IEEE Transactions on Information Theory

Volume 46 Issue 1 • Jan. 2000

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Displaying Results 1 - 25 of 31
  • Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture

    Publication Year: 2000, Page(s):4 - 8
    Cited by:  Papers (61)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (279 KB)

    We prove the long-standing conjecture of Welch stating that for odd n=2m+1, the power function x/sup d/ with d=2/sup m/+3 is maximally nonlinear on GF(2/sup n/) or, in other terms, that the crosscorrelation function between a binary maximum-length linear shift register sequence of degree n and a decimation of that sequence by 2/sup m/+3 takes on precisely the three values -1, -1/spl plusmn/2/sup m... View full abstract»

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  • The geometry of turbo-decoding dynamics

    Publication Year: 2000, Page(s):9 - 23
    Cited by:  Papers (97)  |  Patents (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (502 KB)

    The spectacular performance offered by turbo codes sparked intense interest in them. A considerable amount of research has simplified, formalized, and extended the ideas inherent in the original turbo code construction. Nevertheless, the nature of the relatively simple ad hoc turbo-decoding algorithm has remained something of a mystery. We present a geometric interpretation of the turbo-decoding a... View full abstract»

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  • Improved upper bounds on the ML decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum

    Publication Year: 2000, Page(s):24 - 47
    Cited by:  Papers (55)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (904 KB)

    The ensemble performance of parallel and serial concatenated turbo codes is considered, where the ensemble is generated by a uniform choice of the interleaver and of the component codes taken from the set of time-varying recursive systematic convolutional codes. Following the derivation of the input-output weight enumeration functions of the ensembles of random parallel and serial concatenated tur... View full abstract»

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  • An Assmus-Mattson theorem for Z/sub 4/-codes

    Publication Year: 2000, Page(s):48 - 53
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (344 KB)

    The Assmus-Mattson theorem is a method to find designs in linear codes over a finite field. The purpose of this paper is to give an analog of this theorem for Z/sub 4/-codes by using the harmonic weight enumerator introduced by Bachoc. This theorem can find some 5-designs in the lifted Golay code over Z/sub 4/ which were discovered previously by other methods. View full abstract»

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  • Polynomial invariants of quantum codes

    Publication Year: 2000, Page(s):54 - 59
    Cited by:  Papers (41)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (280 KB)

    The weight enumerators (Shor and Laflamme 1997) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher degree polynomial invariants. We show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one-to-one correspondence with S/... View full abstract»

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  • Generalized minimum distance decoding in Euclidean space: performance analysis

    Publication Year: 2000, Page(s):60 - 83
    Cited by:  Papers (39)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (834 KB)

    We present a detailed analysis of generalized minimum distance (GMD) decoding algorithms for Euclidean space codes. In particular, we completely characterize GMD decoding regions in terms of receiver front-end properties. This characterization is used to show that GMD decoding regions have intricate geometry. We prove that although these decoding regions are polyhedral, they are essentially always... View full abstract»

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  • Nonparametric threshold decision rule, coverings, and some consequences

    Publication Year: 2000, Page(s):84 - 96
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (612 KB)

    Threshold decision is a decision rule for errors and erasures decoding such that the decoder accepts the decoded codeword if its likelihood is larger than a given threshold value. This decision rule involves a parameter that needs to be optimized. We propose a nonparametric version of threshold decision and show that this nonparametric threshold decision allows us to extend some results on decisio... View full abstract»

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  • Improved error exponent for time-invariant and periodically time-variant convolutional codes

    Publication Year: 2000, Page(s):97 - 103
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (301 KB)

    An improved upper bound on the error probability (first error event) of time-invariant convolutional codes, and the resulting error exponent, is derived. The improved error bound depends on both the delay of the code K and its width (the number of symbols that enter the delay line in parallel) b. Determining the error exponent of time-invariant convolutional codes is an open problem. While the pre... View full abstract»

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  • Generalized Reed-Muller codes and power control in OFDM modulation

