IEEE Transactions on Information Theory

Volume 38 Issue 3 • May 1992

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Displaying Results 1 - 25 of 33
  • New multilevel codes over GF(q)

    Publication Year: 1992, Page(s):933 - 939
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (748 KB)

    Set partitioning is applied to multidimensional signal spaces over GF(q), i.e., GF/sup n1/(q) (n1<or=q), and it is shown how to construct both multilevel block codes and multilevel trellis codes over GF(q). Multilevel (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d/sub min/>or=d are presented. These codes use Reed-Solomon codes as... View full abstract»

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  • Constructions of binary constant-weight cyclic codes and cyclically permutable codes

    Publication Year: 1992, Page(s):940 - 949
    Cited by:  Papers (114)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1100 KB)

    A general theorem is proved showing how to obtain a constant-weight binary cyclic code from a p-ary linear cyclic code, where p is a prime, by using a representation of GF(p) as cyclic shifts of a binary p-tuple. Based on this theorem, constructions are given for four classes of binary constant-weight codes. The first two classes are shown to achieve the Johnson upper bound on minimum distance asy... View full abstract»

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  • Cyclic concatenated codes with constacyclic outer codes

    Publication Year: 1992, Page(s):950 - 959
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (979 KB)

    The known construction of cyclic concatenated codes is based on the fact that the inner is a cyclic minimal code, the outer code is cyclic, and the lengths of the inner and outer codes are relatively prime. It is shown that if the outer code is a suitably chosen constacyclic code the overall concatenated code is always cyclic regardless of the length of the outer code. Moreover, it follows that an... View full abstract»

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  • Studying the locator polynomials of minimum weight codewords of BCH codes

    Publication Year: 1992, Page(s):960 - 973
    Cited by:  Papers (31)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1048 KB)

    Primitive binary cyclic codes of length n=2/sup m/ are considered. A BCH code with designed distance delta is denoted B(n, delta ). A BCH code is always a narrow-sense BCH code. A codeword is identified with its locator polynomial, whose coefficients are the symmetric functions of the locators. The definition of the code by its zeros-set involves some properties for the power sums of the locators.... View full abstract»

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  • The algebraic decoding of the (41, 21, 9) quadratic residue code

    Publication Year: 1992, Page(s):974 - 986
    Cited by:  Papers (59)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (998 KB)

    A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code, is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadr... View full abstract»

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  • Sequential decoding based on an error criterion

    Publication Year: 1992, Page(s):987 - 1001
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1315 KB)

    An analysis of sequential decoding is presented that is based on the requirement that a set probability error P/sub e/ be achieved. The error criterion implies a bounded tree or trellis search region: the shape of this is calculated for the case of a binary symmetric channel with crossover probability P and random tree codes of rate R. Since the search region is finite at all combinations of p and... View full abstract»

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  • A sequential algorithm for the universal coding of finite memory sources

    Publication Year: 1992, Page(s):1002 - 1014
    Cited by:  Papers (50)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1058 KB)

    The estimation and universal compression of discrete sources are considered, and a sequential algorithm for the universal coding of finite memory sources, attaining asymptotically minimum redundancy, is presented. The algorithm performs an online estimation of the source states and uses an arithmetic code.<<ETX>> View full abstract»

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  • Multiloop sigma-delta quantization

    Publication Year: 1992, Page(s):1015 - 1028
    Cited by:  Papers (37)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1183 KB)

    It is shown that, for a multiloop sigma-delta modulator driven by a DC input, the statistical behavior (described by long-term time averages) of the error process from an inner (multibit) quantizer is consistent with that of a signal-independent. white. uniform noise. The same result also holds for sinusoidal inputs, provided that the modulator has three or more loops. This behavior is exploited t... View full abstract»

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  • On the statistics of the error in predictive coding for stationary Ornstein-Uhlenbeck processes

    Publication Year: 1992, Page(s):1029 - 1040
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1000 KB)

