<![CDATA[ IEEE Transactions on Information Theory - new TOC ]]>
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TOC Alert for Publication# 18 2017November 16<![CDATA[Table of contents]]>6311C1C4152<![CDATA[IEEE Transactions on Information Theory publication information]]>6311C2C2191<![CDATA[Sampling and Distortion Tradeoffs for Indirect Source Retrieval]]>631168336848871<![CDATA[A Sharpening of the Welch Bounds and the Existence of Real and Complex Spherical $t$ –Designs]]>631168496857208<![CDATA[Polarization of the Rényi Information Dimension With Applications to Compressed Sensing]]>631168586868544<![CDATA[Linear Convergence of Stochastic Iterative Greedy Algorithms With Sparse Constraints]]>1 in expectation to the solution within a specified tolerance. This generalized framework is specialized to the problems of sparse signal recovery in compressed sensing and low-rank matrix recovery, giving methods with provable convergence guarantees that often outperform their deterministic counterparts. We also analyze the settings, where gradients and projections can only be computed approximately, and prove the methods are robust to these approximations. We include many numerical experiments, which align with the theoretical analysis and demonstrate these improvements in several different settings.]]>6311686968952053<![CDATA[Does $ell _{p}$ -Minimization Outperform $ell _{1}$ -Minimization?]]>$x_{o} in mathbb {R}^{N}$ from its undersampled set of noisy observations $y in mathbb {R}^{n}$ , $y= A x_{o}+ w$ . The last decade has witnessed a surge of algorithms and theoretical results to address this question. One of the most popular schemes is the $ell _{p}$ -regularized least squares given by the following formulation:$hat x(gamma ,p ) in {arg min }_{x}~({1}/{2})| {y - Ax} |_{2}^{2} + gamma {| x |_{p}^{p}}$ , where $p in [{0, 1}]$ . Among these optimization problems, the case $p = 1$ , also known as LASSO, is the best accepted in practice, for the following two reasons. First, thanks to the extensive studies performed in the fields of high-dimensional statistics and compressed sensing, we have a clear picture of LASSO’s performance. Second, it is convex and efficient algorithms exist for finding its global minima. Unfortunately, neither of the above two properties hold for $0 leq p<1$ . However, they are still appealing because of the following folklores in the high-dimensional statistics. First, $hat x(gamma , p )$ is closer to $x_{o}$ than -
$hat {x}(gamma ,1)$ . Second, if we employ iterative methods that aim to converge to a local minima of $ {arg min }_{x}~({1}/{2})| {y - Ax} |_{2}^{2} + gamma {| x |_{p}^{p}}$ , then under good initialization, these algorithms converge to a solution that is still closer to $x_{o}$ than $hat {x}(gamma ,1)$ . In spite of the existence of plenty of empirical results that support these folklore theorems, the theoretical progress to establish them has been very limited. This paper aims to study the above-mentioned folklore theorems and establish their scope of validity. Starting with approximate message passing (AMP) algorithm as a heuristic method for solving $ell _{p}$ -regularized least squares, we study the following questions. First, what is the impact of initialization on the performance of the algorithm? Second, when does the algorithm recover the sparse signal $x_{o}$ under a “good” initialization? Third, when does the algorithm converge to the sparse signal regardless of the initialization? Studying these questions will not only shed light on the second folklore theorem, but also lead us to the answer the first one, i.e., the performance of the global optima $hat x(gamma , p )$ . For that purpose, we employ the replica analysis^{1} to show the connection between the solution of AMP and $hat {x}(gamma , p)$ in the ]]>6311689669352209<![CDATA[Bounds on Variance for Unimodal Distributions]]>631169366949470<![CDATA[Information Theoretic Cutting of a Cake]]>6311695069781477<![CDATA[Information Complexity Density and Simulation of Protocols]]>631169797002489<![CDATA[On Distributed Computing for Functions With Certain Structures]]>631170037017679<![CDATA[Information-Theoretic Caching: The Multi-User Case]]>6311701870371172<![CDATA[The Rate Region for Secure Distributed Storage Systems]]>631170387051351<![CDATA[Dual Capacity Upper Bounds for Noisy Runlength Constrained Channels]]>631170527065889<![CDATA[Linear Programming-Based Converses for Finite Blocklength Lossy Joint Source-Channel