IEEE Transactions on Information Theory

Volume 45 Issue 2 • March 1999

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Displaying Results 1 - 25 of 45
  • New upper bounds on error exponents

    Publication Year: 1999, Page(s):385 - 398
    Cited by:  Papers (39)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (682 KB)

    We derive new upper bounds on the error exponents for the maximum-likelihood decoding and error detecting in the binary symmetric channels. This is an improvement on the best earlier known bounds by Shannon-Gallager-Berlekamp (1967) and McEliece-Omura (1977). For the probability of undetected error the new bounds are better than the bounds by Levenshtein (1978, 1989) and the bound by Abdel-Ghaffar... View full abstract»

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  • Good error-correcting codes based on very sparse matrices

    Publication Year: 1999, Page(s):399 - 431
    Cited by:  Papers (2130)  |  Patents (243)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (1431 KB)

    We study two families of error-correcting codes defined in terms of very sparse matrices. "MN" (MacKay-Neal (1995)) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The decoding of both codes can be tackled with a practical sum-product algorithm. We prove that these codes are "very ... View full abstract»

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  • List decoding of algebraic-geometric codes

    Publication Year: 1999, Page(s):432 - 437
    Cited by:  Papers (30)  |  Patents (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (310 KB)

    We generalize Sudan's (see J. Compl., vol.13, p.180-93, 1997) results for Reed-Solomon codes to the class of algebraic-geometric codes, designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error-correction bound (d-1)/2, d being the minimum distance of the code. Our main algorithm is based on an interpolation scheme and factorization of polyn... View full abstract»

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  • Binomial moments of the distance distribution: bounds and applications

    Publication Year: 1999, Page(s):438 - 452
    Cited by:  Papers (25)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (741 KB)

    We study a combinatorial invariant of codes which counts the number of ordered pairs of codewords in all subcodes of restricted support in a code. This invariant can be expressed as a linear form of the components of the distance distribution of the code with binomial numbers as coefficients. For this reason we call it a binomial moment of the distance distribution. Binomial moments appear in the ... View full abstract»

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  • Cyclotomy and duadic codes of prime lengths

    Publication Year: 1999, Page(s):453 - 466
    Cited by:  Papers (20)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (613 KB)

    We present a cyclotomic approach to the construction of all binary duadic codes of prime lengths. We calculate the number of all binary duadic codes for a given prime length and that of all duadic codes that are not quadratic residue codes. We give necessary and sufficient conditions for p such that all binary duadic codes of length p are quadratic residue (QR) codes. We also show how to determine... View full abstract»

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  • Generalized cyclotomic codes of length p/sub 1//sup e(1)/...p/sub t//sup e(t)/

    Publication Year: 1999, Page(s):467 - 474
    Cited by:  Papers (23)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (449 KB)

    We first introduce a generalized cyclotomy of order 2 with respect to p/sub 1//sup e(1)/...p/sub t//sup e(t)/. We then present two classes of new error-correcting binary cyclic codes of length p/sub 1//sup e(1)/...p/sub t//sup e(t)/ based on this generalized cyclotomy. We prove either a square-root bound or a similar bound on the minimum odd weight of those codes with length n=p/sub 1//sup e(1)/ p... View full abstract»

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  • New families of almost perfect nonlinear power mappings

    Publication Year: 1999, Page(s):475 - 485
    Cited by:  Papers (44)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (595 KB)

    A power mapping f(x)=x/sup d/ over GF(p/sup n/) is said to be differentially k-uniform if k is the maximum number of solutions x/spl isin/GF(p/sup n/) of f(x+a)-f(x)=b where a, b/spl isin/GF(p/sup n/) and a/spl ne/0. A 2-uniform mapping is called almost perfect nonlinear (APN). We construct several new infinite families of nonbinary APN power mappings. View full abstract»

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  • Correlation attacks on up/down and stop/go cascades

    Publication Year: 1999, Page(s):486 - 498
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (542 KB)

    A probabilistic analysis is conducted to determine conditional and unconditional correlation weaknesses of cascades of up/down clocked shift registers. Similar results are also obtained for cascades of stop/go clocked shift registers. It is theoretically explained how to use the derived properties for fast correlation attacks, whose objective is to recover the linear feedback shift-register initia... View full abstract»

