IEEE Transactions on Information Theory

Volume 63 Issue 4 • April 2017

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Displaying Results 1 - 25 of 42
  • Table of contents

    Publication Year: 2017, Page(s):C1 - C4
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  • IEEE Transactions on Information Theory publication information

    Publication Year: 2017, Page(s): C2
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  • Generalized Hamming Weights for Almost Affine Codes

    Publication Year: 2017, Page(s):1941 - 1953
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (265 KB) | HTML iconHTML

    We define generalized Hamming weights for almost affine codes. We show that this definition is natural, since we can extend some well-known properties of the generalized Hamming weights for linear codes, to almost affine codes. In addition, we discuss the duality of almost affine codes, and of the smaller class of multilinear codes. View full abstract»

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  • Efficiently Decoding Reed–Muller Codes From Random Errors

    Publication Year: 2017, Page(s):1954 - 1960
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (387 KB) | HTML iconHTML

    Reed-Muller (RM) codes encode an m-variate polynomial of degree at most r by evaluating it on all points in {0,1}m. We denote this code by RM(r,m). The minimum distance of RM(r,m) is 2m-rand so it cannot correct more than half that number of errors in the worst case. For random errors one may hope for a better result. In this paper we give an efficient algorithm (in the block... View full abstract»

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  • Deletion Codes in the High-Noise and High-Rate Regimes

    Publication Year: 2017, Page(s):1961 - 1970
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (217 KB) | HTML iconHTML

    The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst case deletions, with a focus on constructing efficiently decodable codes for the two extreme regimes of high-noise and high-rate. Specifically, we construct polynomial-time decodable cod... View full abstract»

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  • Codes Correcting a Burst of Deletions or Insertions

    Publication Year: 2017, Page(s):1971 - 1985
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (281 KB) | HTML iconHTML

    This paper studies codes that correct a burst of deletions or insertions. Namely, a code will be called a b-burst-deletion/insertion-correcting code if it can correct a burst of deletions/insertions of any b consecutive bits. While the lower bound on the redundancy of such codes was shown by Levenshtein to be asymptotically log(n) + b - 1, the redundancy of the best code construction by Cheng et a... View full abstract»

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  • Relaxed Polar Codes

    Publication Year: 2017, Page(s):1986 - 2000
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1278 KB) | HTML iconHTML

    Polar codes are the latest breakthrough in coding theory, as they are the first family of codes with explicit construction that provably achieve the symmetric capacity of binary-input discrete memoryless channels. Polar encoding and successive cancellation decoding have the complexities of N log N , for code length N. Although, the complexity bound of N log N is asymptotically favorable, we report... View full abstract»

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  • Explicit Constructions of High-Rate MDS Array Codes With Optimal Repair Bandwidth

    Publication Year: 2017, Page(s):2001 - 2014
    Cited by:  Papers (33)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (277 KB) | HTML iconHTML

    Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure tolerance for a given number of parity nodes. Suppose that an MDS code with k information nodes and r = n - k parity nodes is used to encode data in a distributed storage system. It is known that if h out of the n nodes are inaccessible and d surviving (helper) nodes are use... View full abstract»

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  • Constructions of High-Rate Minimum Storage Regenerating Codes Over Small Fields

    Publication Year: 2017, Page(s):2015 - 2038
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (766 KB) | HTML iconHTML

    A novel technique for construction of minimum storage regenerating (MSR) codes is presented. Based on this technique, three explicit constructions of MSR codes are given. The first two constructions provide access-optimal MSR codes, with two and three parities, respectively, which attain the sub-packetization bound for access-optimal codes. The third construction provides longer MSR codes with thr... View full abstract»

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  • Construction and Encoding of QC-LDPC Codes Using Group Rings

    Publication Year: 2017, Page(s):2039 - 2060
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1902 KB) | HTML iconHTML

    Quasi-cyclic (QC) low-density parity-check (LDPC) codes which are known as QC-LDPC codes, have many applications due to their simple encoding implementation by the means of cyclic shift registers. In this paper, we construct QC-LDPC codes from group rings. A group ring is a free module (at the same time a ring) constructed in a natural way from any given ring and any given group. We present a stru... View full abstract»

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  • Switch Codes: Codes for Fully Parallel Reconstruction

    Publication Year: 2017, Page(s):2061 - 2075
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB) | HTML iconHTML

    Network switches and routers scale in rate by distributing the packet read/write operations across multiple memory banks. Rate scaling is achieved so long as sufficiently many packets can be written and read in parallel. However, due to the non-determinism of the read process, parallel pending read requests may contend on memory banks, and thus significantly lower the switching rate. In this paper... View full abstract»

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  • Blind Index Coding

    Publication Year: 2017, Page(s):2076 - 2097
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1091 KB) | HTML iconHTML

    We introduce the blind index coding (BIC) problem, in which a single sender communicates distinct messages to multiple users over a shared channel. Each user has partial knowledge of each message as side information. However, unlike classical index coding, in BIC, the sender is uncertain of what side information is available to each user. In particular, the sender only knows the amount of bits in ... View full abstract»

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  • Lattice Index Codes From Algebraic Number Fields

    Publication Year: 2017, Page(s):2098 - 2112
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1195 KB) | HTML iconHTML

    Broadcasting K independent messages to multiple users where each user demands all the messages and already has a subset of the messages as side information is studied. Recently, Natarajan et al. proposed a novel broadcasting strategy called lattice index coding, which adopts lattices constructed over some principal ideal domains (PID) for transmission. Using the structure of lattices over PID, the... View full abstract»

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  • Efficient Algorithms for Noisy Group Testing

    Publication Year: 2017, Page(s):2113 - 2136
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2972 KB) | HTML iconHTML

