<![CDATA[ IEEE Transactions on Information Theory - new TOC ]]>
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TOC Alert for Publication# 18 2017July 20<![CDATA[Table of contents]]>638C1C4156<![CDATA[IEEE Transactions on Information Theory publication information]]>638C2C2111<![CDATA[Exact Expression For Information Distance]]>63847254728139<![CDATA[Information Limits for Recovering a Hidden Community]]>$K$ from an $n \times n$ symmetric data matrix $A$ , where for distinct indices $i,j$ , $A_{ij} \sim P$ if $i, j$ both belong to the community and $A_{ij} \sim Q$ otherwise, for two known probability distributions $P$ and $Q$ depending on $n$ . If $P={\mathrm{ Bern}}(p)$ and $Q={\mathrm{ Bern}}(q)$ with $p>q$ , it reduces to the problem of finding a densely connected $K$ -subgraph planted in a large Erdös–Rényi graph; if $P=\mathcal {N}(\mu ,1)$ and $Q=\mathcal {N}(0,1)$ with $\mu >0$ , it corresponds to the problem of locating a principal submatrix of elevated means in a large Gaussian random matrix. We focus on two types of asymptotic recovery guarantees as $n \to \infty $ : 1) weak recovery: expected number of classification errors is $o(K)$ and 2) exact recovery: probability of classifying all indices correctly converges to one. Under mild assumptions on $P$ and $Q$ , and allowing the community size to scale sublinearly with $n$ , we derive a set of sufficient conditions and a set of necessary conditions for recovery, which are asymptotically tight with sharp constants. The results hold, in particular, for the Gaussian case, and for the case of bounded log likelihood ratio, including the Bernoulli case whenever $({p}/{q})$ and $({1-p})/({1-q})$ are bounded away from zero and infinity. Previous work has shown that if weak recovery is achievable; then, exact recovery is achievable in linear additional time by a simple voting procedure. We provide a converse, showing the condition for the voting procedure to succeed is almost necessary for exact recovery.]]>63847294745337<![CDATA[Hammerstein System Identification With the Nearest Neighbor Algorithm]]>a priori information is nonparametric, both the nonlinear characteristic and the impulse response are completely unknown and can be of any form. Local and global properties of the estimate are examined. Whatever the probability density of the input signal, the estimate converges at every continuity point of the characteristic as well as in the global sense. We derive the asymptotic bias and variance of the proposed estimate. As a result, the optimal rate of convergence is established that additionally is independent of the shape of the input density. Results of numerical simulations are also presented.]]>63847464757580<![CDATA[Consistent Estimation of the Filtering and Marginal Smoothing Distributions in Nonparametric Hidden Markov Models]]>$\mathrm {L}^{1}$ -risk of the estimators. It has been proved very recently that statistical inference for finite state space nonparametric HMMs is possible. We study how the recent spectral methods developed in the parametric setting may be extended to the nonparametric framework and we give explicit upper bounds for the $\mathrm {L}^{2}$ -risk of the nonparametric spectral estimators. In the case where the observation space is compact, this provides explicit rates for the filtering and smoothing errors in total variation norm. The performance of the spectral method is assessed with simulated data for both the estimation of the (nonparametric) conditional distribution of the observations and the estimation of the marginal smoothing distributions.]]>63847584777679<![CDATA[Neural Dissimilarity Indices That Predict Oddball Detection in Behaviour]]>$L^{1}$ distance between firing rate vectors associated with two images was strongly correlated with the inverse of decision time in behavior. But why should decision times be correlated with $L^{1}$ distance? What is the decision-theoretic basis? In our decision theoretic formulation, we model visual search as an active sequential hypothesis testing problem with switching costs. Our analysis suggests an appropriate neuronal dissimilarity index, which correlates equally strongly with the inverse of decision time as the $L^{1}$ distance. We also