<![CDATA[ IEEE Transactions on Information Theory - new TOC ]]>
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TOC Alert for Publication# 18 2017February 16<![CDATA[Table of contents]]>633C1C4149<![CDATA[IEEE Transactions on Information Theory publication information]]>633C2C2169<![CDATA[Information Without Rolling Dice]]>$(epsilon ,delta )$ -capacity that extends the Kolmogorov $epsilon $ -capacity to packing sets of overlap at most $delta $ is introduced and compared with the Shannon capacity. The functional form of the results indicates that in both Kolmogorov and Shannon’s settings, capacity and entropy grow linearly with the number of degrees of freedom, but only logarithmically with the signal to noise ratio. This basic insight transcends the details of the stochastic or deterministic description of the information-theoretic model. For $delta =0$ , the analysis leads to a tight asymptotic expression of the Kolmogorov $epsilon $ -entropy of bandlimited signals. A deterministic notion of error exponent is introduced. Applications of the theory are briefly discussed.]]>63313491363598<![CDATA[Capacity of Remotely Powered Communication]]>$n$ -letter mutual information rate under various levels of side information available at the charger. When the charger is finely tunable to different energy levels, referred to as a “precision charger,” we show that these expressions reduce to single-letter form and there is a simple and intuitive joint charging and coding scheme achieving capacity. The precision charger scenario is motivated by the observation that in practice the transferred energy can be controlled by simply changing the amplitude of the beamformed signal. When the charger does not have sufficient precision, for example, when it is restricted to use a few discrete energy levels, we show that the computation of the $n$ -letter capacity can be cast as a Markov decision process if the channel is noiseless. This allows us to numerically compute the capacity for specific cases and obtain insights on the corresponding optimal policy, or even to obtain closed-form analytical solutions by solving the corresponding Bellman equations, as we demonstrate through examples. Our findings provide some surprising insights on how side information at the charger can be used to increase the overall capacity of the system.]]>633136413911521<![CDATA[A Single-Letter Upper Bound on the Feedback Capacity of Unifilar Finite-State Channels]]>$Q$ -context mapping, is based on a construction of a directed graph that is used for a sequential quantization of the receiver’s output sequences to a finite set of contexts. For any choice of $Q$ -graph, the feedback capacity is bounded by a single-letter expression, $C_{mathrm {fb}}leq sup I(X,S;Y|Q)$ , where the supremum is over $p(x|s,q)$ and the distribution of $(S,Q)$ is their stationary distribution. It is shown that the bound is tight for all unifilar FSCs, where feedback capacity is known: channels where the state is a function of the outputs, the trapdoor channel, Ising channels, the no-consecutive-ones input-constrained erasure channel, and the memoryless channel. Its efficiency is also demonstrated by deriving a new capacity result for the dicode erasure channel; the upper bound is obtained directly from the above-mentioned expression and its tightness is concluded with a general sufficient condition on the optimality of the upper bound. This sufficient condition is based on a fixed point principle of the BCJR equation and, indeed, formulated as a simple lower bound on feedback capacity of unifilar FSCs for arbitrary $Q$ -graphs. This upper bound indicates that a single-letter expression might exist for the capacity of finite-state channels with or without feedback based on a construction of auxiliary random variable with specified structure, suc-