Coding]]>6311706670941461<![CDATA[Sequential Necessary and Sufficient Conditions for Capacity Achieving Distributions of Channels With Memory and Feedback]]>0,n^{=Δ} {P_{Xt|Xt-1,Yt-1} : t = 0, ..., n} to maximize the finite-time horizon directed information defined by C_{Xn→Yn}^{FB =Δ} sup_{P0,n} I(X^{n} → Y^{n}), where I(X^{n} → Y^{n}) = Σ_{t=0}^{n} I(X^{t}; Y_{t}|Y^{t-1}), for channel distributions {P_{Yt}|Y^{t-1},Xt: t = 0, ..., n} and {P_{Yt}|Y_{t-M}^{t-1},X_{t} : t = 0, ..., n}, where Y^{t =Δ} {Y^{-1}, Y_{0}, ..., Y_{t}} and X^{t =Δ} {X_{0}, ..., X_{t}} are the channel input and output random processes, and M is a finite non-negative integer. We apply the necessary and sufficient conditions to application examples of time-varying channels with memory to derive recursive closed form expressions of the optimal distributions, which maximize the finite-time horizon directed information. Furthermore, we derive the feedback capacity from the asymptotic properties of the optimal distributions by investigating the limit C_{X∞→Y∞}^{FB =Δ} lim_{n→∞}(1/(n + 1))C_{Xn→Yn}^{FB} without any á priori assumptions, such as stationarity, ergodicity, or irreducibility of the channel distribution. The framework based on sequential necessary and sufficient conditions can be easily applied to a variety of channels with memory, beyond the ones considered in this paper.]]>631170957115818<![CDATA[Optimal Finite-Length and Asymptotic Index Codes for Five or Fewer Receivers]]>2 for any positive integer k. This work complements the result by Arbabjolfaei et al. (ISIT 2013), who solved all unicast index-coding instances with up to five receivers in the asymptotic regime, where the message alphabet size tends to infinity.]]>6311711671301163<![CDATA[Group Testing Schemes From Codes and Designs]]>631171317141229<![CDATA[The Capacity of Bernoulli Nonadaptive Group Testing]]>631171427148282<![CDATA[Computationally Tractable Algorithms for Finding a Subset of Non-Defective Items From a Large Population]]>2 K factor, where K is the number of defective items. We also provide simulation results that compare the relative performance of the different algorithms and reveal insights into their practical utility. The proposed algorithms significantly outperform the straightforward approaches of testing items one-by-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate.]]>631171497165938<![CDATA[Rates of DNA Sequence Profiles for Practical Values of Read Lengths]]>1/2-1, the number of profile vectors is at least q^{κn} with κ very close to 1. In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for certain families of profile vectors.]]>631171667177496<![CDATA[The “Art of Trellis Decoding” Is Fixed-Parameter Tractable]]>1, V_{2},..., V_{n} of the subspaces such that dim((V_{1} + V_{2} + ··· + V_{i}) ∩ (V_{i+1} + ··· + V_{n})) ≤ k for all i; such a linear layout is said to have width at most k. When restricted to 1-dimensional subspaces, this problem is equivalent to computing the trellis-width (or minimum trellis state-complexity) of a linear code in coding theory and computing the path-width of an F-represented matroid in matroid theory. We present a fixed-parameter tractable algorithm to construct a linear layout of width at most k, if it exists, for input subspaces of a finite-dimensional vector space over F. As corollaries, we obtain a fixed-parameter tractable algorithm to produce a path-decomposition of width at most k for an input F-represented matroid of path-width at most k, and a fixed-parameter tractable algorithm to find a linear rank-decomposition of width at most k for an input graph of linear rank-width at most k. In both corollaries, no such algorithms were known previously. Our approach is based on dynamic programming combined with the idea developed by Bodlaender and Kloks (1996) for their work on path-width and tree-width of graphs. It was previously known that a fixed-parameter tractable algorithm exists for the decision version of the problem for matroid path-width; a theorem by Geelen, Gerards, and Whittle (2002) implies that for each fixed finite field F, there are finitely many forbidden F-representable minors for the class of matroids of path-width at most k. An algorithm by Hlinený (2006) can detect a minor in an input F-represented matroid of bounded branch-width. However, this ind-