consider a number of other possibilities, such as the relative entropy (Kullback–Leibler divergence) and the Chernoff entropy of the firing rate distributions. A more stringent test of equality of means, which would have provided a strong backing for our modeling, fails for our proposed as well as the other already discussed dissimilarity indices. However, test statistics from the equality of means test, when used to rank the indices in terms of their ability to explain the observed results, places our proposed dissimilarity index at the top followed by relative entropy, Chernoff entropy, and the $L^{1}$ indices. Computations of the different indices require an estimate of the relative entropy between two Poisson point processes. An estimator is developed and is shown to have near unbiased performance for almost all operating regions.]]>638477847961227<![CDATA[Recursive Distributed Detection for Composite Hypothesis Testing: Nonlinear Observation Models in Additive Gaussian Noise]]>consensus+innovations form are proposed, namely, $\mathcal {CIGLRT-L}$ and $\mathcal {CIGLRT-NL}$ , in which the agents estimate the underlying parameter and in parallel also update their test decision statistics by simultaneously processing the latest local sensed information and information obtained from neighboring agents. For $\mathcal {CIGLRT-NL}$ , for a broad class of nonlinear observation models and under a global observability condition, algorithm parameters which ensure asymptotically decaying probabilities of errors (probability of miss and probability of false detection) are characterized. For $\mathcal {CIGLRT-L}$ , a linear observation model is considered and upper bounds on large deviations decay exponent for the error probabilities are obtained.]]>638479748281037<![CDATA[On Locally Dyadic Stationary Processes]]>63848294837623<![CDATA[Efficient Regression in Metric Spaces via Approximate Lipschitz Extension]]>$O(n^{3})$ , which is prohibitive for large data sets. We design instead a regression algorithm whose speed and generalization performance depend on the intrinsic dimension of the data, to which the algorithm adapts. While our main innovation is algorithmic, the statistical results may also be of independent interest.]]>63848384849262<![CDATA[Compressed Sensing With Combinatorial Designs: Theory and Simulations]]>$4\sqrt {2}$ . We provide new theoretical results and detailed simulations, which indicate that the construction is competitive with Gaussian random matrices, and that recovery is tolerant to noise. A new recovery algorithm tailored to the construction is also given.]]>63848504859586<![CDATA[Compressed Sensing and Parallel Acquisition]]>63848604882733<![CDATA[$\mathbb {Z}_{2}\mathbb {Z}_{2}[u]$ –Cyclic and Constacyclic Codes]]>$\mathbb {Z}_{2}\mathbb {Z}_{4}$ -additive codes, $\mathbb {Z}_{2}\mathbb {Z}_{2}[u]$ -linear codes have been introduced by Aydogdu et al. In this paper, we introduce and study the algebraic structure of cyclic, constacyclic codes and their duals over the $R$ -module $\mathbb {Z}_{2}^\alpha R^\beta $ where $R=\mathbb {Z}_{2}+u\mathbb {Z}_{2}=\left \{{0,1,u,u+1}\right \}$ is the ring with four elements and $u^{2}=0$ . We determine the generating independent sets and the types and sizes of both such codes and their duals. Finally, we present a bound and an optimal family of codes attaining this bound and also give some illustrative examples of binary codes that have good parameters which are obtained from the cyclic codes in $\mathbb {Z}_{2}^\alpha R^\beta $ .]]>63848834893400<![CDATA[Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes]]>638489449272644<![CDATA[Locally Recoverable Codes on Algebraic Curves]]>$r$ ) of other symbols of the codeword. In this paper, we introduce a construction of LRC codes on algebraic curves, extending a recent construction of the Reed–Solomon like codes with locality. We treat the following situations: local recovery of a single erasure, local recovery of multiple erasures, and codes with several disjoint recovery sets for every coordinate (the availability problem). For each of these three problems we describe a general construction of codes on curves and construct several families of LRC codes. We also describe a construction of codes with availability that relies on automorphism groups of curves. We also consider the asymptotic problem for the parameters of the LRC codes on curves. We show that the codes obtained from asymptotically maximal curves (for instance, Garcia-Stichtenoth towers) improve upon the asymptotic versions of the Gilbert-Varshamov bound for LRC codes.]]