    Publication Year: 2000, Page(s):104 - 120
    Cited by:  Papers (207)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (585 KB)

    Controlling the peak-to-mean envelope power ratio (PMEPR) of orthogonal frequency-division multiplexed (OFDM) transmissions is a notoriously difficult problem, though one which is of vital importance for the practical application of OFDM in low-cost applications. The utility of Golay complementary sequences in solving this problem has been recognized for some time. In this paper, a powerful theory... View full abstract»

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  • Optimal prefix codes for sources with two-sided geometric distributions

    Publication Year: 2000, Page(s):121 - 135
    Cited by:  Papers (44)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (520 KB)

    A complete characterization of optimal prefix codes for off-centered, two-sided geometric distributions of the integers is presented. These distributions are often encountered in lossless image compression applications, as probabilistic models for image prediction residuals. The family of optimal codes described is an extension of the Golomb codes, which are optimal for one-sided geometric distrib... View full abstract»

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  • Pointwise redundancy in lossy data compression and universal lossy data compression

    Publication Year: 2000, Page(s):136 - 152
    Cited by:  Papers (32)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (648 KB)

    We characterize the achievable pointwise redundancy rates for lossy data compression at a fixed distortion level. "Pointwise redundancy" refers to the difference between the description length achieved by an nth-order block code and the optimal nR(D) bits. For memoryless sources, we show that the best achievable redundancy rate is of order O(/spl radic/n) in probability. This follows from a second... View full abstract»

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  • Trellis-based scalar vector quantization of sources with memory

    Publication Year: 2000, Page(s):153 - 170
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (511 KB)

    The trellis-based scalar-vector quantizer (TB-SVQ) can achieve the rate-distortion performance bound for memoryless sources. This paper extends the scope of this quantizer to coding of sources with memory. First considered is a simple extension, called the predictive TB-SVQ, which applies a closed-loop predictive coding operation in each survivor path of the Viterbi codebook search algorithm. Alth... View full abstract»

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  • Linear multiuser receivers in random environments

    Publication Year: 2000, Page(s):171 - 188
    Cited by:  Papers (92)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (563 KB)

    We study the signal-to-interference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in "random directions." Such a random environment may arise in a DS-CDMA system with random signature sequences, or in a system with antenna diversity where the randomness is due to channel fading. Assuming that such random directions can be tracked by the... View full abstract»

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  • On coding for block fading channels

    Publication Year: 2000, Page(s):189 - 205
    Cited by:  Papers (281)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (566 KB)

    This work considers the achievable performance for coded systems adapted to a multipath block-fading channel model. This is a particularly useful model for analyzing mobile-radio systems which employ techniques such as slow frequency-hopping under stringent time-delay or bandwidth constraints for slowly time-varying channels. In such systems, coded information is transmitted over a small number of... View full abstract»

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  • Stochastically bounded burstiness for communication networks

    Publication Year: 2000, Page(s):206 - 212
    Cited by:  Papers (63)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (285 KB)

    A network calculus is developed for processes whose burstiness is stochastically bounded by general decreasing functions. This calculus is useful for a large class of input processes, including important processes exhibiting "subexponentially bounded burstiness" such as fractional Brownian motion. Moreover, it allows judicious capture of the salient features of real-time traffic, such as the "cell... View full abstract»

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  • Fast and precise Fourier transforms

    Publication Year: 2000, Page(s):213 - 228
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (618 KB)

    Many applications of fast Fourier transforms (FFTs), such as computer tomography, geophysical signal processing, high-resolution imaging radars, and prediction filters, require high-precision output. An error analysis reveals that the usual method of fixed-point computation of FFTs of vectors of length 2/sup l/ leads to an average loss of l/2 bits of precision. This phenomenon, often referred to a... View full abstract»

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  • Coding of sources with two-sided geometric distributions and unknown parameters

    Publication Year: 2000, Page(s):229 - 236
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (427 KB)