rect approach would not produce an actual path-decomposition. Our algorithm is the first one to construct such a path-decomposition and does not depend on the finiteness of forbidden minors.]]>6311717872051030<![CDATA[On the Correlation Distribution for a Niho Decimation]]>m - 2 with m ≥ 2, and gcd(d, p^{n} - 1) = 1. In this paper, the correlation distribution between a p-ary m-sequence of period p^{n} - 1 and its d-decimation sequence is investigated in a unified approach. Some results for the binary case are extended to the general case. It is shown that the problem of determining the correlation distribution for d can be reduced to that of solving two combinatorial problems related to the unit circle of the finite field F_{pn}. For an arbitrary odd prime p, it seems difficult to solve these two problems. However, for p = 3, by studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over F_{3n}, the two problems are solved, and thus, the corresponding correlation distribution for d is completely determined. It is noteworthy that this is the first time that the correlation distribution for a non-binary Niho decimation has been determined since 1976.]]>631172067218272<![CDATA[Narrow-Sense BCH Codes Over $ {mathrm {GF}}(q)$ With Length $n=frac {q^{m}-1}{q-1}$]]>m -1)/(q -1). Little is known about this class of BCH codes when q > 2. The objective of this paper is to study some of the codes within this class. In particular, the dimension, the minimum distance, and the weight distribution of some ternary BCH codes with length n = (3^{m} - 1)/2 are determined in this paper. A class of ternary BCH codes meeting the Griesmer bound is identified. An application of some of the BCH codes in secret sharing is also investigated.]]>631172197236943<![CDATA[Explicit Construction of AG Codes From a Curve in the Tower of Bassa-Beelen-Garcia-Stichtenoth]]>631172377246387<![CDATA[New Bounds for Frameproof Codes]]>631172477252291<![CDATA[On the Tradeoff Region of Secure Exact-Repair Regenerating Codes]]>631172537266509<![CDATA[An Outer Bound on the Storage-Bandwidth Tradeoff of Exact-Repair Cooperative Regenerating Codes]]>6311726772821089<![CDATA[On Multi-Source Networks: Enumeration, Rate Region Computation, and Hierarchy]]>6311728373033221<![CDATA[$epsilon $ -Almost Selectors and Their Applications to Multiple-Access Communication]]>631173047319295<![CDATA[A Note on Parallel Asynchronous Channels With Arbitrary Skews]]>2(1 + √5) - 1 was recently described for a communication channel composed of parallel asynchronous lines satisfying the so-called no switch assumption. We prove that this is in fact the highest rate attainable, i.e., the zero-error capacity of this channel.]]>631173207321120<![CDATA[A Truncated Prediction Framework for Streaming Over Erasure Channels]]>6311732273511955<![CDATA[Feasibility of Single-Beam Interference Alignment in Multi-Carrier Interference Channels]]>631173527357170<![CDATA[Secret Key Generation With Limited Interaction]]>631173587381785<![CDATA[Perfectly Secure Index Coding]]>631173827395571<![CDATA[Communication in the Presence of a State-Aware Adversary]]>631173967419606<![CDATA[Secure Degrees of Freedom for the MIMO Wire-Tap Channel With a Multi-Antenna Cooperative Jammer]]>t antennas at the transmitter, N_{r} antennas at the legitimate receiver, and Ne antennas at the eavesdropper, for all possible values of the number of antennas, N_{c}, at the cooperative jammer. In establishing the result, several different ranges of N_{c} need to be considered separately. The lower and upper bounds for these ranges of Nc are derived, and are shown to be tight. The achievability techniques developed rely on a variety of signaling, beamforming, and alignment techniques, which vary according to the (relative) number of antennas at each terminal and whether the s.d.o.f. is integer valued. Specifically, it is shown that, whenever the s.d.o.f. is integer valued, Gaussian signaling for both transmission and cooperative jamming, linear precoding at the transmitter and the cooperative jammer, and linear processing at the legitimate receiver, are sufficient for achieving the s.d.o.f. of the channel. By contrast, when the s.d.o.f. is not an integer, the achievable schemes need to rely on structured signaling at the transmitter and the cooperative jammer, and joint signal space and signal scale alignment. The converse is established by combining an upper bound, which allows for full cooperation between the transmitter and the cooperative jammer, with another upper bound which exploits the secrecy and reliability constraints.]]