IEEE Transactions on Information Theory

Volume 19 Issue 5 • September 1973

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Displaying Results 1 - 25 of 35
  • Goppa codes

    Publication Year: 1973, Page(s):590 - 592
    Cited by:  Papers (43)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (403 KB)

    Goppa described a new class of linear noncyclic error-correcting codes in [1] and [2]. This paper is a summary of Goppa's work, which is not yet available in English.<tex>^1</tex>We prove the four most important properties of Goppa codes. 1) There exist<tex>q</tex>-ary Goppa codes with lengths and redundancies comparable to BCH codes. For the same redundancy, the Goppa code... View full abstract»

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  • On the error matrix in optimal linear filtering of stationary processes

    Publication Year: 1973, Page(s):593 - 599
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (799 KB)

    The error covariance matrix corresponding to optimal linear causal filtering of second-order stationary processes in additive noise is considered. Formulas expressing this error matrix in terms of the optimal transfer function are established, and in the nonsingular case the optimal transfer function is expressed in terms of the spectral densities. These are straightforward generalizations of prev... View full abstract»

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  • A representation theorem and its applications to spherically-invariant random processes

    Publication Year: 1973, Page(s):600 - 608
    Cited by:  Papers (159)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1469 KB)

    The<tex>n</tex>th-order characteristic functions (cf) of spherically-invariant random processes (sirp) with zero means are defined as cf, which are functions of<tex>n</tex>th-order quadratic forms of arbitrary positive definite matrices<tex>p</tex>. Every<tex>n</tex>th-order spherically-invariant characteristic function (sicf) is represented as a wei... View full abstract»

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  • Optimum processing for delay-vector estimation in passive signal arrays

    Publication Year: 1973, Page(s):608 - 614
    Cited by:  Papers (149)  |  Patents (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (906 KB)

    For the purpose of localizing a distant noisy target, or, conversely, calibrating a receiving array, the time delays defined by the propagation across the array of the target-generated signal wavefronts are estimated in the presence of sensor-to-sensor-independent array self-noise. The Cramér-Rao matrix bound for the vector delay estimate is derived, and used to show that either properly filtered ... View full abstract»

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  • Short-time spectral and autocorrelation analysis in the Walsh domain

    Publication Year: 1973, Page(s):615 - 623
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1238 KB)

    A short-time dyadic autocorrelation function (dacf) and a short-time Walsh energy spectrum of the first kind are defined in the Walsh-Fourier domain. The "natural" choice of the short-time functions does not lead to a Walsh-Fourier transform pair (dyadic Wiener-Khintchine theorem), and thus a second kind of short-time dacf and short-time Walsh energy spectrum are defined as the Walsh-Fourier trans... View full abstract»

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  • Detection of a PSK signal transmitted through a hard-limited channel

    Publication Year: 1973, Page(s):623 - 630
    Cited by:  Papers (42)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1130 KB)

    This paper considers the problem of the detection of a binary phase-modulated carrier which has been transmitted along with noise through a hard-limiting repeater, corrupted by additional noise, and demodulated by cross correlation and sampling at the receiver. Three equivalent expressions are obtained for the error probability of the receiver output. Two of these expressions take the form of an i... View full abstract»

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  • Sequential estimation with a finite statistic

    Publication Year: 1973, Page(s):631 - 635
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (782 KB)

    A procedure is given for optimizing the sequential estimation of a random variable in the mean-square sense, with the constraint that the data must be summarized by a finite-valued statistic. This finite-valued statistic can be considered to be the memory of the processor. The estimate is constrained to be a function of the contents of the memory and the time of the estimate. An example is given t... View full abstract»

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  • Estimating a binomial parameter with finite memory

    Publication Year: 1973, Page(s):636 - 643
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1147 KB)

    This article treats the asymptotic theory of estimating a binomial parameter<tex>p</tex>with time-invariant finite memory. The approach taken to this problem is as follows. A decision rule is a pair<tex>(t,a)</tex>in which<tex>t</tex>fixes the transition function of a finite automaton, and<tex>a</tex>is a vector of estimates of<tex>p</tex>... View full abstract»