>63849284939527<![CDATA[Deep Holes and MDS Extensions of Reed–Solomon Codes]]>63849404948211<![CDATA[Complex Linear Physical-Layer Network Coding]]>$w_{A}$ and $w_{B}$ , simultaneously to relay R. Based on the simultaneously received signals, relay R computes a linear combination of the symbols, $w_{N}=\alpha w_{A}+\beta w_{B}$ , as a network-coded symbol and then broadcasts $w_{N}$ to nodes A and B. Node A then obtains $w_{B}$ from $w_{N}$ and its self-information $w_{A}$ by $w_{B}=\beta ^{-1}(w_{N}-\alpha w_{A})$ . Node B obtains $w_{B}$ in a similar way. A critical question at relay R is as follows: “given channel gain ratio $\eta = h_{A}/h_{B}$ , where $h_{A}$ and $h_{B}$ are the complex channel gains from nodes A and B to relay R, respectively, what is the optimal coefficients $(\alpha ,\beta )$ that minimizes the symbol error rate (SER) of $w_{N}=\alpha -
_{A}+\beta w_{B}$ when the relay attempts to detect $w_{N}$ in the presence of noise?” Our contributions with respect to this question are as follows: 1) we put forth a general Gaussian-integer formulation for complex linear PNC in which $\alpha ,\beta ,w_{A}, w_{B}$ , and $w_{N}$ are the elements of a finite field of Gaussian integers, that is, the field of $\mathbb {Z}[i]/q$ , where $q$ is a Gaussian prime. Previous vector formulation, in which $w_{A}$ , $w_{B}$ , and $w_{N}$ were represented by 2-D vectors and $\alpha $ and $\beta $ were represented by $2\times 2$ matrices, corresponds to a subcase of our Gaussian-integer formulation, where $q$ is real prime only. Extension to the Gaussian prime $q$ , where $q$ can be complex, gives us a larger set of signal constellations to achieve different rates at different values of SNR; and 2) we show how to divide the complex plane of 638494949812208<![CDATA[Asymmetric Lee Distance Codes for DNA-Based Storage]]>638498249951047<![CDATA[Duplication-Correcting Codes for Data Storage in the DNA of Living Organisms]]>$k$ , where we are primarily focused on the cases of $k=2,3$ . Finally, we provide a full classification of the sets of lengths allowed in tandem duplication that result in a unique root for all sequences.]]>63849965010629<![CDATA[Principal Inertia Components and Applications]]>$X$ and $Y$ . The PICs lie in the intersection of information and estimation theory, and provide a fine-grained decomposition of the dependence between $X$ and $Y$ . Moreover, the PICs describe which functions of $X$ can or cannot be reliably inferred (in terms of MMSE), given an observation of $Y$ . We demonstrate that the PICs play an important role in information theory, and they can be used to characterize information-theoretic limits of certain estimation problems. In privacy settings, we prove that the PICs are related to the fundamental limits of perfect privacy.]]>638501150381279<![CDATA[The Generalized Stochastic Likelihood Decoder: Random Coding and Expurgated Bounds]]>et al.). We also extend the result from pure channel coding to combined source and channel coding (random binning followed by random channel coding) with side information available to the decoder. Finally, returning to pure channel coding, we derive also an expurgated exponent for the stochastic likelihood decoder, which turns out to be at least as tight (and in some cases, strictly so) as the classical expurgated exponent of the maximum likelihood decoder, even though the stochastic likelihood decoder is suboptimal.]]>63850395051368<![CDATA[Feedback and Partial Message Side-Information on the Semideterministic Broadcast Channel]]>63850525073702<![CDATA[Worst-case Redundancy of Optimal Binary AIFV Codes and Their Extended Codes]]>$p_{\max }\geq 1$ /2, where $p_{\max }$ is the probability of the most likely source symbol. In addition, we propose an extension of binary AIFV codes, which use $m$ code trees and allow at most $m$ -bit decoding delay. We show that the worst-case redundancy of the extended binary AIFV codes is $1/m$ for $m \leq 4$ .]]