<![CDATA[ IEEE Transactions on Information Theory - new TOC ]]>
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TOC Alert for Publication# 18 2018August 16<![CDATA[Table of contents]]>649C1C4148<![CDATA[IEEE Transactions on Information Theory publication information]]>649C2C2112<![CDATA[Subset Source Coding]]>649598960122387<![CDATA[Fundamental Distortion Limits of Analog-to-Digital Compression]]>649601360331270<![CDATA[Distortion Bounds for Source Broadcast Problems]]>64960346053953<![CDATA[On the Combinatorial Version of the Slepian–Wolf Problem]]>$X$ and $Y$ , respectively; the length of each string is equal to $n$ , and the Hamming distance between the strings is at most $alpha n$ . The Senders compress their strings and communicate the results to the Receiver. Then, the Receiver must reconstruct both the strings $X$ and $Y$ . The aim is to minimize the lengths of the transmitted messages. For an asymmetric variant of this problem (where one of the Senders transmits the input string to the Receiver without compression) with deterministic encoding, a nontrivial bound was found by Orlitsky and Viswanathany. In this paper, we prove a new lower bound for the schemes with syndrome coding, where at least one of the Senders uses linear encoding of the input string. For the combinatorial Slepian–Wolf problem with randomized encoding, the theoretical optimum of communication complexity was known earlier, even though effective protocols with optimal lengths of messages remained unknown. We close this gap and present a polynomial-time-randomized protocol that achieves the optimal communication complexity.]]>649605460691119<![CDATA[Lossless Compression of Binary Trees With Correlated Vertex Names]]>64960706080596<![CDATA[Lossy Coding of Correlated Sources Over a Multiple Access Channel: Necessary Conditions and Separation Results]]>64960816097753<![CDATA[From Compressed Sensing to Compressed Bit-Streams: Practical Encoders, Tractable Decoders]]>$ Sigma Delta $ (sigma-delta) quantization, and a subsequent encoding (compression) stage that fits within the framework of compressed sensing seamlessly. We prove that, using this method, we can convert analog compressive samples to compressed digital bitstreams and decode using tractable algorithms based on convex optimization. We prove that the proposed analog-to-information converter (AIC) provides a nearly optimal encoding of sparse and compressible signals. Finally, we present numerical experiments illustrating the effectiveness of the proposed AIC.]]>64960986114536<![CDATA[Model Change Detection With the MDL Principle]]>64961156126346<![CDATA[Optimal Inference in Crowdsourced Classification via Belief Propagation]]>64961276138650<![CDATA[Optimal Instance Adaptive Algorithm for the Top-<inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> Ranking Problem]]>$K$ items from noisy pairwise comparisons. In our setting, we are given $r$ pairwise comparisons between each pair of $n$ items, where each comparison has noise constrained by a very general noise model called the strong stochastic transitivity model. Our goal is to provide an optimal instance adaptive algorithm for the top-$K$ ranking problem. In particular, we present a linear time algorithm that has a competitive ratio of $tilde {O}(sqrt {n})$ ^{1}; i.e., to solve any instance of top-$K$ ranking, our algorithm needs at most $tilde {O}(sqrt {n})$ times as many samples needed as the best possible algorithm for that instance [in contrast, all previous known algorithms for the top-$K$ problem have competitive ratios of $tilde {Omega }(n)$ or worse]. We further show that this is tight (up to polylogarithmic factors): any algorithm for the top-$K$ problem has competitive ratio of at least $tilde {Omega }(sqrt {n})$ .

We use $tilde {O}$ and $tilde {Omega }$ notation to hide polylogarithmic factors.