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  • Testing a simple symmetric hypothesis by a finite-memory deterministic algorithm

    Publication Year: 1973, Page(s):644 - 647
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (472 KB)

    A class of finite-memory deterministic algorithms is introduced and investigated. Optimum algorithms are found for small numbers (up to 21) of states. The algorithms provide their own stopping rules. View full abstract»

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  • Simple nonstatistical television compression system

    Publication Year: 1973, Page(s):648 - 652
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1007 KB)

    A television system is proposed which sends a succession of high-bandwidth and low-bandwidth pictures over a channel. If flicker is avoided, the eye judges picture quality from successive presentations of the pictures by taking an average. It appears that an exchange can be effected between the power in the high-frequency components and the actual duration of these components. Using only successiv... View full abstract»

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  • Sample-whitened matched filters

    Publication Year: 1973, Page(s):653 - 660
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1110 KB)

    A sample-whitened matched filter (SWMF) for a channel with intersymbol interference and additive white Gaussian noise is defined as a linear filter with the properties that its output samples are a sufficient statistic for the MAP estimation of the transmitted sequence and have uncorrelated noise components. These filters are shown to exist for ali realistic channels and the complete set of SWMF's... View full abstract»

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  • On general Gilbert bounds

    Publication Year: 1973, Page(s):661 - 666
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (718 KB)

    We define a distance measure for block codes used over memoryless channels and show that it is related to upper and lower bounds on the low-rate error probability in the same way as Hamming distance is for binary block codes used over the binary symmetric channel. We then prove general Gilbert bounds for block codes using this distance measure. Some new relationships between coding theory and rate... View full abstract»

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  • Augmentation techniques for a class of product codes

    Publication Year: 1973, Page(s):666 - 672
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1203 KB)

    A class of product codes for which an augmented syndrome can be defined is studied. By using this augmented syndrome, we are able to add new codewords to a product code while keeping the minimum distance fixed. In many cases the resulting code is as good as any known code. Decoders that may be simpler to implement than existing decoders are described for these augmented codes. It is also seen that... View full abstract»

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  • Dual product codes for correction of multiple low-density burst errors

    Publication Year: 1973, Page(s):672 - 677
    Cited by:  Papers (5)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (818 KB)

    In many communication channels noise disturbances occur in the form of low-density bursts. Codes capable of correcting multiple bursts of low density are efficient tools of error control for such channels. One such class of codes is presented ia this paper. This Class of codes can be decoded by simple majority logic. The approach is to use codes which are the duals of product codes whose component... View full abstract»

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  • On majority-logic-decodable arithmetic codes

    Publication Year: 1973, Page(s):678 - 682
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (711 KB)

    A new class of cyclic multiple-error-correcting arithmetic codes is described, and the minimum distance of these codes is determined analytically. A two-step majority-logic decoding scheme is developed for these arithmetic codes. The new class of codes is extended to a new class of arithmetic codes having a primitive cyclotomic factor as the generator and an<tex>L</tex>-step majority-l... View full abstract»

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  • Addresses for graphs

    Publication Year: 1973, Page(s):683 - 688
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (957 KB)

    The problem of labeling the vertices of an undirected, connected graph with binary<tex>n</tex>-tuple addresses is considered. These addresses are to have the property that if two vertices are a distance<tex>k</tex>apart in the graph then the Hamming distance between the corresponding addresses must be<tex>kd</tex>where<tex>d</tex>is a positive intege... View full abstract»

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  • Maximum-entropy distributions having prescribed first and second moments (Corresp.)

    Publication Year: 1973, Page(s):689 - 693
    Cited by:  Papers (51)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (744 KB)

    The entropy<tex>H</tex>of an absolutely continuous distribution with probability density function<tex>p(x)</tex>is defined as<tex>H = - \int p(x) \log p(x) dx</tex>. The formal maximization of<tex>H</tex>, subject to the moment constraints<tex>\int x^r p(x) dx = \mu_r, r = 0,1,\cdots,m</tex>, leads to<tex>p(x) = \exp (- \sum_{r=0}^m... View full abstract»

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  • Factorization of discrete-process spectral matrices (Corresp.)