    Explicit expression are derived for the conditional expectation and variance of the encoder in a predictive DPCM coder with an N-level quantizer, when a stationary Ornstein-Uhlenbeck process is a source. A representation of the encoder in terms of a stochastic integral is presented. These expressions yield a nonlinear stochastic difference equation for the decoding error process and a stochastic d... View full abstract»

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  • Maximizing the output energy of a linear channel with a time- and amplitude-limited input

    Publication Year: 1992, Page(s):1041 - 1052
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1051 KB)

    The problem of maximizing the output energy of a linear time-invariant channel, given that the input signal is time and amplitude limited, is considered. It is shown that a necessary condition for an input mu to be optimal, assuming a unity amplitude constraint is that it satisfy the fixed-point equation=sgn (F( mu )), where the functional F is the convolution of mu with the autocorrelation functi... View full abstract»

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  • The role of abstract algebra in structured estimation theory

    Publication Year: 1992, Page(s):1053 - 1065
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1302 KB)

    An attempt is made to formalize both structured covariance estimation and autoregressive process parameter estimation in terms of the underlying abstract Jordan algebra, an algebra that differs from the usual noncommutative but associative matrix algebra. The investigation puts one on a firm footing from which to attack future problems in statistical signal processing, rather in the same manner th... View full abstract»

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  • Optimum distributed detection of weak signals in dependent sensors

    Publication Year: 1992, Page(s):1066 - 1079
    Cited by:  Papers (53)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1307 KB)

    Locally optimum (LO) distributed detection is considered for observations that are dependent from sensor to sensor. The necessary conditions are presented for LO distributed sensor detector designs. and a locally optimum fusion rule for an N-sensor parallel distributed detection system with dependent sensor observations is given. Specific solutions are obtained for a random signal additive noise d... View full abstract»

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  • Two-stage Wilcoxon detectors using conditional tests

    Publication Year: 1992, Page(s):1080 - 1090
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (787 KB)

    The idea of the Wilcoxon detector using a conditional test is extended to two-stage detectors, which constitute a class of sequential detectors. Three different two-stage detectors are considered, using the Wilcoxon statistic with conditional tests. The three detectors differ in the usage of the samples of the first stage for computing the test statistic in the second stage. In computing the test ... View full abstract»

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  • Convergence of filters with applications to the Kalman-Bucy case

    Publication Year: 1992, Page(s):1091 - 1100
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (681 KB)

    For each N, and each fixed time T, a signal X/sup N/ and a 'noisy' observation Y/sup N/ are defined by a pair of stochastic difference equations. Under certain conditions (X/sup N/, Y/sup N/) converges in distribution to (X, Y, where dX(t)=f(t, X(t))dt+dV(t), dY(t)=g(t, X(t))dt+dW(t). Conditions are found under which convergence in distribution of the conditional expectations E(F(X/sup N/) mod Y/s... View full abstract»

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  • 4-phase sequences with near-optimum correlation properties

    Publication Year: 1992, Page(s):1101 - 1113
    Cited by:  Papers (168)  |  Patents (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1067 KB)

    Two families of four-phase sequences are constructed using irreducible polynomials over Z/sub 4/. Family A has period L=2/sup r/-1. size L+2. and maximum nontrivial correlation magnitude C/sub max/<or=1+ square root (L+1), where r is a positive integer. Family B has period L=2(2/sup r/-1). size (L+2)/4. and C/sub max/ for complex-valued sequences. Of particular interest, family A has the same s... View full abstract»

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  • Robustness in neural computation: random graphs and sparsity

    Publication Year: 1992, Page(s):1114 - 1119
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (598 KB)

    An attempt is made to mathematically codify the belief that fully interconnected neural networks continue to function efficiently in the presence of component damage. Component damage is introduced in a fully interconnected neural network model of n neurons by randomly deleting the links between neurons. An analysis of the outer-product algorithm for this random graph model of sparse interconnecti... View full abstract»

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  • Balanced codes and nonequiprobable signaling

    Publication Year: 1992, Page(s):1119 - 1122
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (376 KB)

    The problem of shaping signal constellations that are designed for the Gaussian channel is considered. The signal constellation consists of all points from some translate of a lattice Lambda that lie within a region R. The signal constellation is partitioned into T annular subconstellations Omega /sub o/,..., Omega /sub T-1/, by scaling the region R. Signal points in the same subconstellation are ... View full abstract»

