IEEE Transactions on Information Theory

Volume 47 Issue 7 • Nov. 2001

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Displaying Results 1 - 25 of 44
  • Claude E. Shannon: a retrospective on his life, work, and impact

    Publication Year: 2001, Page(s):2681 - 2695
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (354 KB) | HTML iconHTML

    Claude E. Shannon (1948) invented information theory and provided the concepts, insights, and mathematical formulations that now form the basis for modern communication technology. In a surprisingly large number of ways, he enabled the information age. A major part of this influence comes from his two-part monumental 1948 paper, "A Mathematical Theory of Communication." We attempt here to provide ... View full abstract»

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  • Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes

    Publication Year: 2001, Page(s):2696 - 2710
    Cited by:  Papers (106)  |  Patents (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (556 KB) | HTML iconHTML

    We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error p... View full abstract»

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  • Low-density parity-check codes based on finite geometries: a rediscovery and new results

    Publication Year: 2001, Page(s):2711 - 2736
    Cited by:  Papers (769)  |  Patents (62)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (958 KB) | HTML iconHTML

    This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, rangi... View full abstract»

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  • Combinatorial analysis of the minimum distance of turbo codes

    Publication Year: 2001, Page(s):2737 - 2750
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (519 KB) | HTML iconHTML

    In this paper, new upper bounds on the maximum attainable minimum Hamming distance of turbo codes with arbitrary-including the best-interleavers are established using a combinatorial approach. These upper bounds depend on the interleaver length, the code rate, and the scramblers employed in the encoder. Examples of the new bounds for particular turbo codes are given and discussed. The new bounds a... View full abstract»

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  • On the algebraic structure of quasi-cyclic codes .I. Finite fields

    Publication Year: 2001, Page(s):2751 - 2760
    Cited by:  Papers (109)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (419 KB) | HTML iconHTML

    A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese remainder theorem (CRT), or of the discrete Fourier transform (DFT), that ring can be decomposed into a direct product of fields. That ring decomposition in turn yields a code construction from codes of lower len... View full abstract»

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  • Space-time autocoding

    Publication Year: 2001, Page(s):2761 - 2781
    Cited by:  Papers (59)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (709 KB) | HTML iconHTML

    Prior treatments of space-time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval-in which case there is a nonzero "outage capacity"-or multiple fading intervals-in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In sh... View full abstract»

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  • Asymptotical analysis and comparison of two coded modulation schemes using PSK signaling .I

    Publication Year: 2001, Page(s):2782 - 2792
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (408 KB) | HTML iconHTML

    An asymptotical analysis and comparison of two coded modulation systems using phase-shift keying (PSK) signaling with the transmission taking place over the additive white Gaussian noise (AWGN) channel is provided. In this paper, bounds for the decoding error probability of conventional coded modulation are derived. Both block and trellis coding are considered. The state-complexity error exponent ... View full abstract»

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  • Asymptotical analysis and comparison of two coded modulation schemes using PSK signaling .II

    Publication Year: 2001, Page(s):2793 - 2806
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (545 KB) | HTML iconHTML

    For pt.I see ibid., vol.47, no.7, p.2782-92 (2001). In this paper we analyze a multilevel coded modulation system using phase-shift keying (PSK) signaling and transmitting over the additive white Gaussian noise (AWGN) channel. We reduce the analysis of the overall system to the analysis of each decoding level, considering them as a set of related channels. The concept of a "genie-aided communicati... View full abstract»

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  • Lower bounds on the linear complexity of the discrete logarithm in finite fields

    Publication Year: 2001, Page(s):2807 - 2811
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (297 KB) | HTML iconHTML

    Let p be a prime, r a positive integer, q=p/sup r/, and d a divisor of p(q-1). We derive lower bounds on the linear complexity over the residue class ring Z/sub d/ of a (q-periodic) sequence representing the residues modulo d of the discrete logarithm in F/sub q/. Moreover, we investigate a sequence over F/sub q/ representing the values of a certain polynomial over F/sub q/ introduced by Mullen an... View full abstract»

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  • The piling-up approximation in linear cryptanalysis