>638507450861062<![CDATA[Joint Empirical Coordination of Source and Channel]]>638508751141411<![CDATA[Capacity Bounds for Additive Symmetric $\alpha $ -Stable Noise Channels]]>$\alpha $ -stable distribution. At present, the capacity of $\alpha $ -stable noise channels is not well understood, with the exception of Cauchy noise ($\alpha = 1$ ) with a logarithmic constraint and Gaussian noise ($\alpha = 2$ ) with a power constraint. In this paper, we consider additive symmetric $\alpha $ -stable noise channels with $\alpha \in (1,2]$ . We derive bounds for the capacity with an absolute moment constraint. We then compare our bounds with a numerical approximation via the Blahut–Arimoto algorithm, which provides insight into the effect of noise parameters on the bounds. In particular, we find that our lower bound is in good agreement with the numerical approximation for $\alpha $ near 2.]]>63851155123506<![CDATA[On the Capacity of Write-Once Memories]]>$q$ -ary cells that can only increase their value. A WOM code is a coding scheme that allows writing multiple times to the memory without decreasing the levels of the cells. In the conventional model, it is assumed that the encoder can read the memory state before encoding, while the decoder reads only the memory state after encoding. However, there are three more models in this setup, which depend on whether the encoder and the decoder are informed or uninformed with the previous state of the memory. These four models were first introduced by Wolf et al., where they extensively studied the WOM capacity in these models for the binary case. In the non-binary setup, only the model, in which the encoder is informed and the decoder is not, was studied by Fu and Vinck. In this paper, we first present constructions of WOM codes in the models where the encoder is uninformed with the memory state (that is, the encoder cannot read the memory prior to encoding). We then study the capacity regions and maximum sum-rates of non-binary WOM codes for all four models. We extend the results by Wolf et al. and show that the capacity regions for the models in which the encoder is informed and the decoder is informed or uninformed in both the $\epsilon $ -error and the zero-error cases are all identical. We also find the $\epsilon $ -error capacity region; in this case, the encoder is uninformed and the decoder is informed and show that, in contrary to the binary case, it is a proper subset of the capacity region in the first two models. Several more results on the maximum sum-rate are presented as well.]]>63851245137830<![CDATA[Broadcast Channels With Privacy Leakage Constraints]]>63851385161773<![CDATA[Vector Gaussian Rate-Distortion With Variable Side Information]]>63851625178338<![CDATA[Rate Distortion for Lossy In-Network Linear Function Computation and Consensus: Distortion Accumulation and Sequential Reverse Water-Filling]]>[2]. Surprisingly, this accumulation effect of distortion happens even at infinite blocklength. Combining this observation with an inequality on the dominance of mean-square quantities over relative-entropy quantities, we obtain outer bounds on the rate distortion function that are tighter than classical cut-set bounds by a difference, which can be arbitrarily large in both data aggregation and consensus. We also obtain inner bounds on the optimal rate using random Gaussian coding, which differ from the outer bounds by $\mathcal {O}(\sqrt {D})$ , where $D$ is the overall distortion. The obtained inner and outer bounds can provide insights on rate (bit) allocations for both the data aggregation problem and the consensus problem. We show that for tree networks, the rate allocation results have a mathematical structure similar to classical reverse water-filling for parallel Gaussian sources. Apart from data aggregation and distributed consensus, the distortion accumulation analysis framework is also applicab-