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  • Unconditionally secure key agreement and the intrinsic conditional information

    Publication Year: 1999, Page(s):499 - 514
    Cited by:  Papers (117)  |  Patents (16)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (776 KB)

    This paper is concerned with secret-key agreement by public discussion. Assume that two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X, Y, and Z, respectively, with joint distribution P/sub XYZ/. The secret-key rate S(X;Y/spl par/Z) has been defined as the maximal rate at which Alice and Bob can generate a secret key by communication over a... View full abstract»

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  • Hadamard-based soft decoding for vector quantization over noisy channels

    Publication Year: 1999, Page(s):515 - 532
    Cited by:  Papers (40)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (848 KB)

    We present an estimator-based, or soft, vector quantizer decoder for communication over a noisy channel. The decoder is optimal according to the mean-square error criterion, and Hadamard-based in the sense that a Hadamard transform representation of the vector quantizer is utilized in the implementation of the decoder. An efficient algorithm for optimal decoding is derived. We furthermore investig... View full abstract»

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  • High-resolution source coding for non-difference distortion measures: the rate-distortion function

    Publication Year: 1999, Page(s):533 - 547
    Cited by:  Papers (16)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (944 KB)

    The problem of asymptotic (i,e., low-distortion) behavior of the rate-distortion function of a random vector is investigated for a class of non-difference distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference distortion measures. For example, for an input-weighted squared error distortion measure d(x,y)=/spl par/W(x)(y-x)/... View full abstract»

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  • High-resolution source coding for non-difference distortion measures: multidimensional companding

    Publication Year: 1999, Page(s):548 - 561
    Cited by:  Papers (38)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (731 KB)

    Entropy-coded vector quantization is studied using high-resolution multidimensional companding over a class of nondifference distortion measures. For distortion measures which are "locally quadratic" a rigorous derivation of the asymptotic distortion and entropy-coded rate of multidimensional companders is given along with conditions for the optimal choice of the compressor function. This optimum ... View full abstract»

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  • An information criterion for likelihood selection

    Publication Year: 1999, Page(s):562 - 571
    Cited by:  Papers (8)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (476 KB)

    For a given source distribution, we establish properties of the conditional density achieving the rate distortion function lower bound as the distortion parameter varies. In the limit as the distortion tolerated goes to zero, the conditional density achieving the rate distortion function lower bound becomes degenerate in the sense that the channel it defines becomes error-free. As the permitted di... View full abstract»

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  • Asymptotic optimality of likelihood ratio threshold tests in decentralized detection

    Publication Year: 1999, Page(s):572 - 585
    Cited by:  Papers (5)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (741 KB)

    Two distributed systems are considered for discriminating between two finite-alphabet bivariate memoryless sources and for detecting a known signal in stationary bivariate additive Gaussian noise. Each system comprises two sensors, M-ary local quantizers and a fusion center which makes decisions based on quantized source observations. The problem of asymptotically optimal quantization is considere... View full abstract»

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  • Variable-rate trellis source encoding

    Publication Year: 1999, Page(s):586 - 608
    Cited by:  Papers (25)  |  Patents (23)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (1418 KB)

    The fixed slope lossy algorithm derived from the kth-order adaptive arithmetic codeword length function is extended to finite-state decoders or trellis-structured decoders. When this algorithm is used to encode a stationary, ergodic source with a continuous alphabet, the Lagrangian performance converges with probability one to a quantity computable as the infimum of an information-theoretic functi... View full abstract»

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  • On symmetrical multilevel diversity coding

    Publication Year: 1999, Page(s):609 - 621
    Cited by:  Papers (55)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (919 KB)

    Symmetrical multilevel diversity coding with independent data streams has been studied by Roche et al. (1992), and the admissible coding rate region was determined for the case of three levels. In particular, it was shown that coding by superposition is optimal, which means that optimality can be achieved by very simple coding. However, it is very difficult to generalize their proof to an arbitrar... View full abstract»

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  • Spectral efficiency of CDMA with random spreading

    Publication Year: 1999, Page(s):622 - 640
    Cited by:  Papers (618)  |  Patents (6)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (696 KB)