    Publication Year: 2001, Page(s):2812 - 2823
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (478 KB) | HTML iconHTML

    One of the key identities in linear cryptanalysis is the piling-up lemma, which allows one to compute the probability distribution of a sum modulo 2 of binary random variables, when the probability that these are zero is known. However, the lemma holds only for independent random variables. In linear cryptanalysis, one often (mis)uses this identity without knowing whether the random variables are ... View full abstract»

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  • An information-theoretic approach for design and analysis of rooted-tree-based multicast key management schemes

    Publication Year: 2001, Page(s):2824 - 2834
    Cited by:  Papers (34)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (340 KB) | HTML iconHTML

    Previous literature presents several seemingly different approaches to rooted-tree-based multicast key distribution schemes that try to minimize the user key storage while providing efficient member deletion. In this paper, we show that the user key storage on rooted trees can be systematically studied using basic concepts from information theory. We show that the rooted-tree-based multicast key d... View full abstract»

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  • Efficient metering schemes with pricing

    Publication Year: 2001, Page(s):2835 - 2844
    Cited by:  Papers (3)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (404 KB) | HTML iconHTML

    In order to decide on advertisement fees for Web servers, Naor and Pinkas (see Proc. Advances in Cryptology-EUROCRYPT'98 (Lecture Notes in Computer Science). New York: Springer-Verlag, vol.1403, p.576-590, 1998) introduced metering schemes. They proposed metering schemes in which any server is able to compute a proof to be sent to an audit agency if and only if it has been visited by at least a ce... View full abstract»

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  • Uncertainty principles and ideal atomic decomposition

    Publication Year: 2001, Page(s):2845 - 2862
    Cited by:  Papers (882)  |  Patents (30)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (624 KB) | HTML iconHTML

    Suppose a discrete-time signal S(t), 0/spl les/t<N, is a superposition of atoms taken from a combined time-frequency dictionary made of spike sequences 1/sub {t=/spl tau/}/ and sinusoids exp{2/spl pi/iwt/N}//spl radic/N. Can one recover, from knowledge of S alone, the precise collection of atoms going to make up S? Because every discrete-time signal can be represented as a superposition of spik... View full abstract»

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  • Local linear regression estimation under long-range dependence: strong consistency and rates

    Publication Year: 2001, Page(s):2863 - 2875
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (627 KB) | HTML iconHTML

    We consider the nonparametric estimation of multivariate regression functions and their derivatives for a regression model with long-range dependent errors. We adopt a local linear fitting approach and establish strong consistency and rates for the estimators of the regression function and its derivatives. The rates of convergence depend on the amount of smoothing relative to the strength of the l... View full abstract»

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  • On inverse problems with unknown operators

    Publication Year: 2001, Page(s):2876 - 2894
    Cited by:  Papers (31)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (765 KB) | HTML iconHTML

    Consider a problem of recovery of a smooth function (signal, image) f/spl isin//spl Fscr//spl isin/L/sub 2/([0, 1]/sup d/) passed through an unknown filter and then contaminated by a noise. A typical model discussed in the paper is described by a stochastic differential equation dY/sub f//sup /spl epsi//(t)=(Hf)(t)dt+/spl epsi/dW(t), t/spl isin/[0, 1]/sup d/, /spl epsi/>0 where H is a linear op... View full abstract»

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  • Estimating a function from ergodic samples with additive noise

    Publication Year: 2001, Page(s):2895 - 2902
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (376 KB) | HTML iconHTML

    We study the problem of estimating an unknown function from ergodic samples corrupted by additive noise. It is shown that one can consistently recover an unknown measurable function in this setting, if the one-dimensional (1-D) distribution of the samples is comparable to a known reference distribution, and the noise is independent of the samples and has known mixing rates. The estimates are appli... View full abstract»

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  • Thresholding method for dimensionality reduction in recognition systems

    Publication Year: 2001, Page(s):2903 - 2920
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (643 KB) | HTML iconHTML

    Often recognition systems must be designed with a relatively small amount of training data. Plug-in test statistics suffer from large estimation errors, often causing the performance to degrade as the measurement vector dimension increases. Choosing a better test statistic or applying a method of dimensionality reduction are two possible solutions to this problem. In this paper, we consider a reco... View full abstract»