]]>64961396160442<![CDATA[Social Learning and Distributed Hypothesis Testing]]>649616161791613<![CDATA[A Fundamental Limitation on Maximum Parameter Dimension for Accurate Estimation With Quantized Data]]>64961806195951<![CDATA[Converse Theorems for the DMC With Mismatched Decoding]]>$q$ for a discrete memoryless channel $W$ is addressed. We study two kinds of decoders. The $delta $ -margin mismatched decoder outputs a message whose metric with the channel output exceeds that of all the other codewords by at least $delta $ . The $tau $ -threshold decoder outputs a single message whose metric with the channel output exceeds a threshold $tau $ . It is proved that the mismatch capacity with a constant margin decoder is equal to the “product-space” improvement of the random coding lower bound on the mismatch capacity, $C_{q}^{(infty)}(W)$ , which was introduced by Csiszár and Narayan. We next consider sequences of $P$ -constant composition codebooks. Using the Central Limit Theorem, it is shown that for such sequences of codebooks the supremum of achievable rates with constant threshold decoding is upper bounded by the supremum of the achievable rates with a constant margin decoder, and therefore also by $C_{q}^{(infty)}(W)$ . Further, a soft converse is proved stating that if the average probability of error of a sequence of codebooks with ordinary mismatched decoding converges to zero sufficiently fast, the rate of the code sequence is upper bounde-
by $C_{q}^{(infty)}(W)$ . In particular, if $q$ is a bounded rational metric, and the average probability of error converges to zero faster than $O(n^{-1})$ , then $Rleq C_{q}^{(infty)}(W)$ . Finally, a max-min multi-letter upper bound on the mismatch capacity that bears some resemblance to $C_{q}^{(infty)}(W)$ is presented.]]>64961966207299<![CDATA[Bounds on the Reliability Function of Typewriter Channels]]>$q$ -ary symmetric channels, $qgeq 49$ . Here we prove, by introducing dependence between codewords of a random ensemble, that the conjecture is false even for a typewriter channel with $q=4$ inputs. In the process, we also demonstrate that Lovász’s proof of the capacity of the pentagon was implicitly contained (but unnoticed!) in the works of Jelinek and Gallager on the expurgated bound done at least ten years before Lovász. In the opposite direction, new upper bounds on the reliability function are derived for channels with an odd number of inputs by using an adaptation of Delsarte’s linear programming bound. First, we derive a bound based on the minimum distance, which combines Lovász’s construction for bounding the graph capacity with the McEliece-Rodemich-Rumsey-Welch construction for bounding the minimum distance of codes in the Hamming space. Then, for the particular case of cross-over probability 1/2, we derive an improved bound by also using the method of Kalai and Linial to study the spectrum distribution of codes.]]>64962086222911<![CDATA[Error Exponents of Typical Random Codes]]>expectation of the logarithm of the error probability of the random code, as opposed to the traditional random coding error exponent, which is the limit of the negative normalized logarithm of the expectation of the error probability. For the ensemble of uniformly randomly drawn fixed composition codes, we provide exact error exponents of TRCs for a general discrete memoryless channel and a wide class of (stochastic) decoders, collectively referred to as the generalized likelihood decoder (GLD). This ensemble of fixed composition codes is shown to be no worse than any other ensemble of independent codewords that are drawn under a permutation-invariant distribution (e.g., independent identically distributed codewords). We also present relationships between the error exponent of the TRC and the ordinary random coding error exponent, as well as the expurgated exponent for the GLD. Finally, we demonstrate that our analysis technique is applicable also to more general communication scenarios, such as list decoding (for fixed-size lists) as well as the decoding with an erasure/list option in Forney’s sense.]]