as the $Q$ -graph, and not with i.i.d distribution. The upper bound also serves as a non-trivial bound on the capacity of channels without feedback, a problem that is still open.]]>63313921409834<![CDATA[Channel Upgradation for Non-Binary Input Alphabets and MACs]]>63314101424776<![CDATA[The Structure of Dual Schubert Union Codes]]>63314251433213<![CDATA[New MDS Self-Dual Codes From Generalized Reed—Solomon Codes]]>$q$ -ary MDS self-dual codes for various lengths has been investigated extensively. The problem is completely solved for the case where $q$ is even. This paper focuses on the case where $q$ is odd. We construct a few classes of new MDS self-dual codes through generalized Reed–Solomon codes. More precisely, we show that for any given even length $n$ , we have a $q$ -ary MDS code as long as $qequiv 1bmod {4}$ and $q$ is sufficiently large (say $qge 4^{n}times n^{2})$ . Furthermore, we prove that there exists a $q$ -ary MDS self-dual code of length $n$ if $q=r^{2}$ and $n$ satisfies one of the three conditions: 1) $nle r$ and $n$ is even; 2) $q$ is odd and $n-1$ is an odd divisor of $q-1$ ; and 3) $requiv 3mod {4}$ and $n=2tr$ for any $tle (r-1)/2$ .]]>63314341438229<![CDATA[Edge Coloring and Stopping Sets Analysis in Product Codes With MDS Components]]>$M$ . Then, we propose a differential evolution edge coloring algorithm that produces colorings with a large population of minimal rootcheck order symbols. The complexity of this algorithm per iteration is $o(M^{aleph })$ , for a given differential evolution parameter $aleph $ , where $M^{aleph }$ itself is small with respect to the huge cardinality of the coloring ensemble. Stopping sets of a product code are defined in the context of MDS components and a relationship is established with the graph representation. A full characterization of these stopping sets is given up to a size $(d+1)^{2}$ , where $d$ is the minimum Hamming distance of the MDS component code. The performance of MDS-based product codes with and without double-diversity coloring is analyzed in presence of both the block and the independent erasures. In the latter case, ML and iterative decoding are proven to coincide at small channel erasure probability. Furthermore, numerical results show excellent performance in presence of unequal erasure probability due to double-diversity colorings.]]>633143914621532<![CDATA[Weight Distributions of Non-Binary Multi-Edge Type LDPC Code Ensembles: Analysis and Efficient Evaluation]]>633146314751322<![CDATA[Capacity-Achieving Sparse Superposition Codes via Approximate Message Passing Decoding]]>63314761500727<![CDATA[On the Construction of Polar Codes for Channels With Moderate Input Alphabet Sizes]]>63315011509222<![CDATA[On Secrecy Capacity of Minimum Storage Regenerating Codes]]>$(l_{1},l_{2})$ -eavesdropper model, where the eavesdropper has access to data stored on $l_{1}$ nodes and the repair data for an additional $l_{2}$ nodes. We study it from the information-theoretic perspective. First, some general properties of MSR codes as well as a simple and generally applicable upper bound on secrecy capacity are given. Second, a new concept of stable MSR codes is introduced, where the stable property is shown to be closely linked with secrecy capacity. Finally, a comprehensive and explicit result on secrecy capacity in the linear MSR scenario is present, which generalizes all related works in the literature and also predicts certain results for some unexplored linear MSR codes.]]>63315101524447<![CDATA[Nonadaptive Group Testing Based on Sparse Pooling Graphs]]>sparse pooling graphs is presented. A pooling graph is a bipartite graph for which the adjacency matrix is a pooling matrix. The binary status of the objects to be tested are modeled by independent identically distributed. Bernoulli random variables with probability $p$ . An $(l, r, n)$ -regular pooling graph is a bipartite graph in which the left nodes have degree $l$ , the right nodes have degree $r$ , and $n$ is the number of left nodes. The main contribution of this paper is a direct coding theorem that gives the conditions for the existence of an estimator that can achieve an arbitrarily small probability of error. An estimator is a function that uses observations to infer the state of an object. The direct coding theorem is proved by averaging the upper bound on the probability of the estimation error of the typical set estimator over an $(l, r, n)$ -regular pooling graph ensemble. Numerical results indicate sharp threshold behaviors in the asymptotic regime. These results can provide a concrete benchmark for nonadaptive group testing of existing and emerging detection algorithms over a noiseless system.]]