    Publication Year: 1973, Page(s):693 - 696
    Cited by:  Papers (13)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (579 KB)

    In this correspondence, we consider factoring the spectral matrix of discrete-time systems. The factoring involves finding a matrix<tex>H(z)</tex>such that<tex>H(z^{-1})H^T (z)</tex>equals the spectral matrix and that both<tex>H(z)</tex>and<tex>H^{-1} (z)</tex>are stable and nonanticipatory. The purpose of this paper is to present a new method for ob... View full abstract»

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  • Convergence of the edited nearest neighbor (Corresp.)

    Publication Year: 1973, Page(s):696 - 697
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (307 KB)

    The edited<tex>k</tex>nearest neighbor rule (<tex>k</tex>-NNR) consists of 1) eliminating those samples from the data which are not classified correctly by the<tex>k</tex>-NNR and the remainder of the data, and 2) using the NNR with the samples which remain from 1) to classify new observations. Wilson has shown that this rule has an asymptotic probability of err... View full abstract»

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  • The nearest-neighbor rule for small samples drawn from uniform distributions (Corresp.)

    Publication Year: 1973, Page(s):697 - 699
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (546 KB)

    It is shown in the classification problem, when independent samples are taken from uniform distributions, that for small sample sizes the probability of misclassification when using the nearest-neighbor rule is "close" to its asymptotic value. It is also shown that when using this rule the probability of classification in many cases is close to its Bayes optimum even for small sample sizes. Moreov... View full abstract»

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  • An estimate of the upper bound on error probability for maximum-likelihood sequence estimation on channels having a finite-duration pulse response (Corresp.)

    Publication Year: 1973, Page(s):699 - 702
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (615 KB)

    An estimate of an upper bound on performance in terms of probability of error is developed for maximum-likelihood sequence estimation over channels for which only the pulse response energy and duration are known. This bound is evaluated for channels with a pulse response duration up to 10 signaling intervals, and the related minimum-distance channel codes are presented. View full abstract»

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  • On the expected duration of a search for a fixed pattern in random data (Corresp.)

    Publication Year: 1973, Page(s):702 - 704
    Cited by:  Papers (51)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (482 KB)

    An expression is obtained for the expected duration of a search to find a given<tex>L</tex>-ary sequence in a semi-infinite stream of random<tex>L</tex>-ary data. The search time is found to be an increasing function of the lengths of the "bifices" of the pattern, where the term bifix denotes a sequence which is both a prefix and a suffix. View full abstract»

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  • A note on bifix-free sequences (Corresp.)

    Publication Year: 1973, Page(s):704 - 706
    Cited by:  Papers (25)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (442 KB)

    A bifix of an<tex>L</tex>-ary<tex>n</tex>-tuple is a sequence which is both a prefix and a suffix of that<tex>n</tex>-tuple. The practical importance of bifix-free patterns is emphasized, and we devise a systematic way of generating all such sequences and determine their number. View full abstract»

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  • Bounds on rate-distortion functions for stationary sources and context-dependent fidelity criteria (Corresp.)

    Publication Year: 1973, Page(s):706 - 708
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (419 KB)

    A class of lower bounds to rate-distortion functions of stationary sources with context-dependent fidelity criteria is derived by mapping the source and distortion measure into an equivalent restricted-transition stationary source with a single-letter fidelity criterion, and then applying the composite bound. This approach is seen to yield bounds which, although sometimes quite loose, apply to gen... View full abstract»

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  • An upper bound on the speed of convergence of the Blahut algorithm for computing rate-distortion functions (Corresp.)

    Publication Year: 1973, Page(s):708 - 709
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (233 KB)

    An upper bound on the speed of convergence of Blahut algorithm is derived. This bound is inversely proportional to the number of iterations. View full abstract»

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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