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  • A semidefinite program for distillable entanglement

    Publication Year: 2001, Page(s):2921 - 2933
    Cited by:  Papers (151)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (490 KB) | HTML iconHTML

    We show that the maximum fidelity obtained by a positive partial transpose (p.p.t.) distillation protocol is given by the solution to a certain semidefinite program. This gives a number of new lower and upper bounds on p.p.t. distillable entanglement (and thus new upper bounds on 2-locally distillable entanglement). In the presence of symmetry, the semidefinite program simplifies considerably, bec... View full abstract»

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  • Almost difference sets and their sequences with optimal autocorrelation

    Publication Year: 2001, Page(s):2934 - 2943
    Cited by:  Papers (105)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (440 KB) | HTML iconHTML

    Almost difference sets have interesting applications in cryptography and coding theory. We give a well-rounded treatment of known families of almost difference sets, establish relations between some difference sets and some almost difference sets, and determine the numerical multiplier group of some families of almost difference sets. We also construct six new classes of almost difference sets, an... View full abstract»

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  • Inequalities between entropy and index of coincidence derived from information diagrams

    Publication Year: 2001, Page(s):2944 - 2960
    Cited by:  Papers (34)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (641 KB) | HTML iconHTML

    To any discrete probability distribution P we can associate its entropy H(P)=-/spl Sigma/p/sub i/ ln p/sub i/ and its index of coincidence IC(P)=/spl Sigma/p/sub i//sup 2/. The main result of the paper is the determination of the precise range of the map P/spl rarr/(IC(P), H(P)). The range looks much like that of the map P/spl rarr/(P/sub max/, H(P)) where P/sub max/ is the maximal point probabili... View full abstract»

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  • On optimal permutation codes

    Publication Year: 2001, Page(s):2961 - 2971
    Cited by:  Papers (17)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (424 KB) | HTML iconHTML

    Permutation codes are vector quantizers whose codewords are related by permutations and, in one variant, sign changes. Asymptotically, as the vector dimension grows, optimal Variant I permutation code design is identical to optimal entropy-constrained scalar quantizer (ECSQ) design. However, contradicting intuition and previously published assertions, there are finite block length permutation code... View full abstract»

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  • On the support of MSE-optimal, fixed-rate, scalar quantizers

    Publication Year: 2001, Page(s):2972 - 2982
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (446 KB) | HTML iconHTML

    This paper determines how the support regions of optimal and asymptotically optimal fixed-rate scalar quantizers (with respect to mean-squared error) depend on the number of quantization points N and the probability density of the variable being quantized. It shows that for asymptotic optimality it is necessary and sufficient that the support region grow fast enough that the outer (or overload) di... View full abstract»

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  • Exact spectral evaluation of the family of digital pulse interval modulated signals

    Publication Year: 2001, Page(s):2983 - 2992
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (413 KB) | HTML iconHTML

    This paper presents a closed-form spectral evaluation of the family of digital pulse interval modulation (DPIM) schemes, where the information is contained in the relative distance between successive pulses. The framework for spectral evaluation is that of stationary symbol sequences derived from variable-length word sequences, which considers the issue of stationarization, a preliminary task to s... View full abstract»

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  • The iterative turbo decoding algorithm has fixed points

    Publication Year: 2001, Page(s):2993 - 2995
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (259 KB) | HTML iconHTML

    It is shown that the iterative decoding algorithm proposed to decode "turbo codes" has fixed points regardless of the specific constituent codes and regardless of the noise variance of the additive white Gaussian noise (AWGN) channel. View full abstract»

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  • A Vandermonde code construction

    Publication Year: 2001, Page(s):2995 - 2998
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (293 KB) | HTML iconHTML

    We use a Vandermonde matrix to construct a code of length mn from m codes of length n. A distance estimate for the construction is given. When the starting codes are suitable constacyclic codes, the constructed code is cyclic and from this we obtain new cyclic codes. The results generalize those of Hughes (see ibid., vol.46, p.674-80, 2000) on the u+/spl upsi/|u-/spl upsi/ construction. 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.

Full Aims & Scope

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