>63315251534481<![CDATA[Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets]]>63315351554583<![CDATA[Quantitative Recovery Conditions for Tree-Based Compressed Sensing]]>et al. (2010), signals whose wavelet coefficients exhibit a rooted tree structure can be recovered using specially adapted compressed sensing algorithms from just $n=mathcal {O}(k)$ measurements, where $k$ is the sparsity of the signal. Motivated by these results, we introduce a simplified proportional-dimensional asymptotic framework, which enables the quantitative evaluation of recovery guarantees for tree-based compressed sensing. In the context of Gaussian matrices, we apply this framework to existing worst-case analysis of the iterative tree projection (ITP) algorithm, which makes use of the tree-based restricted isometry property (RIP). Within the same framework, we then obtain quantitative results based on a new method of analysis, which considers the fixed points of the algorithm. By exploiting the realistic average-case assumption that the measurements are statistically independent of the signal, we obtain significant quantitative improvements when compared with the tree-based RIP analysis. Our results have a refreshingly simple interpretation, explicitly determining a bound on the number of measurements that are required as a multiple of the sparsity. For example, we prove that exact recovery of binary tree-based signals from noiseless Gaussian measurements is asymptotically guaranteed for ITP with constant stepsize provided $ngeq 50k$ . All our results extend to the more realistic case in which measurements are corrupted by noise.]]>63315551571772<![CDATA[On the Limitation of Spectral Methods: From the Gaussian Hidden Clique Problem to Rank One Perturbations of Gaussian Tensors]]>$n$ , distinguish between the hypothesis that all upper triangular variables are independent and identically distributed (i.i.d). Gaussians variables with mean 0 and variance 1 and the hypothesis, where X is the sum of such matrix and an independent rank-one perturbation. This setup applies to the situation, where under the alternative, there is a planted principal submatrix B of size $L$ for which all upper triangular variables are i.i.d. Gaussians with mean 1 and variance 1, whereas all other upper triangular elements of X not in B are i.i.d. Gaussians variables with mean 0 and variance 1. We refer to this as the “Gaussian hidden clique problem.” When $L=(1+epsilon )sqrt {n}$ ($epsilon >0$ ), it is possible to solve this detection problem with probability $1-o_{n}(1)$ by computing the spectrum of X and considering the largest eigenvalue of X. We prove that this condition is tight in the following sense: when $L<(1-epsilon )sqrt {n}$ no algorithm that examines only the eigenvalues of X can detect the existence of a hidden Gaussian clique, with error probability vanishing as $nto infty $ . We prove this result as an immediate consequence of a more general result on rank-one perturbations of $k$ -dimensional Gaussian te-
sors. In this context, we establish a lower bound on the critical signal-to-noise ratio below which a rank-one signal cannot be detected.]]>63315721579222<![CDATA[Information-Theoretic Lower Bounds on Bayes Risk in Decentralized Estimation]]>63315801600709<![CDATA[High-Dimensional Estimation of Structured Signals From Non-Linear Observations With General Convex Loss Functions]]>structured signal $ {x}_{0}in mathbb {R}^{n}$ from non-linear and noisy Gaussian observations. Supposing that $ {x}_{0}$ is contained in a certain convex subset$ Ksubset mathbb {R}^{n}$ , we prove that accurate recovery is already feasible if the number of observations exceeds the effective dimension of $ K$ . It will turn out that the possibly unknown non-linearity of our model affects the error rate only by a multiplicative constant. This achievement is based on recent works by Plan and Vershynin, who have suggested to treat the non-linearity rather as noise, which perturbs a linear measurement process. Using the concept of restricted strong convexity, we show that their results for the generalized Lasso can be extended to a fairly large class of convex loss functions. Moreover, we shall allow for the presence of adversarial noise so that even deterministic model inaccuracies can be coped with. These generalizations particularly give further evidence of why many standard estimators perform surprisingly well in practice, although they do not rely on any knowledge of the underlying output rule. To this end, our results provide a unified framework for signal reconstruction in high dimensions, covering various challenges from the fields of compressed sensing, signal processing, and statistical learning.]]