e in large-scale data summarization through histograms and linear sketching, e.g., word counting tasks for document summarization.]]>63851795206584<![CDATA[Distributed Binary Detection With Lossy Data Compression]]>rate-error-distortion region, describing the tradeoff between: the communication rate, the error exponent induced by the detection, and the distortion incurred by the source reconstruction. In the special case of testing against independence, where the alternative hypothesis implies that the sources are independent, the optimal rate-error-distortion region is characterized. An application example to binary symmetric sources is given subsequently and the explicit expression for the rate-error-distortion region is provided as well. The case of “general hypotheses” is also investigated. A new achievable rate-error-distortion region is derived based on the use of non-asymptotic binning, improving the quality of communicated descriptions. Further improvement of performance in the general case is shown to be possible when the requirement of source reconstruction is relaxed, which stands in contrast to the case of general hypotheses.]]>63852075227703<![CDATA[The Rate-Distortion Function and Excess-Distortion Exponent of Sparse Regression Codes With Optimal Encoding]]>$R^{*}(D)$ as well as the optimal excess-distortion exponent. This completes a previous result which showed that $R^{*}(D)$ and the optimal exponent were achievable for distortions below a certain threshold. The proof of the rate-distortion result is based on the second moment method, a popular technique to show that a non-negative random variable $X$ is strictly positive with high probability. In our context, $X$ is the number of code words within target distortion $D$ of the source sequence. We first identify the reason behind the failure of the standard second moment method for certain distortions, and illustrate the different failure modes via a stylized example. We then use a refinement of the second moment method to show that $R^{*}(D)$ is achievable for all distortion values. Finally, the refinement technique is applied to Suen’s correlation inequality to prove the achievability of the optimal Gaussian excess-distortion exponent.]]>63852285243486<![CDATA[Feedback Enhances Simultaneous Wireless Information and Energy Transmission in Multiple Access Channels]]>638524452651350<![CDATA[On the High-SNR Capacity of the Gaussian Interference Channel and New Capacity Bounds]]>$g^{2}=P^{-1/3}$ , where $P$ is the symmetric power constraint and $g$ is the symmetric real cross-channel coefficient. In this paper, we pay attention to the moderate interference regime where $g^{2}\in ~(\max (0.086, P^{-1/3}),1)$ . We propose a new upper-bounding technique that utilizes noisy observation of interfering signals as genie signals and applies time sharing to the genie signals at the receivers. A conditional version of the worst additive noise lemma is also introduced to derive new capacity bounds. The resulting upper (outer) bounds on the sum capacity (capacity region) are shown to be tighter than the existing bounds in a certain range of the moderate interference regime. Using the new upper bounds and the HK lower bound, we show that $R_{\text {sym}}^{*}=\frac {1}{2}\log \big (|g|P+|g|^{-1}(P+1)\big )$ characterizes the capacity of the symmetric real GIC to within 0.104 b/channel use in the moderate interference regime at any signal-to-noise ratio (SNR). We further establish a high-SNR characterization of the symmetric real GIC, where the proposed upper bound is at most 0.1 b far from a certain HK ac-
ievable scheme with Gaussian signalling and time sharing for $g^{2}\in ~(0,1]$ . In particular, $R_{\text {sym}}^{*}$ is achievable at high SNR by the proposed HK scheme and turns out to be the high-SNR capacity at least at $g^{2}=0.25, 0.5$ . We finally point out that there are two subregimes at high SNR in the weak interference regime, where $g^{2}\in (0,1]$ .]]>638526652851164<![CDATA[On the Capacity of Block Multiantenna Channels]]>63852865298263<![CDATA[The Degrees of Freedom of the Interference Channel With a Cognitive Relay Under Delayed Feedback]]>without feedback cannot improve the sum-DoF in the two-user single-input single-output interference channel, delayed feedback in the same scenario can increase the sum-DoF to $4/3$ . For the multiple-input multiple-output case, achievable schemes are obtained via extensions of retrospective interference alignment, leading to the DoF regions that meet the respective upper bounds.]]