IEEE Transactions on Information Theory

Volume 18 Issue 3 • May 1972

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Displaying Results 1 - 25 of 37
  • Lower and upper bounds on the optimal filtering error of certain diffusion processes

    Publication Year: 1972, Page(s):325 - 331
    Cited by:  Papers (33)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (839 KB)

    The optimal nonlinear filtering of certain vector-valued diffusion processes embedded in white noise is considered. We derive upper and lower bounds on the minimal causal mean-square error. The derivation of the lower bound is based on information-theoretic considerations, namely the rate-distortion function (<tex>\varepsilon</tex>-entropy). The upper bounds are based on linear-filteri... View full abstract»

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  • Limiting of signals in random noise

    Publication Year: 1972, Page(s):332 - 340
    Cited by:  Papers (25)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1178 KB)

    The effect of ideal bandpass limiting on a signal lying in narrowband Gaussian noise is analyzed. General analytic expressions for the limiter output components are derived using an integral representation for the limiter characteristic. This method allows retention of the phases of all the signals and the intermodulation products at the limiter output, which are destroyed in the characteristic-fu... View full abstract»

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  • Some relations among RKHS norms, Fredholm equations, and innovations representations

    Publication Year: 1972, Page(s):341 - 348
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1099 KB)

    We first show how reproducing kernel Hilbert space (RKHS) norms can be determined for a large class of covariance functions by methods based on the solution of a Riccati differential equation or a Wiener-Hopf integral equation. Efficient numerical algorithms for such equations have been extensively studied, especially in the control literature. The innovations representations enter in that it is t... View full abstract»

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  • A new look at the Barankin lower bound

    Publication Year: 1972, Page(s):349 - 356
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1025 KB)

    This paper is primarily tutorial in nature and presents an alternative derivation of the Barankin estimator. The approach presented here places clearly in evidence the significance of the choice of parameter points that one must make in obtaining a Barankin lower bound. Specifically, for any finite set of parameter points, the corresponding Barankin bound is the variance of the locally best estima... View full abstract»

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  • An upper bound on the probability of error due to intersymbol interference for correlated digital signals

    Publication Year: 1972, Page(s):356 - 363
    Cited by:  Papers (59)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1022 KB)

    An upper bound on the probability of error due to intersymbol interference in a baseband digital communication system for both correlated and uncorrelated digital signals is derived. Examples of the bound are presented for common data communication systems, and in the uncorrelated case, comparison is made with other published results. The bound is computationally simple to apply and in most cases ... View full abstract»

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  • Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference

    Publication Year: 1972, Page(s):363 - 378
    Cited by:  Papers (1716)  |  Patents (250)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2476 KB)

    A maximum-likelihood sequence estimator for a digital pulse-amplitude-modulated sequence in the presence of finite intersymbol interference and white Gaussian noise is developed, The structure comprises a sampled linear filter, called a whitened matched filter, and a recursive nonlinear processor, called the Viterbi algorithm. The outputs of the whitened matched filter, sampled once for each input... View full abstract»

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  • Rate-distortion theory for context-dependent fidelity criteria

    Publication Year: 1972, Page(s):378 - 384
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (962 KB)

    A lower bound<tex>R_L (D)</tex>is obtained to the rate-distortion function<tex>R(D)</tex>of a finite-alphabet stationary source with respect to a context-dependent fidelity criterion. For equiprobable memoryless sources and modular distortion measures,<tex>R(D) = R_L (D)</tex>for all<tex>D</tex>. It is conjectured that, for a broad class of finite-al... View full abstract»

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  • Coding of sources with unknown statistics--I: Probability of encoding error

    Publication Year: 1972, Page(s):384 - 389
    Cited by:  Papers (23)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (759 KB)

    It is well known that it is often possible to obtain considerable data compression by encoding messages in long blocks. Usually the coding scheme for a specific source depends parametrically on the statistics of the source. Universal codes which are independent of the source statistics are introduced. These codes are shown to be asymptotically optimal in the sense that the probability of encoding ... View full abstract»

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  • Coding of sources with unknown statistics--II: Distortion relative to a fidelity criterion

    Publication Year: 1972, Page(s):389 - 394
    Cited by:  Papers (73)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (750 KB)

    The encoding of sources with unknown statistics is considered. The average distortion that is obtained with universal coding schemes that are independent of the source statistics is shown to be asymptotically identical to the smallest average distortion that can be achieved with the best individual coding scheme (i.e., a code that is based on the specific statistics of the source). This result is ... View full abstract»

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  • An algorithm for source coding

    Publication Year: 1972, Page(s):395 - 399
    Cited by:  Papers (72)  |  Patents (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (705 KB)

    We derive a simple algorithm for the ranking of binary sequences of length<tex>n</tex>and weight<tex>w</tex>. This algorithm is then used for source encoding a memoryless binary source that generates O's with probability<tex>q</tex>and l's with probability<tex>p = 1 - q</tex>. View full abstract»

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  • On the existence of group codes for the Gaussian channel

    Publication Year: 1972, Page(s):399 - 402
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (599 KB)

    A number of theorems are given, which give insight into the algebraic structure of group codes for the Gaussian channel, as defined by Slepian. The problem of the existence of group codes for a given pair of defining parameters (i.e., number of codewords<tex>M</tex>, and dimension of the signal space<tex>n</tex>) is partially solved. View full abstract»

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  • Some results on the minimum distance structure of cyclic codes

    Publication Year: 1972, Page(s):402 - 409
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1167 KB)