>64962236235341<![CDATA[Beta–Beta Bounds: Finite-Blocklength Analog of the Golden Formula]]>$beta $ functions (beta–beta converse bound); and 2) a novel beta–beta channel-coding achievability bound, expressed again as the ratio of two Neyman–Pearson $beta $ functions. To demonstrate the usefulness of this finite-blocklength extension of the golden formula, the beta–beta achievability and converse bounds are used to obtain a finite-blocklength extension of Verdú’s wideband-slope approximation. The proof parallels the derivation of the latter, with the beta–beta bounds used in place of the golden formula. The beta–beta (achievability) bound is also shown to be useful in cases where the capacity-achieving output distribution is not a product distribution due to, e.g., a cost constraint or structural constraints on the codebook, such as orthogonality or constant composition. As an example, the bound is used to characterize the channel dispersion of the additive exponential-noise channel and to obtain a finite-blocklength achievability bound (the tightest to date) for multiple-input multiple-output Rayleigh-fading channels with perfect channel state information at the receiver.]]>64962366256765<![CDATA[A Generic Transformation to Enable Optimal Repair in MDS Codes for Distributed Storage Systems]]>$(n=k{+}r,k)$ maximum distance separable (MDS) code into another $(n,k)$ MDS code over the same field such that: 1) some arbitrarily chosen $r$ nodes have the optimal repair bandwidth and the optimal rebuilding access; 2) for the remaining $k$ nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved; and 3) the sub-packetization level is increased only by a factor of $r$ . Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary $(n,k)$ scalar MDS code can be converted into an $(n,k)$ MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal.]]>649625762671249<![CDATA[Two-Point Codes for the Generalized GK Curve]]>64962686276720<![CDATA[Algebraic Geometry Codes With Complementary Duals Exceed the Asymptotic Gilbert-Varshamov Bound]]>64962776282217<![CDATA[Mutually Uncorrelated Primers for DNA-Based Data Storage]]>64962836296621<![CDATA[List Decoding of Insertions and Deletions]]>64962976304400<![CDATA[On Cyclic Codes of Composite Length and the Minimum Distance]]>64963056314601<![CDATA[New Constant-Dimension Subspace Codes from Maximum Rank Distance Codes]]>${mathbf{A}}_{q}(n,d,k)$ of a set of $k$ -dimensional subspaces in ${mathbf{F}}_{q}^{n}$ such that the subspace distance satisfies $d(U,V) geq d$ for any two different subspaces $U$ and $V$ in this set. In this paper, we give a direct construction of constant-dimension subspace codes from two parallel versions of maximum rank-distance codes. The problem about the sizes of our constructed constant-dimension subspace codes is transformed into finding a suitable sufficient condition to restrict number of the roots of $L_{1}(L_{2}(x))-x$ where $L_{1}$ and $L_{2}$ are $q$ -polynomials over the extension field ${mathbf{F}}_{q^{n}}$ . New lower bounds for ${mathbf{A}}_{q}(4k,2k,2k)$ , ${mathbf{A}}_{q}(4k+2,2k,2k+1)$ , and ${mathbf{A}}_{q}(4k+2,2(k-1),2k+1)$ are presented. Many new constant-dimension subspace codes better than previously best known codes with small paramete-
s are constructed.]]>64963156319653<![CDATA[Encoding and Indexing of Lattice Codes]]>$Lambda_{mathrm c}$ and shaping lattice $Lambda_{mathrm s}$ satisfy $Lambda _{mathrm s}subseteq Lambda _{mathrm c}$ , then $Lambda _{mathrm c}/ Lambda _{mathrm s}$ is a quotient group that can be used to form a (nested) lattice code $mathcal C$ . Conway and Sloane’s method of encoding and indexing does not apply when the lattices are not self-similar. Results are provided for two classes of lattices. 1) If $Lambda _{mathrm c}$ and $Lambda _{mathrm s}$ both have generator matrices in a triangular form that satisfies $Lambda _{mathrm s}subseteq Lambda _{mathrm c}$ , then encoding is always possible. 2) When $Lambda _{mathrm c}$ and $Lambda _{mathrm s}$ are described by full generator matrices, if a solution to a linear diophantine equation exists, then encoding is possible. In addition, special cases where $mathcal C$ is a cyclic code are considered. A condition for the existence of a group isomorphism between the information and $mathcal C$ is given. The results are applicable to a variety of coding lattices, including Construction A, Construction D, and low-density lattice codes. A variety of shaping lattices may be used as well, including convolutional code lattices and the direct sum of important lattices such as $D_{4}$ , $E_{8}$ , etc. Thus, a lattice code $mathcal C$ can be designed by selecting $Lambda _{mathrm c}$ and $Lambda _{mathrm s}$ separately, avoiding the competing design requirements of self-similar lattice codes.]]