    Group-testing refers to the problem of identifying (with high probability) a (small) subset of D defectives from a (large) set of N items via a “small” number of “pooled” tests (i.e., tests that have a positive outcome if at least one of the items being tested in the pool is defective, else have a negative outcome). For ease of presentation in this paper, we focus on the regime when D = O(N1-... View full abstract»

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  • Optimal Shrinkage of Singular Values

    Publication Year: 2017, Page(s):2137 - 2152
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (983 KB) | HTML iconHTML

    We consider the recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values. We adopt an asymptotic framework, in which the matrix size is much larger than the rank of the signal matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. For a variety o... View full abstract»

    Open Access
  • Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices

    Publication Year: 2017, Page(s):2153 - 2170
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (396 KB) | HTML iconHTML

    Data, which lie in the space Pm, of m × m symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications, including medical imaging, computer vision, and radar signal processing. An open challenge, for these applications, is to find a class of probability distributions, which is able to capture the statistical properties of data in Pm<... View full abstract»

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  • Recipes for Stable Linear Embeddings From Hilbert Spaces to $ {\mathbb {R}}^{m}$

    Publication Year: 2017, Page(s):2171 - 2187
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (612 KB) | HTML iconHTML

    We consider the problem of constructing a linear map from a Hilbert space H (possibly infinite dimensional) to ℝmthat satisfies a restricted isometry property (RIP) on an arbitrary signal model, i.e., a subset of H. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove th... View full abstract»

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  • On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Mobile Sensor

    Publication Year: 2017, Page(s):2188 - 2200
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (532 KB) | HTML iconHTML

    Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and addresses some aspects of a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations? In a field (signal) sampling setup, unknown sampling locations, sample quantization, unknown bandwidth of the field, and presence of measurement-noise presen... View full abstract»

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  • Adversarial Top- $K$ Ranking

    Publication Year: 2017, Page(s):2201 - 2225
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (989 KB) | HTML iconHTML

    We study the top-K ranking problem where the goal is to recover the set of top-K ranked items out of a large collection of items based on partially revealed preferences. We consider an adversarial crowdsourced setting where there are two population sets, and pairwise comparison samples drawn from one of the populations follow the standard Bradley-Terry-Luce model (i.e., the chance of item i beatin... View full abstract»

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  • A Class of Weiss–Weinstein Bounds and Its Relationship With the Bobrovsky–Mayer-Wolf–Zakaï Bounds

    Publication Year: 2017, Page(s):2226 - 2240
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (490 KB) | HTML iconHTML

    A fairly general class of Bayesian “large-error” lower bounds of the Weiss-Weinstein family, essentially free from regularity conditions on the probability density functions support, and for which a limiting form yields a generalized Bayesian Cramér-Rao bound (BCRB), is introduced. In a large number of cases, the generalized BCRB appears to be the Bobrovsky-Mayer-Wolf-Zakai bound (BMZB). Interesti... View full abstract»

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  • The $\rho $ -Capacity of a Graph

    Publication Year: 2017, Page(s):2241 - 2253
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (368 KB) | HTML iconHTML

    Motivated by the problem of zero-error broadcasting, we introduce a new notion of graph capacity, termed ρ-capacity, that generalizes the Shannon capacity of a graph. We derive upper and lower bounds on the p-capacity of arbitrary graphs, and provide a Lovász-type upper bound for regular graphs. We study the behavior of the ρ-capacity under two graph operations: the strong product and the disjoint... View full abstract»

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  • Improving on the Cut-Set Bound via Geometric Analysis of Typical Sets

    Publication Year: 2017, Page(s):2254 - 2277
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (918 KB) | HTML iconHTML

    We consider the discrete memoryless symmetric primitive relay channel, where, a source X wants to send information to a destination Y with the help of a relay Z and the relay can communicate to the destination via an error-free digital link of rate R0, while Y and Z are conditionally independent and identically distributed given X. We develop two new upper bounds on the capacity of this... View full abstract»

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  • The Log-Volume of Optimal Codes for Memoryless Channels, Asymptotically Within a Few Nats

    Publication Year: 2017, Page(s):2278 - 2313
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1364 KB) | HTML iconHTML

    Shannon's analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume M*avg(n, ∈) of length-n codes subject to an average decoding error probability ∈ is shown to satisfy the following tight asymptotic lower and upper bounds as n → ∞: A∈+ o(1) ≤ log M*avg(n, ∈) - [nC - √n... View full abstract»

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  • Information-Theoretic Lower Bounds for Distributed Function Computation

    Publication Year: 2017, Page(s):2314 - 2337
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1094 KB) | HTML iconHTML

    We derive information-theoretic converses (i.e., lower bounds) for the minimum time required by any algorithm for distributed function computation over a network of point-to-point channels with finite capacity, where each node of the network initially has a random observation and aims to compute a common function of all observations to a given accuracy with a given confidence by exchanging message... View full abstract»

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  • On the Capacity of Generalized Ising Channels

    Publication Year: 2017, Page(s):2338 - 2356
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1496 KB) | HTML iconHTML

    Nearly tight lower and upper bounds on the capacity of generalized Ising channels are presented. For the case where feedback is allowed, a closed-form expression for the capacity is found for channel error probability p ∈ [0, p0], where p0 ≈ 0.398324. A near-capacity-achieving family of encoders is presented for the values p ∈ [0, p0]. Two lower bounds on that capacity for larger values of p are p... View full abstract»

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Aims & Scope

IEEE Transactions on Information Theory publishes papers concerned with the transmission, processing, and utilization of information.

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Meet Our Editors

Editor-in-Chief
Alexander Barg

Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland

email: abarg-ittrans@ece.umd.edu