    This paper presents a number of interesting results relating to the determination of actual minimum distance of cyclic codes. Codes with multiple sets of consecutive roots are constructed. A bound on the minimum weight of odd-weight codewords is determined. Relations on the distribution of roots of the generator polynomial are investigated. Location polynomials of reversible codes are examined. Th... View full abstract»

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  • Gleason's theorem on self-dual codes

    Publication Year: 1972, Page(s):409 - 414
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (777 KB)

    The weight enumerator of a code is the polynomial \begin{equation} W(x,y)= \sum_{r=0}^n A_r x^{n-r} y^r, \end{equation} where<tex>n</tex>denotes the block length and<tex>A_r</tex>, denotes the number of codewords of weight<tex>r</tex>. Let<tex>C</tex>be a self-dual code over<tex>GF(q)</tex>in which every weight is divisible by<tex>c... View full abstract»

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  • Long primitive binary BCH codes have distance<tex>d leq 2n ln R^{-1}/log n cdots</tex>

    Publication Year: 1972, Page(s):415 - 426
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1480 KB)

    In this paper, we obtain upper and lower bounds on the designed and actual distances of any sequence of extended primitive BCH codes of increasing lengths<tex>n</tex>and fixed rate<tex>R</tex>. The results of this paper are based on [1, ch. 12], which gives an exact expression for the rates of any sequence of extended primitive BCH codes of increasing length and fixed ratio... View full abstract»

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  • Some Comments Concerning Walsh Functions

    Publication Year: 1972, Page(s):427 - 428
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (323 KB)

    The use of explicit forms for Walsh functions removes much of the confusion surrounding these interesting functions and permits simple proofs of their properties. Thus, for example, their period is far easier to determine than Alexandridis found, but their Fourier spectra are more complex than Schreiber's approximation suggests. For wave-form analysis, certain Walsh functions--the regular symmetri... View full abstract»

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  • On the distance criterion of Patrick and Fischer (Corresp.)

    Publication Year: 1972, Page(s): 428
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (129 KB)

    An upper bound on the probability of misrecognition is obtained in terms of Patrick and Fischer's measure of distance and its maximization is shown to minimize the upper bound on the probability of error. View full abstract»

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  • Hypothesis testing with finite memory in finite time (Corresp.)

    Publication Year: 1972, Page(s):429 - 431
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (458 KB)

    The hypothesis-testing problem has recently been studied under a finite-memory constraint. However, most work has been concerned with the large-sample theory. Here we study the small-sample theory for binary-valued observations. View full abstract»

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  • The reduced nearest neighbor rule (Corresp.)

    Publication Year: 1972, Page(s):431 - 433
    Cited by:  Papers (299)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (537 KB)

    A further modification to Cover and Hart's nearest neighbor decision rule, the reduced nearest neighbor rule, is introduced. Experimental results demonstrate its accuracy and efficiency. View full abstract»

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  • On the minimum distortion of block codes for a binary symmetric source (Corresp.)

    Publication Year: 1972, Page(s):433 - 435
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (456 KB)

    It is shown that the mixture of two codes of block length<tex>n</tex>can have a distortion strictly less than the distortion of the best possible code of block length<tex>n</tex>having the same rate. The seeming contradiction is explained by offering two interpretations for the mixture of two codes and then explaining why the bound for the performance of the best code canno... View full abstract»

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  • Contained convolutional codes (Corresp.)

    Publication Year: 1972, Page(s):435 - 437
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (449 KB)

    Sullivan's recent extension of Gallager's time diversity encoding scheme for combating bursts when there are errors in the guard space is based on the concept of one convolutional code that is contained in another. This paper shows that Sullivan's necessary and sufficient conditions for containment imply a simple factorization of the contained code. Implications for code design, encoders, and deco... View full abstract»

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  • An efficient algorithm for computing free distance (Corresp.)

    Publication Year: 1972, Page(s):437 - 439
    Cited by:  Papers (44)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (542 KB)

    An efficient bidirectional search algorithm for computing the free distance of convolutional codes is described. View full abstract»

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  • A note on the minimum distance structure of cyclic codes (Corresp.)

    Publication Year: 1972, Page(s):439 - 440
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (349 KB)

    In this correspondence the Mattson-Solomon formulation is applied to cyclic codes with multiple sets of consecutive roots of the generator polynomial and better estimates of the minimum distance of many cyclic codes are obtained. View full abstract»

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  • Decoding beyond the BCH bound (Corresp.)

    Publication Year: 1972, Page(s):441 - 444
    Cited by:  Papers (19)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (676 KB)

    In this correspondence, a decoding algorithm to decode beyond the BCH bound is introduced. It gives a complete minimum distance decoding for any cyclic code. A comparison between this decoding algorithm and previously existing ones is also given. View full abstract»

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  • Permutation decoding of certain triple-error-correcting binary codes (Corresp.)

    Publication Year: 1972, Page(s):444 - 446
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (412 KB)

    In a recent note [1] an analysis of certain binary double-error-correcting cyclic codes was made from the point of view of permutation decodability. Specifically, upper bounds on the rates of these codes were established so that the codes would be permutation decodable. The object of the present correspondence is to give corresponding results for binary triple-error-correcting cyclic codes of cert... View full abstract»

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  • One-step weighted-majority decoding (Corresp.)

    Publication Year: 1972, Page(s):446 - 448
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (384 KB)

    It is shown that any decoding function for a linear binary code can be realized as a weighted majority of nonorthogonal parity checks. An example is given of a four-error-correcting code that is neither L-step orthogonalizable nor one-step majority decodable using non-orthogonal parity checks and yet is one-step weighted-majority decodable using only ten nonorthogonal parity checks. 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