>631174207441927<![CDATA[Joint Source-Channel Secrecy Using Uncoded Schemes: Towards Secure Source Broadcast]]>6311744274631456<![CDATA[Fundamental Tradeoff Between Storage and Latency in Cache-Aided Wireless Interference Networks]]>631174647491821<![CDATA[Update or Wait: How to Keep Your Data Fresh]]>6311749275081178<![CDATA[Network Navigation With Scheduling: Error Evolution]]>6311750975341401<![CDATA[Channel Probing in Opportunistic Communication Systems]]>6311753575521164<![CDATA[From Log-Determinant Inequalities to Gaussian Entanglement via Recoverability Theory]]>AC+ln det V_{BC}-ln det V_{ABC}-ln det V_{C} ≥ 0 for all 3 × 3 block matrices V_{ABC}, where subscripts identify principal submatrices. We shall refer to the above-mentioned inequality as SSA of log-det entropy. In this paper, we develop further insights on the properties of the above-mentioned inequality and its applications to classical and quantum information theory. In the first part of this paper, we show how to find known and new necessary and sufficient conditions under which saturation with equality occurs. Subsequently, we discuss the role of the classical transpose channel (also known as Petz recovery map) in this problem and find its action explicitly. We then prove some extensions of the saturation theorem, by finding faithful lower bounds on a log-det conditional mutual information. In the second part, we focus on quantum Gaussian states, whose covariance matrices are not only positive but obey additional constraints due to the uncertainty relation. For Gaussian states, the log-det entropy is equivalent to the Rényi entropy of order 2. We provide a strengthening of log-det SSA for quantum covariance matrices that involves the so-called Gaussian Rényi-2 entanglement of formation, a well-behaved entanglement measure defined via a Gaussian convex roof construction. We then employ this result to define a log-det entropy equivalent of the squashed entanglement measure, which is remarkably shown to coincide with the Gaussian Rényi-2 entanglement of formation. This allows us to establish useful properties of such measure(s), such as monogamy, faithfulness, and additivity on Ga-
ssian states.]]>631175537568305<![CDATA[Testing Equality in Communication Graphs]]>631175697574318<![CDATA[A Generalisation of Dillon's APN Permutation With the Best Known Differential and Nonlinear Properties for All Fields of Size $2^{4k+2}$]]>631175757591546<![CDATA[Amplifying the Randomness of Weak Sources Correlated With Devices]]>(1/12) - 1)/(2(2^{(1/12)} + 1)) ≈ 0.0144). We also study a device-independent protocol that allows for correlations between the sequence of boxes used in the protocol and the SV source bits used to choose the particular box from whose output the randomness is obtained. Assuming the SV-like condition for devices, we show that the honest parties can achieve amplification of the weak source, for the parameter range 0 ≤ ε <; 0.0132, against a class of attacks given as a mixture of product box sequences, made of extremal no-signaling boxes, with additional symmetry conditions. Composable security proof against this class of attacks is provided.]]>6311759276111606<![CDATA[Comments on the Proof of Adaptive Stochastic Set Cover Based on Adaptive Submodularity and Its Implications for the Group Identification Problem in “Group-Based Active Query Selection for Rapid Diagnosis in Time-Critical Situations”]]>631176127614244<![CDATA[Corrections to “Weight Distribution of Cosets of Small Codes With Good Dual Properties” [Dec 15 6493-6504]]]>[1] which do not affect the validity of any of the the reported results. First, we note that Conjecture 9 on page 6497 is not correct; a counter example follows from Cohen’s theorem [2] which asserts the existence of linear codes with covering radius up to the sphere-covering bound. The second correction is related to the “Proof of Theorem 2 using Theorem 5” on page 6496. In that proof, the $n$ -point Discrete Fourier Transform (DFT) should be on $n+1$ points. The other steps of the proof hold without modification. We reproduce below the corrected proof with the needed modifications in bold. The issue with the $n$ -point DFT is that it makes Identity (1) below incorrect for $b=n$ .]]>63117615761579<![CDATA[Correction to “Cyclic Orbit Codes” [Nov 13 7386-7404]]]>Proposition 28 and Theorem 29 of the original paper [1]. The correct formulation for these two statements is as follows.]]>63117616761664<![CDATA[IEEE Transactions on Information Theory information for authors]]>6311C3C382