>64963206332430<![CDATA[Estimating the Signal-to-Noise Ratio Under Repeated Sampling of the Same Centered Signal: Applications to Side-Channel Attacks on a Cryptoprocessor]]>$n$ of times. The estimator has the structure of a $U$ -statistic from which derives many desirable properties: it is unbiased, consistent and, being a Rao-Blackwellisation of existing proposals, is closer to optimal variance-wise. However, its variance is numerically difficult to evaluate and two approximations are obtained to facilitate its use in practice. These allow quantifying the improvement in variance, which is found to be substantial as the estimator needs roughly one-third of the data previously required to perform similarly. Moreover, a simulation shows that the estimator is approximately normally distributed for $n$ as small as 10, which allows for accurate inference. The estimator is then applied to data arising in a cryptanalysis, where the numerical security of a cryptoprocessor is tested against a side-channel attack. This problem is a representative of situations where the signal-to-noise ratio must be precisely estimated for small $n$ . We derive a rigorous data-driven approach that is shown to much enhance the efficiency of standard side-channel attacks.]]>64963336339779<![CDATA[Interference Reduction in Multi-Cell Massive MIMO Systems With Large-Scale Fading Precoding]]>649634063611048<![CDATA[Gaussian Broadcast Channels With Intermittent Connectivity and Hybrid State Information at the Transmitter]]>intermittence channel states, and study the impact of the corresponding channel state information at the transmitter (CSIT) in a two-user Gaussian broadcast channel (BC). Moreover, due to the heterogeneous timeliness of intermittence channel states, the CSIT considered in this paper is hybrid. More specifically, the CSIT of each link can be perfectly (causally or non-causally) available, delayed, or not available. When the links are connected, we adopt a general setting that the received signal-to-noise ratios can be different. Our contribution is the characterization of the capacity regions of intermittent Gaussian BC to within bounded gaps for all combinations of hybrid CSIT, except for scenario DN (delayed CSIT of receiver 1, no CSIT of receiver 2). For scenario DN, we propose an opportunistic physical layer network coding scheme that achieves a strictly larger degree-of-freedom (DoF) region than the no-CSIT DoF region. As a corollary, single-user CSIT is able to increase the sum DoF for intermittent Gaussian BC (also the capacity region for the erasure BC, as a by-product). This result is in sharp contrast to the recent negative result by Davoodi and Jafar, where it is shown that for fast-fading multiple-input single-output BC with continuous channel states, single-user CSIT does not help at all in terms of sum DoF.]]>649636263831177<![CDATA[Capacity Achieving Distributions and Separation Principle for Feedback Gaussian Channels With Memory: the LQG Theory of Directed Information]]>$n$ -block length feedback capacity, by information lossless randomized strategies. The method is applied to compute closed form expressions for the FTFI capacity and feedback capacity, of nonstationary, nonergodic, unstable, multiple input multiple output Gaussian channels with memory on past channel outputs, subject to average transmission cost constraints of quadratic form in the channel inputs and outputs. It is shown that randomized strategies decompose into two orthogonal parts-an deterministic part, which controls the channel output process, and an innovation part, which transmits new information over the channel. Then a separation principle is shown between the computation of the optimal deterministic part and the random part of the optimal randomized strategies. Finally, the ergodic theory of linear-quadratic-Gaussian stochastic optimal control theory, is applied to identify sufficient conditions, expressed in terms of solutions to matrix difference and algebraic Riccati equations, so that the optimal control part of randomized strategies induces asymptotic stationarity and ergodicity, and feedback capacity is characterized by the per unit time limit of the FTFI capacity. The method reveals an interaction of the control and the information transmission parts of the optimal randomized strategies, and that whether feedback increases capacity, is directly related to the channel parameters and the transmission cost function, through the solutions of the matrix Riccati equations. For unstable channels, it is shown that feedback capacity exists and it is strictly positive, provided the power exceeds a critical threshold.]]