>638529953131291<![CDATA[Greedy Constructions of Optical Queues With a Limited Number of Recirculations]]>$1\leq k\leq M$ , we seek for an $M$ -sequence ${\mathbf{d}}_{M}=(d_{1},d_{2},\ldots, d_{M})$ of positive integers to maximize the number of consecutive integers (starting from 0) that can be represented by the ${\mathcal{ C}}$ -transform (a generalization of the well-known binary representation) with respect to ${\mathbf{d}}_{M}$ such that there are at most $k$ 1-entries in their ${\mathcal{ C}}$ -transforms. Then, we propose a class of greedy constructions of ${\mathbf{d}}_{M}$ , in which $d_{1},d_{2},\ldots, d_{M}$ are obtained recursively in a greedy man-
er so that the number of representable consecutive integers by using $d_{1},d_{2},\ldots, d_{i}$ is larger than that by using $d_{1},d_{2},\ldots, d_{i-1}$ for all $i$ . Finally, we show that every optimal construction (in the sense of maximizing the number of representable consecutive integers) must be a greedy construction. As a result, the complexity of searching for an optimal construction can be greatly reduced from exponential time to polynomial time by only considering the greedy constructions rather than performing an exhaustive search. The solution of such an integer representation problem can be applied to the constructions of optical 2-to-1 FIFO multiplexers with a limited number of recirculations. Similar results can be obtained for the constructions of optical linear compressors/decompressors with a limited number of recirculations.]]>63853145326504<![CDATA[The Global Packing Number of a Fat-Tree Network]]>global packing number and by presenting explicit algorithms for the construction of optimal, load-balanced routing solutions. Consider an optical network that employs wavelength division multiplexing in which every user node sets up a connection with every other user node. The global packing number is basically the number of wavelengths required by the network to support such a traffic load, under the restriction that each source-to-destination connection is assigned a wavelength that remains constant in the network. In mathematical terms, consider a bidirectional, simple graph, $G$ and let $N\subseteq V(G)$ be a set of nodes. A path system $\mathcal {P}$ of $G$ with respect to $N$ consists of $|N|(|N|-1)$ directed paths, one path to connect each of the source-destination node pairs in $N$ . The global packing number of a path system $\mathcal {P}$ , denoted by $\Phi (G,N,\mathcal {P})$ $k$ to guarantee the existence of a mapping $\phi :\mathcal {P}\to \{1,2,\ldots, k\}$ , such that $\phi (P)\neq \phi (\widehat {P})$ if $P$ and $\widehat {P}$ have common arc(s). The global packing number of $(G,N)$ , denoted by $\Phi (G,N)$ , is defined to be the minimum $\Phi (G,N,\mathcal {P})$ among all possible path systems $\mathcal {P}$ . In additional to wavelength division optical networks, this number also carries significance for networks employing time division multiple access. In this paper, we compute by explicit route construction the global packing number of $(\text {T}_{n},N)$ , where T_{n} denotes the topology of the $n$ -ary fat-tree network, and $N$ is considered to be the set of all edge switches or the set of all supported hosts. We show that the constructed routes are load-balanced and require minimal link capacity at all network links.]]>63853275335706<![CDATA[Constructing Bent Functions Outside the Maiorana–McFarland Class Using a General Form of Rothaus]]>$n/2$ -dimensional subspace. This simplification allows us to treat the induced bent conditions more easily, also implying the possibility to specify the initial functions in the partial spread class and most notably to identify several instances of the so-called non-normal bent functions. Affine inequivalent bent functions within this class are then identified using a suitable selection of initial bent functions within the partial spread class (stemming from the complete Desarguesian spread). It is also shown that when the initial bent functions belong to the class $\mathcal {D}$ , then, under certain conditions, the constructed functions provably do not belong to the completed Maiorana–McFarland class. We conjecture that our method potentially generates an infinite class of non-normal bent functions (all tested ten-variable functions are non-normal but unfortunately they are weakly normal) though there are no efficient computational tools for confirming this.]]