IEEE Transactions on Information Theory

Volume 43 Issue 6 • Nov. 1997

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Displaying Results 1 - 25 of 37
  • The intractability of computing the minimum distance of a code

    Publication Year: 1997, Page(s):1757 - 1766
    Cited by:  Papers (131)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (388 KB)

    It is shown that the problem of computing the minimum distance of a binary linear code is NP-hard, and the corresponding decision problem is NP-complete. This result constitutes a proof of the conjecture of Berlekamp, McEliece, and van Tilborg (1978). Extensions and applications of this result to other problems in coding theory are discussed. View full abstract»

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  • Averaging bounds for lattices and linear codes

    Publication Year: 1997, Page(s):1767 - 1773
    Cited by:  Papers (160)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (282 KB)

    General random coding theorems for lattices are derived from the Minkowski-Hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out. A new version of the Minkowski-Hlawka theorem itself is obtained as the limit, for p/spl rarr//spl infin/, of a simple lemma for linear codes over GF(p) used with p-level amplitude modulation. The rela... View full abstract»

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  • Asymptotically dense spherical codes. I. Wrapped spherical codes

    Publication Year: 1997, Page(s):1774 - 1785
    Cited by:  Papers (14)  |  Patents (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (538 KB)

    A new class of spherical codes called wrapped spherical codes is constructed by "wrapping" any sphere packing /spl Lambda/ in Euclidean space onto a finite subset of the unit sphere in one higher dimension. The mapping preserves much of the structure of /spl Lambda/, and unlike previously proposed maps, the density of the wrapped spherical codes approaches the density of /spl Lambda/ as the minimu... View full abstract»

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  • Asymptotically dense spherical codes .II. laminated spherical codes

    Publication Year: 1997, Page(s):1786 - 1798
    Cited by:  Papers (26)  |  Patents (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (726 KB)

    For pt. I see ibid., vol.43, no.6, p.1774-85, 1997. New spherical codes called laminated spherical codes are constructed in dimensions 2-49 using a technique similar to the construction of laminated lattices. Each spherical code is recursively constructed from existing spherical codes in one lower dimension. Laminated spherical codes outperform the best known spherical codes in the minimum distanc... View full abstract»

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  • Generalized Bezout's theorem and its applications in coding theory

    Publication Year: 1997, Page(s):1799 - 1810
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (731 KB)

    This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more plane curves. A new approach to determine a lower bound on the minimum distance for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient line... View full abstract»

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  • Parameters of Goppa codes revisited

    Publication Year: 1997, Page(s):1811 - 1819
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (461 KB)

    We discuss parameters of Goppa (1970) codes, such as minimum distance, covering radius, distance distribution, and generalized Hamming weights. By a variation on the exponential sums method and combinatorial arguments, we sharpen known bounds on these parameters. View full abstract»

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  • The Newton radius of codes

    Publication Year: 1997, Page(s):1820 - 1831
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (736 KB)

    For a binary linear code C of minimum distance d, if t>(d-1)/2, then there are errors of weight t which are not uniquely correctable. However, in many cases there are also errors of weight t which are uniquely correctable. The Newton radius of a code is defined to be the largest weight of a uniquely correctable error. Bounds and exact values of the Newton radius are given for several classes of... View full abstract»

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  • On the weight hierarchy of Preparata codes over Z/sub 4/

    Publication Year: 1997, Page(s):1832 - 1842
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (646 KB)

    Hammons et al. (see ibid., vol.40, p.301-19, 1994) showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code over Z/sub 4/, the so called Preparata code over Z/sub 4/. We consider the rth generalized Hamming weight d/sub r/(m) of the Preparata code of length 2/sup m/ over Z/sub 4/. For any m/spl ges/3, d/sub r/(m) is exactly determin... View full abstract»

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  • A class of array codes correcting multiple column erasures

    Publication Year: 1997, Page(s):1843 - 1851
    Cited by:  Papers (9)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (483 KB)