>63316011619519<![CDATA[Nonparametric Regression Based on Hierarchical Interaction Models]]>$m: { mathbb {R}^{d}}rightarrow mathbb {R}$ is done in several layers, where in each layer a function of at most $d^{*}$ inputs computed by the previous layer is evaluated. We investigate two different regression estimates based on polynomial splines and on neural networks, and show that if the regression function satisfies a hierarchical interaction model and all occurring functions in the model are smooth, the rate of convergence of these estimates depends on $d^{*}$ (and not on $d$ ). Hence, in this case, the estimates can achieve good rate of convergence even for large $d$ , and are in this sense able to circumvent the so-called curse of dimensionality.]]>63316201630231<![CDATA[Delay on Broadcast Erasure Channels Under Random Linear Combinations]]>$d$ ) formed from a block of $c$ packets to a collection of $n$ receivers, where the channels between the transmitter and each receiver are independent erasure channels with reception probabilities $ mathrm {q}= (q_{1},ldots ,q_{n})$ . We establish several properties of the random delay until all $n$ receivers have recovered all $c$ packets, denoted $Y_{n:n}^{(c)}$ . First, we provide lower and upper bounds, exact expressions, and a recurrence for the moments of $Y_{n:n}^{(c)}$ . Second, we study the delay per packet $Y_{n:n}^{(c)}/c$ as a function of $c$ , including the asymptotic delay (as $c to infty $ ) and monotonicity (in $c$ ) properties of the delay per packet. Third, we employ extreme value theory to investigate $Y_{n:n}^{(c)}$ as a function of $n$ (as $n to infty $ ). Several results are new, some-
results are extensions of existing results, and some results are the proofs of known results using new (probabilistic) proof techniques.]]>633163116611899<![CDATA[Wireless Multihop Device-to-Device Caching Networks]]>$n$ nodes are uniformly distributed at random over the network area. We let each node caches $M$ files from a library of size $mgeq M$ . Each node in the network requests a file from the library independently at random, according to a popularity distribution, and is served by other nodes having the requested file in their local cache via (possibly) multihop transmissions. Under the classical “protocol model” of wireless networks, we characterize the optimal per-node capacity scaling law for a broad class of heavy-tailed popularity distributions, including Zipf distributions with exponent less than one. In the parameter regime of interest, i.e., $m=o(nM)$ , we show that a decentralized random caching strategy with uniform probability over the library yields the optimal per-node capacity scaling of $Theta (sqrt {M/m})$ for heavy-tailed popularity distributions. This scaling is constant with $n$ , thus yielding throughput scalability with the network size. Furthermore, the multihop capacity scaling can be significantly better than for the case of single-hop caching networks, for which the per-node capacity is $Theta (M/m)$ . The multihop capacity scaling law can be further improved for a Zipf distribution with exponent larger than some threshold > 1, by using a decentralized random caching uniformly across a subset of most popular files in the library. Name-
y, ignoring a subset of less popular files (i.e., effectively reducing the size of the library) can significantly improve the throughput scaling while guaranteeing that all nodes will be served with high probability as $n$ increases.]]>63316621676592<![CDATA[$k$ -Connectivity in Random $K$ -Out Graphs Intersecting Erdős-Rényi Graphs]]>$k$ -connectivity in secure wireless sensor networks under the random pairwise key predistribution scheme with unreliable links. When wireless communication links are modeled as independent on-off channels, this amounts to analyzing a random graph model formed by intersecting a random $K$ -out graph and an Erdős-Rényi graph. We present conditions on how to scale the parameters of this intersection model so that the resulting graph is $k$ -connected with probability approaching to one (resp. zero) as the number of nodes gets large. The resulting zero-one law is shown to improve and sharpen the previous result on the 1-connectivity of the same model. We also provide numerical results to support our analysis.]]