>63853365349344<![CDATA[On the Non-Existence of Certain Classes of Perfect $p$ -Ary Sequences and Perfect Almost $p$ -Ary Sequences]]>$p$ -ary sequences with period $n$ (called type $[p, n]$ ). The first case contains a class with type $[p\equiv 5\pmod 8,p^{a}qn']$ . The second case contains five types $[p\equiv 3\pmod 4,p^{a}q^{l}n']$ for certain $p, q$ , and $l$ . Moreover, we also obtain similar non-existence results of perfect almost $p$ -ary sequences.]]>63853505359229<![CDATA[The Cost of Randomness for Converting a Tripartite Quantum State to be Approximately Recoverable]]>$n$ copies of a tripartite state $\rho ^{ABC}$ , and is transformed by a random unitary operation on $A^{n}$ to another state, which is approximately recoverable from its reduced state on $A^{n}B^{n}$ (Case 1) or $B^{n}C^{n}$ (Case 2). We analyze the minimum cost of randomness per copy required for the task in an asymptotic limit of infinite copies and vanishingly small error of recovery, mainly focusing on the case of pure states. We prove that the minimum cost in Case 1 is equal to the Markovianizing cost of the state, for which a single-letter formula is known. With an additional requirement on the convergence speed of the recovery error, we prove that the minimum cost in Case 2 is also equal to the Markovianizing cost. Our results have an application for distributed quantum computation.]]>63853605371365<![CDATA[A Coding Theorem for Bipartite Unitaries in Distributed Quantum Computation]]>$1/n^{4}$ , where $n$ is the number of input pairs. The formula is given by the “Markovianizing cost” of a tripartite state associated with the unitary, which can be computed by a finite-step algorithm. We also derive a lower bound on the minimum cost of resources, which applies for protocols with arbitrary number of rounds.]]>63853725403975<![CDATA[Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and Their Subcodes]]>error correcting pair (ECP), or an error correcting array (ECA) from the single data of an arbitrary generator matrix of a code. An ECP provides a decoding algorithm, that corrects up to $(({d^{*}-1-g})/{2})$ errors, where $d^{*}$ denotes the designed distance and $g$ denotes the genus of the corresponding curve, while with an ECA the decoding algorithm corrects up to $(({d^{*}-1})/{2})$ errors. Roughly speaking, for a public code of length $n$ over $ \mathbb {F}_{q}$ , these attacks run in $O(n^{4}\log (n))$ operations in $\mathbb F_{q}$ for the reconstruction of an ECP and $O(n^{5})$ operations for the reconstruction of an ECA. A probabilistic shortcut allows to reduce the complexities respectively to $O(n^{3+\varepsilon } \log (n))$ and $O(n^{4+\varepsilon })$ . Compared with the previous known attack due to Faure and Minder, our attack is efficient on codes from curves of arbitrary genus. Furthermore, we invest-
gate how far these methods apply to subcodes of AG codes.]]>63854045418639<![CDATA[Physical-Layer Cryptography Through Massive MIMO]]>63854195436849<![CDATA[Comments on and Corrections to “On the Equivalence of Generalized Concatenated Codes and Generalized Error Location Codes”]]>63854375439116<![CDATA[Comments On “Information-Theoretic Key Agreement of Multiple Terminals—Part I”]]>IEEE Transactions on Information Theory, vol. 56, no. 8, pp. 3973-3996, 2010, states an upper bound on the secrecy capacity for the source model problem. It has a three page proof given in Appendix B of the paper. Unfortunately, we show that this bound does not provide any improvement over the simpler bound given in Corollary 1 of the paper. We also provide an example of a family of two agent source model problems where the one-way secrecy rate in each direction is zero, but the secrecy rate is nonzero and can be determined exactly as a conditional mutual information.]]>63854405442126<![CDATA[[Blank page]]]>638B5443B54442<![CDATA[IEEE Transactions on Information Theory information for authors]]>638C3C381