>649638464181062<![CDATA[On the Age of Information With Packet Deadlines]]>age of information, which is a measure of the freshness of a continually updated piece of information as observed at a remote monitor. The age of information metric has been studied for a variety of different queueing systems, and in this paper, we introduce a packet deadline as a control mechanism to study its impact on the average age of information for an M/M/1/2 queueing system. We analyze the system for the cases of a fixed deadline and a random exponential deadline and derive closed-form expressions for the average age. We also derive a closed-form expression for the optimal average deadline for the random exponential case. Our numerical results show the relationship of the age performance to that of the M/M/1/1 and M/M/1/2 systems, and we demonstrate that using a deadline can outperform both the M/M/1/1 and M/M/1/2 without deadline.]]>64964196428499<![CDATA[On Minimum Period of Nonlinear Feedback Shift Registers in Grain-Like Structure]]>$n$ -stage NFSR and any given nonzero initial state of an $m$ -stage LFSR, the probability that the sequence generated by the NFSR in Grain-like structure achieves the minimum period $2^{m}-1$ is at most $2^{-n}$ . This implies that the probability of the cascade connection used in Grain achievi-
g the minimum period is very small.]]>64964296442502<![CDATA[Characterizations of the Differential Uniformity of Vectorial Functions by the Walsh Transform]]>$n$ and $m$ and every even positive integer $delta $ , we derive inequalities satisfied by the Walsh transforms of all vectorial $(n,m)$ -functions and prove that the case of equality characterizes differential $delta $ -uniformity. This provides a generalization to all differentially $delta $ -uniform functions of the characterization of Almost Perfect Nonlinear (APN) functions due to Chabaud and Vaudenay, by means of the fourth moment of the Walsh transform. Such generalization has been missing since the introduction of the notion of differential uniformity by Nyberg in 1994 and since Chabaud-Vaudenay’s result in the same year. Moreover, for each even $delta geq 2$ , we find several (in fact, an infinity of) such characterizations. In particular, when $delta =2$ and $delta =4$ , we have that, for any $(n,n)$ -function [resp. any $(n,n-1)$ -function)], the arithmetic mean of $W_{F}^{2}(u_{1},v_{1})W_{F}^{2}(u_{2},v_{2})W_{F}^{2}(u_{1}+u_{2},v_{1}+v_{2})$ when $u_{1},u_{2}$ range independe-
tly over ${mathbb F}_{2}^{n}$ and $v_{1},v_{2}$ are nonzero and distinct and range independently over ${mathbb F}_{2}^{m}$ is at least $2^{3n}$ , and that $F$ is APN (resp. is differentially 4-uniform) if and only if this arithmetic mean equals $2^{3n}$ (which is the value we would get with a bent function if such function could exist). These inequalities give more knowledge on the Walsh spectrum of $(n,m)$ -functions. We deduce in particular a property of the Walsh support of highly nonlinear functions. We also consider the completely open question of knowing if the nonlinearity of APN functions is necessarily non-weak (as it is the case for known APN functions); we prove new lower bounds which cover all power APN functions (and hence a large part of known APN functions), which explain why their nonlinearities are not bad, and we discuss the question of the nonlinearity of APN quadratic functions (since almost all other known APN functions are quadratic).]]>64964436453355<![CDATA[Comments on Cut-Set Bounds on Network Function Computation]]>64964546459308<![CDATA[Corrections to “Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques”]]>[1] in response to an error reported by Vaddi and Rajan [2]. To this effect, we add one extra condition for the definition of an $mathsf {IC}$ structure on page 3696.]]>64964606460136<![CDATA[IEEE Transactions on Information Theory information for authors]]>649C3C366