    Lossless compression is studied for a countably infinite alphabet source with an unknown, off-centered, two-sided geometric (TSG) distribution, which is a commonly used statistical model for image prediction residuals. We demonstrate that arithmetic coding based on a simple strategy of model adaptation, essentially attains the theoretical lower bound to the universal coding redundancy associated w... View full abstract»

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  • Sequential coding of correlated sources

    Publication Year: 2000, Page(s):236 - 246
    Cited by:  Papers (38)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (506 KB)

    We study a generalization of the successive refinement coding problem called the sequential coding of correlated sources. In successive refinement source coding one first describes the given source using a few bits of information, and then subsequently improves the description of the same source when more information is supplied. Sequential coding differs from successive refinement in that the sec... View full abstract»

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  • Efficient decoding of Reed-Solomon codes beyond half the minimum distance

    Publication Year: 2000, Page(s):246 - 257
    Cited by:  Papers (121)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (565 KB)

    A list decoding algorithm is presented for [n,k] Reed-Solomon (RS) codes over GF(q), which is capable of correcting more than [(n-k)/2] errors. Based on a previous work of Sudan (see J. Compl., vol.13, p.180-93, 1997), an extended key equation (EKE) is derived for RS codes, which reduces to the classical key equation when the number of errors is limited to [(n-k)/2]. Generalizing Massey's (1969) a... View full abstract»

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  • Soft-decision majority decoding of Reed-Muller codes

    Publication Year: 2000, Page(s):258 - 264
    Cited by:  Papers (16)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (438 KB)

    We present a new soft-decision majority decoding algorithm for Reed-Muller codes RM(r,m). First, the reliabilities of 2/sup m/ transmitted symbols are recalculated into the reliabilities of 2/sup m-r/ parity checks that represent each information bit. In turn, information bits are obtained by the weighted majority that gives more weight to more reliable parity checks. It is proven that for long lo... View full abstract»

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  • MDR codes over Z/sub k/

    Publication Year: 2000, Page(s):265 - 269
    Cited by:  Papers (21)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (334 KB)

    In this correspondence, we study maximum distance with respect to rank (MDR) codes over the ring Z/sub k/. We generalize the construction of Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon codes and apply the generalized Chinese remainder theorem to construct codes. View full abstract»

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  • A single asymmetric error-correcting code with 2/sup 13/ codewords of dimension 17

    Publication Year: 2000, Page(s):269 - 271
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (284 KB)

    A new single asymmetric error-correcting code is proposed. This code is constructed using a product of two codes of smaller dimensions. The proposed code is of dimension 17 and of size 8192, i.e., with 2/sup 13/ codewords. The best known code of dimension 17 has size 7968 and capable of handling 12 information bits only. The only other three known cases of single asymmetric codes accommodating one... View full abstract»

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  • Optimal double circulant self-dual codes over F/sub 4/

    Publication Year: 2000, Page(s):271 - 274
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (301 KB)

    Optimal double circulant self-dual codes over F/sub 4/ have been found for each length n/spl les/40. For lengths n/spl les/14, 20, 22, 24, 28, and 30, these codes are optimal self-dual codes. For length 26, the code attains the highest known minimum weight. For n/spl ges/32, the codes presented provide the highest known minimum weights. The [36,18,12] self-dual code improves the lower bound on the... View full abstract»

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  • An improved upper bound on the minimum distance of doubly-even self-dual codes

    Publication Year: 2000, Page(s):274 - 278
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (309 KB)

    We derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives lim/sub n/spl rarr//spl infin// sup d/n/spl les/(5-5/sup 3/4/)/10<0.165630, thus improving on the Mallows-Odlyzko-Sloane bound of 1/6 and our recent bound of 0.166315. View full abstract»

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  • On the nonexistence of completely transitive codes

    Publication Year: 2000, Page(s):279 - 280
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (225 KB)

    Completely transitive codes were introduced by P. Sole (1990) as a special case of binary linear completely regular codes. The existence of such codes is closely related to the existence of certain permutation groups. The nonexistence of highly transitive permutation groups allows us to prove the nonexistence of completely transitive codes with error-correcting capability greater than 4. 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