>63316771692519<![CDATA[A New Framework for the Performance Analysis of Wireless Communications Under Hoyt (Nakagami- $q$ ) Fading]]>Hoyt transform method, that allows to analyze the performance of a wireless link under Hoyt (Nakagami-$q$ ) fading in a very simple way. We illustrate that many performance metrics for Hoyt fading can be calculated by leveraging well-known results for Rayleigh fading and only performing a finite-range integral. We use this technique to obtain novel results for some information and communication-theoretic metrics in Hoyt fading channels.]]>63316931702547<![CDATA[Diversity-Multiplexing Trade-Off of Half-Duplex Single Relay Networks]]>63317031720964<![CDATA[Retrospective Interference Alignment: Degrees of Freedom Scaling With Distributed Transmitters]]>$K$ -user single-input single-output interference channel with delayed channel state information at the transmitters (CSIT). Our main contribution is to show that even with delayed CSIT and distributed transmitters, the achievable degrees of freedom (DoFs) still scale with the number of users. More specifically, we propose a method that achieves $K/(2sqrt {K} - 1) geq sqrt {K}/2$ DoF. The main idea behind the proposed method is to use interference alignment (IA) at the receiver side in conjunction with repetition coding at the transmitters. Repetition coding repeats the data $R$ times while IA makes the interference generated by a given transmitter identical: 1) at all non-intended receivers and 2) all transmission repetitions. Therefore, one retransmission per transmitter is sufficient to cancel all the interference. This reduces significantly the overhead required for interference removal since the number of interference terms is reduced from $RK(K-1)$ to $K$ .]]>63317211730472<![CDATA[Asymptotic Analysis of Rayleigh Product Channels: A Free Probability Approach]]>63317311745841<![CDATA[On Gaussian Channels With Feedback Under Expected Power Constraints and With Non-Vanishing Error Probabilities]]>$ varepsilon $ -capacity and show that it depends on $ varepsilon $ in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that for any positive integer $L$ , the second-order term is bounded between a term proportional to $-ln _{(L)} n$ (where $ln _{(L)}(cdot )$ is the $L$ -fold nested logarithm function) and a term proportional to $+(nln n)^{1/2}$ , where $n$ is the blocklength. The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available. In our second contribution, we establish the $ varepsilon $ -capacity region for the AWGN multiple access channel with feedback under the expected power constraint by combining ideas from -
ypothesis testing, information spectrum analysis, Ozarow’s coding scheme, and power control.]]>63317461765412<![CDATA[Discrete Lossy Gray–Wyner Revisited: Second-Order Asymptotics, Large and Moderate Deviations]]>63317661791612<![CDATA[Converse Bounds for Private Communication Over Quantum Channels]]>63317921817616<![CDATA[Additive Bounds of Minimum Output Entropies for Unital Channels and an Exact Qubit Formula]]>$alpha =2$ . Moreover, since our upper bound is additive under tensor product, we get as a corollary an upper bound for the classical capacity of unital quantum channels. Interestingly, our upper bound for the classical capacity depends only on the operator norm of matrix representations of channels on the space of traceless Hermitian operators, and is tight in the sense that it gives the precise quantity of classical capacity of the Werner–Holevo channel. As an example, we study quantum channels with operator sum representation that is made of the discrete Weyl operators (generalized Pauli operators), and explain how our formula works in this case. Finally, we find new examples for which the minimum output Rényi 2-entropy is additive.]]>63318181828294<![CDATA[Second-Order Asymptotics of Conversions of Distributions and Entangled States Based on Rayleigh-Normal Probability Distributions]]>633182918571215<![CDATA[Coding Schemes for Achieving Strong Secrecy at Negligible Cost]]>negligible cost, in the sense of maintaining the overall communication rate of the same channel without secrecy constraints. Specifically, we propose and analyze two source-channel coding architectures, in which secrecy is achieved by multiplexing public and confidential messages. In both cases, our main contribution is to show that secrecy can be achieved without compromising communication rate and by requiring only randomness of asymptotically vanishing rate. Our first source-channel coding architecture relies on a modified wiretap channel code, in which randomization is performed using the output of a source code. In contrast, our second architecture relies on a standard wiretap code combined with a modified source code termed uniform compression code, in which a small shared secret seed is used to enhance the uniformity of the source code output. We carry out a detailed analysis of uniform compression codes and characterize the optimal size of the shared seed.]]