    The CDMA channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods. Furthermore, its analysis provides a comparison baseline for CDMA channels with deterministic signature waveforms spanning one symbol period. We analyze the spectral efficiency (total capacity per chip) as a function of the number of user... View full abstract»

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  • Linear multiuser receivers: effective interference, effective bandwidth and user capacity

    Publication Year: 1999, Page(s):641 - 657
    Cited by:  Papers (644)  |  Patents (4)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (629 KB)

    Multiuser receivers improve the performance of spread-spectrum and antenna-array systems by exploiting the structure of the multiaccess interference when demodulating the signal of a user. Much of the previous work on the performance analysis of multiuser receivers has focused on their ability to reject worst case interference. Their performance in a power-controlled network and the resulting user... View full abstract»

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  • Active distances for convolutional codes

    Publication Year: 1999, Page(s):658 - 669
    Cited by:  Papers (37)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (516 KB)

    A family of active distance measures for general convolutional codes is defined. These distances are generalizations of the extended distances introduced by Thommesen and Justesen (1983) for unit memory convolutional codes. It is shown that the error correcting capability of a convolutional code is determined by the active distances. The ensemble of periodically time-varying convolutional codes is... View full abstract»

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  • Universal bound on the performance of lattice codes

    Publication Year: 1999, Page(s):670 - 681
    Cited by:  Papers (52)  |  Patents (7)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (496 KB)

    We present a lower bound on the probability of symbol error for maximum-likelihood decoding of lattices and lattice codes on a Gaussian channel. The bound is tight for error probabilities and signal-to-noise ratios of practical interest, as opposed to most existing bounds that become tight asymptotically for high signal-to-noise ratios. The bound is also universal; it provides a limit on the highe... View full abstract»

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  • Improved rates and asymptotic normality for nonparametric neural network estimators

    Publication Year: 1999, Page(s):682 - 691
    Cited by:  Papers (29)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (572 KB)

    We obtain an improved approximation rate (in Sobolev norm) of r/sup -1/2-/spl alpha//(d+1)/ for a large class of single hidden layer feedforward artificial neural networks (ANN) with r hidden units and possibly nonsigmoid activation functions when the target function satisfies certain smoothness conditions. Here, d is the dimension of the domain of the target function, and /spl alpha//spl isin/(0,... View full abstract»

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  • Binary sequences with two-level autocorrelation

    Publication Year: 1999, Page(s):692 - 693
    Cited by:  Papers (9)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (99 KB)

    We derive the values of the Fourier spectrum, a decomposition, and an achievable upper bound on the linear span, for binary sequences with two-level autocorrelation. View full abstract»

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  • Linear complexity of de Bruijn sequences-old and new results

    Publication Year: 1999, Page(s):693 - 698
    Cited by:  Papers (12)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (301 KB)

    The linear complexity of a de Bruijn sequence is the degree of the shortest linear recursion which generates the sequence. It is well known that the complexity of a binary de Bruijn sequence of length 2/sup n/ is bounded below by 2/sup n-1/+n and above by 2/sup n-/1 for n/spl ges/3. We briefly survey the known knowledge in this area. Some new results are also presented, in particular, it is shown ... View full abstract»

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  • Every binary (2/sup m/-2, 2/sup 2(m)-2-m/, 3) code can be lengthened to form a perfect code of length 2/sup m/-1

    Publication Year: 1999, Page(s):698 - 700
    Cited by:  Papers (6)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (163 KB)

    We answer a problem posed by Etzion and Vardy (1998) by showing that a binary code of length N=2(m)-2 with 2(N-m) codewords and minimum distance three can always be lengthened to form a perfect code of length 2(m-1). View full abstract»

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  • All Reed-Muller codes are linearly representable over the ring of dual numbers over Z/sub 2/

    Publication Year: 1999, Page(s):700 - 701
    Cited by:  Papers (4)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (114 KB)

    The statement given in the title is proved. Linear codes over chain rings (commutative and noncommutative) are a natural generalization of linear codes over finite fields and of linear codes over integer residue class rings of prime power order. In matters of linear representability there is no obvious reason why we should prefer one chain ring to the other. Yet, apart from Z/sub 4/, there is one ... 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