orthogonality defect of KZ reduced matrices which are even polynomially and exponentially smaller than those of boosted KZ reduced matrices, respectively. Then, we derive upper bounds on the magnitudes of the entries of any solution of a shortest vector problem (SVP) when its basis matrix is LLL reduced. These upper bounds are useful for analyzing the complexity and understanding numerical stability of the basis expansion in a KZ reduction algorithm. Finally, we propose a new KZ reduction algorithm by modifying the commonly used Schnorr–Euchner search strategy for solving SVPs and the basis expansion method proposed by Zhang et al. Simulation results show that the new KZ reduction algorithm is much faster and more numerically reliable than the KZ reduction algorithm proposed by Zhang et al., especially when the basis matrix is ill conditioned.]]>65319211935890<![CDATA[Line Codes Generated by Finite Coxeter Groups]]>$b$ bits over $b+1$ wires, and admitting especially simple encoding and decoding algorithms. With these codes, resistance to common-mode noise is obtained by using codewords whose components sum to zero, simultaneous switching output noise is reduced by using constant-energy signals, and the effects of intersymbol interference are reduced by having decisions based on only two values at the input of the final slicers. Codebook design is based on the theory of Group Codes for the Gaussian Channel, as specialized to Coxeter matrix groups generated by reflections in orthogonal hyperplanes. A number of designs are exhibited, some of them being novel or improving on previously obtained codes.]]>653193619471265<![CDATA[Feedback Capacity of Gaussian Channels Revisited]]>65319481960337<![CDATA[AWGN-Goodness Is Enough: Capacity-Achieving Lattice Codes Based on Dithered Probabilistic Shaping]]>65319611971366<![CDATA[Blank page]]>653B1972B19723<![CDATA[IEEE Transactions on Information Theory information for authors]]>653C3C391