>63318581873622<![CDATA[The Secrecy Capacity of Gaussian MIMO Channels With Finite Memory]]>finite memory, subject to a per-symbol average power constraint on the MIMO channel input. MIMO channels with finite memory are very common in wireless communications as well as in wireline communications (e.g., in communications over power lines). To derive the secrecy capacity of the Gaussian MIMO WTC with finite memory, we first construct an asymptotically equivalent block-memoryless MIMO WTC, which is then transformed into a set of parallel, independent, memoryless MIMO WTCs in the frequency domain. The secrecy capacity of the Gaussian MIMO WTC with finite memory is obtained as the secrecy capacity of the set of parallel, independent, memoryless MIMO WTCs, and is expressed as maximization over the input covariance matrices in the frequency domain. Finally, we detail two applications of our result: First, we show that the secrecy capacity of the Gaussian scalar WTC with finite memory can be achieved by waterfilling, and obtain a closed-form expression for this secrecy capacity. Then, we use our result to characterize the secrecy capacity of narrowband powerline channels, thereby resolving one of the major open issues for this channel model.]]>63318741897477<![CDATA[Secure Degrees of Freedom of One-Hop Wireless Networks With No Eavesdropper CSIT]]>$M$ helpers, the $K$ -user multiple access wiretap channel, and the $K$ -user interference channel with an external eavesdropper, when no eavesdropper’s channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper’s channel state information at the transmitter (CSIT) does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper’s CSIT, the $K$ -user multiple access wiretap channel reduces to a wiretap channel with $(K-1)$ helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from $frac {K(K-1)}{K(K-1)+1}$ to $frac {K-1}{K}$ . For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from $frac {K(K-1)}{2K-1}$ to $frac {K-1}{2}$ in the absence of the eavesdropper’s CSIT. Our results show that the lack of eavesdropper’s CSI-
does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. This implies that physical layer security can be made robust to the unavailability of eavesdropper CSIT at high signal-to-noise ratio regimes by the careful modification of the achievable schemes as demonstrated in this paper.]]>633189819221014<![CDATA[Secrecy Capacity Scaling in Large Cooperative Wireless Networks]]>large wireless networks subject to security constraints. In contrast to point-to-point, interference-limited communications considered in prior works, we propose active cooperative relaying-based schemes. We consider a network with $n_{l}$ legitimate nodes, $n_{e}$ eavesdroppers, and path loss exponent $alpha geq 2$ . As long as $n_{e}^{2}big (log (n_{e})big )^{gamma }=o(n_{l})$ , for some positive $gamma $ , we show that one can obtain unbounded secure aggregate rate. This means zero-cost secure communication, given fixed total power constraint for the entire network. We achieve this result through: 1) the source using Wyner randomized encoder and a serial (multi-stage) block Markov scheme, to cooperate with the relays and 2) the relays acting as a virtual multi-antenna to apply beamforming against the eavesdroppers. Our simpler parallel (two-stage) relaying scheme can achieve the same unbounded secure aggregate rate when $n_{e}^{alpha /{2}+1}big (log (n_{e})big )^{gamma +delta ({alpha }/{2}+1)}=o(n_{l})$ holds, for some positive $gamma ,delta $ . Finally, we study the improvement (to the detriment of legitimate nodes) that the eavesdroppers achieve in terms of the information leakage rate in a large cooperative network in the case of collusion. We show that again the zero-cost secure communication is possible, if $n_{e}^{(2+{2}/{alpha })}big (log n_{e}big )^{gamma }=o(n_{l})$ holds, for some positive $gamma $ ; that is, in the case of collusion slightly fewer eavesdroppers can be tolerated compared with the non-colluding case.]]>63319231939781<![CDATA[Blank page]]>633B1940B19402<![CDATA[IEEE Transactions on Information Theory information for authors]]>633C3C354