IEEE Transactions on Information Theory

Issue 5 • May 2015

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Displaying Results 1 - 25 of 46
  • Table of contents

    Publication Year: 2015, Page(s):C1 - C4
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  • IEEE Transactions on Information Theory publication information

    Publication Year: 2015, Page(s): C2
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  • List Decoding of Polar Codes

    Publication Year: 2015, Page(s):2213 - 2226
    Cited by:  Papers (99)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1015 KB) | HTML iconHTML

    We describe a successive-cancellation list decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Arıkan. In the proposed list decoder, L decoding paths are considered concurrently at each decoding stage, where L is an integer parameter. At the end of the decoding process, the most likely among the L paths is selected as the single codeword at t... View full abstract»

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  • Binary Polarization Kernels From Code Decompositions

    Publication Year: 2015, Page(s):2227 - 2239
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1095 KB) | HTML iconHTML

    In this paper, code decompositions (a.k.a. code nestings) are used to design binary polarization kernels. The proposed kernels are in general nonlinear. They provide a better polarization exponent than the previously known kernels of the same dimensions. In particular, nonlinear kernels of dimensions 14, 15, and 16 are constructed and are shown to have optimal asymptotic error-correction performan... View full abstract»

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  • Impact of Redundant Checks on the LP Decoding Thresholds of LDPC Codes

    Publication Year: 2015, Page(s):2240 - 2255
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (463 KB) | HTML iconHTML

    Feldman et al. [11] asked whether the performance of the linear programming (LP) decoder can be improved by adding redundant parity checks to tighten the LP relaxation. We prove in this paper that for low-density parity-check codes, even if we include all redundant parity checks, asymptotically there is no gain in the LP decoder threshold on the binary symmetric channel under certain conditions on... View full abstract»

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  • Correcting Grain-Errors in Magnetic Media

    Publication Year: 2015, Page(s):2256 - 2272
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (828 KB) | HTML iconHTML

    This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can co... View full abstract»

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  • Construction A of Lattices Over Number Fields and Block Fading (Wiretap) Coding

    Publication Year: 2015, Page(s):2273 - 2282
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (343 KB) | HTML iconHTML

    We propose a lattice construction from totally real and complex multiplication fields, which naturally generalizes Construction A of lattices from p-ary codes obtained from the cyclotomic field Q(ζp), p a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield Q(ζp View full abstract»

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  • On the Algebraic Structure of Linear Tail-Biting Trellises

    Publication Year: 2015, Page(s):2283 - 2299
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (907 KB) | HTML iconHTML

    Tail-biting trellises are important graphical representations of codes, which can be simpler to decode than conventional trellises. While conventional trellises are well understood, the general theory of (tail-biting) trellises is still under development. In this paper we first develop a new algebraic framework for a systematic analysis of linear trellises which enables us to address open foundati... View full abstract»

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  • A Characterization of the Number of Subsequences Obtained via the Deletion Channel

    Publication Year: 2015, Page(s):2300 - 2312
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (904 KB) | HTML iconHTML

    Motivated by the study of deletion channels, this paper presents improved bounds on the number of subsequences obtained from a binary string X of length n under t deletions. It is known that the number of subsequences in this setting strongly depends on the number of runs in the string X; where a run is a maximal substring of the same character. Our improved bounds are obtained by a structural ana... View full abstract»

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  • Generalized Sphere Packing Bound

    Publication Year: 2015, Page(s):2313 - 2334
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (2023 KB) | HTML iconHTML

    Kulkarni and Kiyavash recently introduced a new method to establish upper bounds on the size of deletion-correcting codes. This method is based upon tools from hypergraph theory. The deletion channel is represented by a hypergraph whose edges are the deletion balls (or spheres), so that a deletion-correcting code becomes a matching in this hypergraph. Consequently, a bound on the size of such a co... View full abstract»

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  • Elias Bound for General Distances and Stable Sets in Edge-Weighted Graphs

    Publication Year: 2015, Page(s):2335 - 2350
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (494 KB) | HTML iconHTML

    This paper presents an extension of the Elias bound on the minimum distance of codes for discrete alphabets with general, possibly infinite valued, distances. The bound is obtained by combining a previous extension of the Elias bound, introduced by Blahut, with an extension of a bound previously introduced by the author which builds upon ideas of Gallager, Lovász, and Marton. The result ca... View full abstract»

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  • The Bose and Minimum Distance of a Class of BCH Codes

    Publication Year: 2015, Page(s):2351 - 2356
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (521 KB) | HTML iconHTML

    Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms. Bose-Ray-Chaudhuri-Hocquenghem (BCH) codes form a subclass of cyclic codes and are very important in both theory and practice as they have good error-correcting capability and are widely used in communication systems, storage devices, and consumer electronics. However, the dimension and m... View full abstract»

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  • Common Subexpression Algorithms for Space-Complexity Reduction of Gaussian Normal Basis Multiplication

    Publication Year: 2015, Page(s):2357 - 2369
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (991 KB) | HTML iconHTML

    The use of normal bases for representing elements in a binary field is attractive in some applications because it is easy to perform squaring operations in hardware. In such cases, the costs of implementing the multiplication operation become a primary concern. We present new algorithms for reducing the space complexity of Gaussian normal basis multipliers over binary fields GF(2m), whe... View full abstract»

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  • Faster Algorithms for Multivariate Interpolation With Multiplicities and Simultaneous Polynomial Approximations

    Publication Year: 2015, Page(s):2370 - 2387
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (852 KB) | HTML iconHTML

