IEEE Transactions on Information Theory

Issue 4 • April 2016

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Displaying Results 1 - 25 of 55
  • Table of contents

    Publication Year: 2016, Page(s):C1 - C4
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  • IEEE Transactions on Information Theory publication information

    Publication Year: 2016, Page(s): C2
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  • Constructions and Decoding of Cyclic Codes Over $b$ -Symbol Read Channels

    Publication Year: 2016, Page(s):1541 - 1551
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (252 KB) | HTML iconHTML

    Symbol-pair read channels, in which the outputs of the read process are pairs of consecutive symbols, were recently studied by Cassuto and Blaum. This new paradigm is motivated by the limitations of the reading process in high density data storage systems. They studied error correction in this new paradigm, specifically, the relationship between the minimum Hamming distance of an error correcting ... View full abstract»

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  • Efficient Search of Girth-Optimal QC-LDPC Codes

    Publication Year: 2016, Page(s):1552 - 1564
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2960 KB) | HTML iconHTML

    In this paper, we study the cycle structure of quasi-cyclic (QC) low-density parity-check (LDPC) codes with the goal of obtaining the shortest code with a given degree distribution and girth. We focus on QC-LDPC codes, whose Tanner graphs are cyclic liftings of fully connected base graphs of size 3 × n, n ≥ 4, and obtain minimal lifting degrees that result in girths 6 and 8. This is ... View full abstract»

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  • Fractional Repetition Codes With Flexible Repair From Combinatorial Designs

    Publication Year: 2016, Page(s):1565 - 1591
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2988 KB) | HTML iconHTML

    Fractional repetition (FR) codes are a class of regenerating codes for distributed storage systems with an exact (table-based) repair process that is also uncoded, i.e., upon failure, a node is regenerated by simply downloading packets from the surviving nodes. In this paper, we present the constructions of FR codes based on Steiner systems and resolvable combinatorial designs, such as affine geom... View full abstract»

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  • Batch Codes Through Dense Graphs Without Short Cycles

    Publication Year: 2016, Page(s):1592 - 1604
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (845 KB) | HTML iconHTML

    Consider a large database of n data items that need to be stored using m servers. We study how to encode information so that a large number k of read requests can be performed in parallel, while the rate remains constant (and ideally approaches one). This problem is equivalent to the design of multiset batch codes introduced by Ishai et al. We give the families of multiset batch codes with asympto... View full abstract»

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  • Some Gabidulin Codes Cannot Be List Decoded Efficiently at any Radius

    Publication Year: 2016, Page(s):1605 - 1615
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (417 KB) | HTML iconHTML

    Gabidulin codes can be seen as the rank-metric equivalent of Reed-Solomon codes. It was recently proved, using subspace polynomials, that Gabidulin codes cannot be list decoded beyond the so-called Johnson radius. In another result, cyclic subspace codes were constructed by inspecting the connection between subspaces and their subspace polynomials. In this paper, these subspace codes are used to p... View full abstract»

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  • Optimal Ferrers Diagram Rank-Metric Codes

    Publication Year: 2016, Page(s):1616 - 1630
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (876 KB) | HTML iconHTML

    Optimal rank-metric codes in Ferrers diagrams are considered. Such codes consist of matrices having zeros at certain fixed positions and can be used to construct good codes in the projective space. First, we consider rank-metric anticodes and prove a code-anticode bound for Ferrers diagram rank-metric codes. The size of optimal linear anticodes is given. Four techniques and constructions of Ferrer... View full abstract»

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  • LP-Decodable Multipermutation Codes

    Publication Year: 2016, Page(s):1631 - 1648
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1386 KB) | HTML iconHTML

    In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are the permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called multipermutation matrices, each of which corresponds to a unique and distinct multipermutation. By enforcing a set of linear constraints on these matrices, we... View full abstract»

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  • On the Capacity of Constrained Permutation Codes for Rank Modulation

    Publication Year: 2016, Page(s):1649 - 1666
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (376 KB) | HTML iconHTML

    Motivated by the rank modulation scheme, a recent study by Sala and Dolecek explored the idea of constraint codes for permutations. The constraint studied by them is inherited by the inter-cell interference phenomenon in flash memories, where high-level cells can inadvertently increase the level of lowlevel cells. A permutation σ ∈ Sn satisfies the single-neighbor k-constr... View full abstract»

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  • Linear Boolean Classification, Coding and the Critical Problem

    Publication Year: 2016, Page(s):1667 - 1673
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (195 KB) | HTML iconHTML

    This paper considers the problem of linear Boolean classification, where the goal is to determine in which set, among two given sets of Boolean vectors, an unknown vector belongs to by making linear queries. Finding the least number of queries is equivalent to determining the minimal rank of a matrix over GF(2), whose kernel does not intersect a given set S. In the case where S is a Hamming ball, ... View full abstract»

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  • Code Construction and Decoding Algorithms for Semi-Quantitative Group Testing With Nonuniform Thresholds

    Publication Year: 2016, Page(s):1674 - 1687
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (703 KB) | HTML iconHTML

    We analyze a new group-testing scheme, termed semi-quantitative group testing, which may be viewed as a concatenation of an adder channel and a discrete quantizer. Our focus is on non-uniform quantizers with arbitrary thresholds. For the most general semi-quantitative group-testing model, we define three new families of sequences capturing the constraints on the code design imposed by the choice o... View full abstract»

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  • Semiconstrained Systems

    Publication Year: 2016, Page(s):1688 - 1702
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (389 KB) | HTML iconHTML

    When transmitting information over a noisy channel, two approaches, dating back to Shannon's work, are common: assuming the channel errors are independent of the transmitted content and devising an error-correcting code or assuming the errors are data dependent and devising a constrained-coding scheme that eliminates all offending data patterns. In this paper, we analyze a middle road, which we ca... View full abstract»