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  • Algebraic decoding of the ternary (13,7,5) quadratic residue code

    Publication Year: 1992, Page(s):1122 - 1125
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (344 KB)

    An algebraic decoding algorithm for the ternary (13,7,5) quadratic residue code is presented. This seems to be the first attempt to provide an algebraic decoding algorithm for a quadratic residue code over a nonbinary field.<<ETX>> View full abstract»

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  • On the generalized Hamming weights of several classes of cyclic cods

    Publication Year: 1992, Page(s):1125 - 1130
    Cited by:  Papers (37)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (591 KB)

    The generalized Hamming weights of a linear code are fundamental code parameters related to the minimal overlap structures of the subcodes. They were introduced by V.K. Wei (1991) and shown to characterize the performance of the linear code in certain cryptographical applications. Results are presented on the generalized Hamming weights of several classes of binary cyclic codes, including primitiv... View full abstract»

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  • The trace operator and redundancy of Goppa codes

    Publication Year: 1992, Page(s):1130 - 1133
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (453 KB)

    The dimension of subfield subcodes and in particular generalized Goppa codes is studied using the kernel of an associated trace map. Bounds on the dimension for a particular general class of binary Goppa codes are obtained. Deeper study of some special cases and other related polynomials yields still tighter bounds for any s>1.<<ETX>> View full abstract»

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  • Generalized Hamming weights of linear codes

    Publication Year: 1992, Page(s):1133 - 1140
    Cited by:  Papers (66)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (621 KB)

    The generalized Hamming weight, d/sub r/(C), of a binary linear code C is the size of the smallest support of any r-dimensional subcode of C. The parameter d/sub r/(C) determines the code's performance on the wire-tap channel of Type II. Bounds on d/sub r/(C), and in some cases exact expressions, are derived. In particular, a generalized Griesmer bound for d/sub r/(C) is presented and examples are... View full abstract»

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  • When are two geometric Goppa codes equal?

    Publication Year: 1992, Page(s):1140 - 1142
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (342 KB)

    Sufficient and necessary conditions are obtained for which the geometric Goppa codes C(D,G) and C(D,H) are equal for two divisors G and H. In particular, it is proven that if G and H are two effective divisors of the same degree smaller than n-1, then C(D,G) and C(D,H) are equal, if and only if G=H.<<ETX>> View full abstract»

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  • Disjoint uniquely decodable codebooks for noiseless synchronized multiple-access adder channels generated by integer sets

    Publication Year: 1992, Page(s):1142 - 1146
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (573 KB)

    Disjoint uniquely decodable codebooks for noiseless synchronized multiple-access adder channels are studied. Codebooks are applicable to multiple access systems in which the number of transmitting users varies over the life of the system. Several designs of codebooks, based on certain integer sets from (0,1,2,3,. . .,2/sup n/-1), are presented. They are restricted to codebooks which have the rate ... View full abstract»

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  • The structure of the I-measure of a Markov chain

    Publication Year: 1992, Page(s):1146 - 1149
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (428 KB)

    The underlying mathematical structure of Shannon's information measures was studied in a paper by R.W. Yeung (1991), and the I-Measure mu *, which is a signed measure defined on a proper sigma -field F, was introduced. The I-Measure is a natural extension of Shannon's information measures and is uniquely defined by them. They also introduced as a consequence the I-Diagram as a geometric tool for v... View full abstract»

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  • Self-reciprocal polynomials and generalized Fermat numbers

    Publication Year: 1992, Page(s):1149 - 1154
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (553 KB)

    Self-reciprocal polynomials (SRPs) over GF(q), where q is a prime power, q=p/sup k/, are investigated. The maximum possible component for these polynomials is found for q odd. The construction of Fermat maximum exponent self-reciprocal polynomials (MRPs) over GF(2) is extended to GF(2/sup k/) with the aid of generalized Fermat numbers. These polynomials leads to a bound on the maximum possible exp... 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