    The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This problem has been extended to three or more variables; for this generalization, all fast algorithms proposed so far rely on the lattice approach. In this paper, we red... View full abstract»

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  • Randomness and Dependencies Extraction via Polarization, With Applications to Slepian–Wolf Coding and Secrecy

    Publication Year: 2015, Page(s):2388 - 2398
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (257 KB) | HTML iconHTML

    The polarization phenomenon for a single source is extended to a framework with multiple correlated sources. It is shown in addition to extracting the randomness of the source, the polar transforms take the original arbitrary dependencies to extremal dependencies. Polar coding schemes for the Slepian-Wolf (SW) coding problem and for secret key generations are then proposed based on this phenomenon... View full abstract»

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  • Abelian Group Codes for Channel Coding and Source Coding

    Publication Year: 2015, Page(s):2399 - 2414
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (321 KB) | HTML iconHTML

    In this paper, we study the asymptotic performance of Abelian group codes for the channel coding problem for arbitrary discrete (finite alphabet) memoryless channels as well as the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources. For the channel coding problem, we find the capacity characterized in a single-letter information-theoretic form. This simplifies ... View full abstract»

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  • Channels With Cost Constraints: Strong Converse and Dispersion

    Publication Year: 2015, Page(s):2415 - 2429
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (337 KB) | HTML iconHTML

    This paper shows the strong converse and the dispersion of memoryless channels with cost constraints and performs a refined analysis of the third-order term in the asymptotic expansion of the maximum achievable channel coding rate, showing that it is equal to (1/2)((log n)/n) in most cases of interest. The analysis is based on a nonasymptotic converse bound expressed in terms of the distribution o... View full abstract»

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  • The Third-Order Term in the Normal Approximation for the AWGN Channel

    Publication Year: 2015, Page(s):2430 - 2438
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (407 KB) | HTML iconHTML

    This paper shows that, under the average error probability formalism, the third-order term in the normal approximation for the additive white Gaussian noise channel with a maximal or equal power constraint is at least (1/2) log n + O(1). This improves on the lower bound by Polyanskiy-Poor-Verdú (2010) and matches the upper bound proved by the same authors. View full abstract»

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  • A Case Where Interference Does Not Affect the Channel Dispersion

    Publication Year: 2015, Page(s):2439 - 2453
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (469 KB) | HTML iconHTML

    In 1975, Carleial presented a special case of an interference channel, called the very strong interference regime, in which the interference does not reduce the capacity of the constituent point-to-point Gaussian channels. In this paper, we show that in the strictly very strong interference regime, the dispersions are similarly unaffected. More precisely, in this paper, we characterize the second-... View full abstract»

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  • Statistical Physics of Random Binning

    Publication Year: 2015, Page(s):2454 - 2464
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (432 KB) | HTML iconHTML

    We consider the model of random binning and finite-temperature decoding for Slepian-Wolf codes, from a statistical-mechanical perspective. While ordinary random channel coding is intimately related to the random energy model-a statistical-mechanical model of disordered magnetic materials, it turns out that random binning (for Slepian-Wolf coding) is analogous to another, related statistical-mechan... View full abstract»

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  • Broadcasting Correlated Vector Gaussians

    Publication Year: 2015, Page(s):2465 - 2477
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (623 KB) | HTML iconHTML

    The problem of sending two correlated vector Gaussian sources over a bandwidth-matched two-user scalar Gaussian broadcast channel is studied in this paper, where each receiver wishes to reconstruct its target source under a covariance distortion constraint. We derive a lower bound on the optimal tradeoff between the transmit power and the achievable reconstruction distortion pair. Our derivation i... View full abstract»

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  • An Equivalence Between Network Coding and Index Coding

    Publication Year: 2015, Page(s):2478 - 2487
    Cited by:  Papers (26)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (465 KB) | HTML iconHTML

    We show that the network coding and index coding problems are equivalent. This equivalence holds in the general setting which includes linear and nonlinear codes. Specifically, we present a reduction that maps a network coding instance to an index coding instance while preserving feasibility, i.e., the network coding instance has a feasible solution if and only if the corresponding index coding in... View full abstract»

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  • Achievable Rate Regions for Network Coding

    Publication Year: 2015, Page(s):2488 - 2509
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (950 KB) | HTML iconHTML

    Determining the achievable rate region for networks using routing, linear coding, or nonlinear coding is thought to be a difficult task in general, and few are known. We describe the achievable rate regions for four interesting networks (completely for three and partially for the fourth). In addition to the known matrix-computation method for proving outer bounds for linear coding, we present a ne... View full abstract»

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  • Characteristic-Dependent Linear Rank Inequalities With Applications to Network Coding

    Publication Year: 2015, Page(s):2510 - 2530
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (518 KB) | HTML iconHTML

    Two characteristic-dependent linear rank inequalities are given for eight variables. In particular, the first inequality holds for all finite fields whose characteristic is not three and does not in general hold over characteristic three. The second inequality holds for all finite fields whose characteristic is three and does not in general hold over characteristics other than three. Applications ... View full abstract»

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  • Secure Compute-and-Forward in a Bidirectional Relay

    Publication Year: 2015, Page(s):2531 - 2556
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1591 KB) | HTML iconHTML

    We consider the basic bidirectional relaying problem, in which two users in a wireless network wish to exchange messages through an intermediate relay node. In the compute-and-forward strategy, the relay computes a function of the two messages using the naturally occurring sum of symbols simultaneously transmitted by user nodes in a Gaussian multiple-access channel (MAC), and the computed function... 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
Prakash Narayan 

Department of Electrical and Computer Engineering