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  • Pseudo-cyclic Codes and the Construction of Quantum MDS Codes

    Publication Year: 2016, Page(s):1703 - 1710
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (211 KB) | HTML iconHTML

    Constacyclic codes which generalize the classical cyclic codes have played important roles in recent constructions of many new quantum maximum distance separable (MDS) codes. However, the mathematical mechanism may not have been fully understood. In this paper, we use pseudo-cyclic codes, which is a further generalization of constacyclic codes, to construct the quantum MDS codes. We can not only p... View full abstract»

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  • A Generalization of Majorization that Characterizes Shannon Entropy

    Publication Year: 2016, Page(s):1711 - 1720
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (351 KB) | HTML iconHTML

    We introduce a binary relation on the finite discrete probability distributions, which generalizes notions of majorization that have been studied in quantum information theory. Motivated by questions in thermodynamics, our relation describes the transitions induced by bistochastic maps in the presence of additional auxiliary systems, which may become correlated in the process. We show that this re... View full abstract»

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  • Completely Reducible Maps in Quantum Information Theory

    Publication Year: 2016, Page(s):1721 - 1732
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (321 KB) | HTML iconHTML

    In order to compute the Schmidt decomposition of A ∈ Mk ⊗ Mm, we must consider an associated self-adjoint map. Here, we show that if A is positive under partial transposition (PPT) or symmetric with positive coefficients (SPCs) or invariant under realignment, then its associated self-adjoint map is completely reducible. We give applications of this fact in quant... View full abstract»

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  • Quantum Channel Capacities With Passive Environment Assistance

    Publication Year: 2016, Page(s):1733 - 1747
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1029 KB) | HTML iconHTML

    We initiate the study of passive environment-assisted communication via a quantum channel, modeled as a unitary interaction between the information carrying system and an environment. In this model, the environment is controlled by a benevolent helper, who can set its initial state such as to assist sender and receiver of the communication link (the case of a malicious environment, also known as j... View full abstract»

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  • Tight Bound on Randomness for Violating the Clauser–Horne–Shimony–Holt Inequality

    Publication Year: 2016, Page(s):1748 - 1757
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (502 KB) | HTML iconHTML

    Free will (or randomness) has been studied to achieve loophole-free Bell's inequality test and to provide device-independent quantum key distribution security proofs. The required randomness such that a local hidden variable model (LHVM) can violate the Clauser-Horne-Shimony-Holt (CHSH) inequality has been studied, but a tight bound has not been proved for a practical case that: 1) the device sett... View full abstract»

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  • The Fidelity of Recovery Is Multiplicative

    Publication Year: 2016, Page(s):1758 - 1763
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (266 KB) | HTML iconHTML

    Fawzi and Renner recently established a lower bound on the conditional quantum mutual information (CQMI) of tripartite quantum states ABC in terms of the fidelity of recovery (FoR), i.e., the maximal fidelity of the state ABC with a state reconstructed from its marginal BC by acting only on the C system. The FoR measures quantum correlations by the local recoverability of global states and has man... View full abstract»

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  • A Source-Channel Separation Theorem With Application to the Source Broadcast Problem

    Publication Year: 2016, Page(s):1764 - 1781
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (757 KB) | HTML iconHTML

    A converse method is developed for the source broadcast problem. Specifically, it is shown that the separation architecture is optimal for a variant of the source broadcast problem, and the associated source-channel separation theorem can be leveraged, via a reduction argument, to establish a necessary condition for the original problem, which unifies several existing results in the literature. So... View full abstract»

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  • Superposition Coding Is Almost Always Optimal for the Poisson Broadcast Channel

    Publication Year: 2016, Page(s):1782 - 1794
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2636 KB) | HTML iconHTML

    This paper shows that the capacity region of the continuous-time Poisson broadcast channel is achieved via superposition coding for most channel parameter values. Interestingly, the channel in some subset of these parameter values does not belong to any of the existing classes of broadcast channels for which superposition coding is optimal (e.g., degraded, less noisy, and more capable). In particu... View full abstract»

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  • Uniform Random Number Generation From Markov Chains: Non-Asymptotic and Asymptotic Analyses

    Publication Year: 2016, Page(s):1795 - 1822
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1023 KB) | HTML iconHTML

    In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on the block length. We also characterize the asymptotic behaviors of the large deviation regime and the moderate deviation regime by using our bounds, which impl... View full abstract»

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  • Rate Region of the Vector Gaussian CEO Problem With the Trace Distortion Constraint

    Publication Year: 2016, Page(s):1823 - 1835
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (332 KB) | HTML iconHTML

    We establish a new extremal inequality, which is further leveraged to give a complete characterization of the rate region of the vector Gaussian CEO problem with the trace distortion constraint. The proof of this extremal inequality hinges on a careful analysis of the Karush-Kuhn-Tucker necessary conditions for the non-convex optimization problem associated with the Berger-Tung scheme, which enabl... View full abstract»

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  • The Likelihood Encoder for Lossy Compression

    Publication Year: 2016, Page(s):1836 - 1849
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (548 KB) | HTML iconHTML

    A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma yields simple achievability proofs for classical source coding problems. The cases of the point-to-point rate-distortion function, the rate-distortion fun... View full abstract»

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  • Cut-Set Bounds on Network Information Flow

    Publication Year: 2016, Page(s):1850 - 1865
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (771 KB) | HTML iconHTML

    Explicit characterization of the capacity region of communication networks is a long-standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general. Characterizing the network coding capacity region requires the determination of the set of all entropic vectors. Furthermore, computing the explicitly known linear prog... 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