    A family of binary array codes of size (p-1)/spl times/n, with p a prime, correcting multiple column erasures is proposed. The codes coincide with a subclass of shortened Reed-Solomon codes and achieve the maximum possible correcting capability. Complexity of encoding and decoding is proportional to rnp, where r is the number of correctable erasures, i.e., is simpler than the Forney decoding algor... View full abstract»

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  • Systematic proximity-detecting codes

    Publication Year: 1997, Page(s):1852 - 1863
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (489 KB)

    This paper defines t-proximity-detecting (t-PD) codes that can detect when a received word is within distance t from the transmitted codeword, when using a four-phase asynchronous communication protocol (or other similar protocols). Proximity-detecting codes can be used to improve the performance of asynchronous buses. A nontrivial t-proximity-detecting code must be unordered. However, not all uno... View full abstract»

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  • Decoding real-number convolutional codes: change detection, Kalman estimation

    Publication Year: 1997, Page(s):1864 - 1876
    Cited by:  Papers (12)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (394 KB)

    Convolutional codes which employ real-number symbols are difficult to decode because of the size of the alphabet and the numerical and roundoff noise inherent in arithmetic operations. Such codes find applications in both channel coding for communication systems and in fault-tolerance support for signal processing subsystems. A new method for error correction based on optimum mean-square recursive... View full abstract»

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  • Information-theoretic considerations for symmetric, cellular, multiple-access fading channels. I

    Publication Year: 1997, Page(s):1877 - 1894
    Cited by:  Papers (177)  |  Patents (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (649 KB)

    A simple idealized linear (and planar) uplink cellular multiple-access communication model, where only adjacent cell interference is present and all signals may experience fading, is considered. Shannon theoretic arguments are invoked to gain insight into the implications on performance of the main system parameters and multiple-access techniques. We specialize to the linear model and address the ... View full abstract»

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  • Information-theoretic considerations for symmetric, cellular, multiple-access fading channels. II

    Publication Year: 1997, Page(s):1895 - 1911
    Cited by:  Papers (63)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (669 KB)

    For pt.I see ibid., vol.43, no.6, p.1877-94 (1997). A simple idealized linear (and planar) uplink, cellular, multiple-access communication model, where only adjacent cell interference is present and all signals may experience fading is considered. Shannon theoretic arguments are invoked to gain insight into the implications on performance of the main system parameters and multiple-access technique... View full abstract»

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  • Gaussian multiterminal source coding

    Publication Year: 1997, Page(s):1912 - 1923
    Cited by:  Papers (182)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (795 KB)

    In this paper, we consider the problem of separate coding for two correlated memoryless Gaussian sources. We determine the rate-distortion region in the special case when one source provides partial side information to the other source. We also show that the previously obtained inner region of the rate-distortion region is partially tight. A rigorous proof of the direct coding theorem is also give... View full abstract»

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  • A framework for linear information inequalities

    Publication Year: 1997, Page(s):1924 - 1934
    Cited by:  Papers (79)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (501 KB)

    We present a framework for information inequalities, namely, inequalities involving only Shannon's information measures, for discrete random variables. A region in IR(2/sup n/-1), denoted by /spl Gamma/*, is identified to be the origin of all information inequalities involving n random variables in the sense that all such inequalities are partial characterizations of /spl Gamma/*. A product from t... View full abstract»

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  • Reconstruction sequences and equipartition measures: an examination of the asymptotic equipartition property

    Publication Year: 1997, Page(s):1935 - 1947
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (594 KB)

    We consider a stationary source emitting letters from a finite alphabet A. The source is described by a stationary probability measure /spl alpha/ on the space /spl Omega/:=A/sup IN/ of sequences of letters. Denote by /spl Omega//sub n/ the set of words of length n and by /spl alpha//sub n/ the probability measure induced on /spl Omega//sub n/ by /spl alpha/. We consider sequences {/spl Gamma//sub... View full abstract»

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  • Stochastic approximation algorithms for partition function estimation of Gibbs random fields

    Publication Year: 1997, Page(s):1948 - 1965
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1144 KB)

    We present an analysis of previously proposed Monte Carlo algorithms for estimating the partition function of a Gibbs random field. We show that this problem reduces to estimating one or more expectations of suitable functionals of the Gibbs states with respect to properly chosen Gibbs distributions. As expected, the resulting estimators are consistent. Certain generalizations are also provided. W... View full abstract»

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  • On fixed-database universal data compression with limited memory

    Publication Year: 1997, Page(s):1966 - 1976
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (650 KB)

    The amount of fixed side information required for lossless data compression is discussed. Nonasymptotic coding and converse theorems are derived for data-compression algorithms with fixed statistical side information ("training sequence") that is not large enough so as to yield the ultimate compression, namely, the entropy of the source. View full abstract»

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  • Zero-error list capacities of discrete memoryless channels

    Publication Year: 1997, Page(s):1977 - 1982
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (297 KB)

    We define zero-error list capacities for discrete memoryless channels. We find lower bounds to, and a characterization of these capacities. As is usual for such zero-error problems in information theory, the characterization is not generally a single-letter one. Nonetheless, we exhibit a class of channels for which a single letter characterization exists. We also show how the computational cutoff ... View full abstract»

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  • A non-Shannon-type conditional inequality of information quantities

    Publication Year: 1997, Page(s):1982 - 1986
    Cited by:  Papers (81)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (194 KB)

    Given n discrete random variables /spl Omega/={X/sub 1/,...,X/sub n/}, associated with any subset /spl alpha/ of {1,2,...,n}, there is a joint entropy H(X/sub /spl alpha//) where X/sub /spl alpha//={X/sub i/: i/spl isin//spl alpha/}. This can be viewed as a function defined on 2/sup {1,2,...,n}/ taking values in [0, +/spl infin/). We call this function the entropy function of /spl Omega/. The nonn... View full abstract»

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  • Capacity of fading channels with channel side information

    Publication Year: 1997, Page(s):1986 - 1992
    Cited by:  Papers (1294)  |  Patents (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (240 KB)

    We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "water-pouring" in time, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels. Inverting the channel results in a large capacity penalty in severe fading. View full abstract»

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  • Exact performance analysis of linear block codes in frequency-hop spread spectrum communication systems

    Publication Year: 1997, Page(s):1993 - 1999
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (341 KB)

    We present a framework for determining the exact decoder error and failure probabilities for linear block codes in a frequency-hop communication channel with an arbitrary number of conditional symbol error and erasure probabilities. Applications are demonstrated for type-I hybrid ARQ systems by deriving equations for the packet error probability and throughput. Because these quantities are too sma... View full abstract»

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  • Extended sonar sequences

    Publication Year: 1997, Page(s):1999 - 2005
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (241 KB)

    Sonar sequences were introduced by Golomb and Taylor in 1982. We introduce the concept of extended sonar sequences, which is similar to that of sonar sequences except that blank columns are permitted. Several constructions for extended sonar sequences are offered here. Some of these are close to constructions for ordinary sonar sequences, but they provide improvements to the list of best sonar seq... View full abstract»

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  • Use of /spl sigma/-trees as constellations in trellis-coded modulation

    Publication Year: 1997, Page(s):2005 - 2012
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (270 KB)

    Sigma-trees (/spl sigma/-trees) are a class of geometric structures that include lattices as a constrained special case. These structures allow for signal sets, in spaces of arbitrary dimension, that are more spherical in shape than signal sets based on lattices. In this correspondence, it is shown that /spl sigma/-trees can be used in the construction of non-lattice trellis-coded modulation schem... View full abstract»

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  • Sequential decoding of trellis codes at high spectral efficiencies

    Publication Year: 1997, Page(s):2013 - 2019
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (189 KB)

    A probabilistic algorithm is used to construct large constraint length trellis codes at high spectral efficiencies for use with sequential decoding. Linear trellis codes for two- and four-dimensional constellations with constraint lengths up to 19 are obtained. These codes can achieve 180/spl deg/ rotational invariance. To achieve full 90/spl deg/ rotational invariance, nonlinear trellis codes for... 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
Alexander Barg

Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland

email: abarg-ittrans@ece.umd.edu