IEEE Transactions on Information Theory

Volume 17 Issue 6 • November 1971

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Displaying Results 1 - 25 of 25
  • Prior probability and uncertainty

    Publication Year: 1971, Page(s):641 - 650
    Cited by:  Papers (30)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1338 KB)

    Consider a stochastic system with output <tex>Y</tex> whose probability density <tex>(pY \mid \Lambda)</tex> is a known function of the parameter <tex>\Lambda</tex> whose true value is unknown. Our aim is to assign a prior probability density <tex> b(\Lambda)</tex> for <tex>\Lambda</tex> using all the available knowledge so that we can as... View full abstract»

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  • Sampling series for band-limited generalized functions

    Publication Year: 1971, Page(s):650 - 654
    Cited by:  Papers (30)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (730 KB)

    For an arbitrary band-limited generalized function<tex>H(t)</tex>a representation is obtained that is a combination of a Taylor series and a conventional sampling series. A parameter<tex>N</tex>that enters can be chosen such as to make the series rapidly convergent. Furthermore, it is shown that, for suitably restricted test functions,<tex>H(t)</tex>can be repre... View full abstract»

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  • Bounds on the mean-square error and the quality of domain decisions based on mutual information

    Publication Year: 1971, Page(s):655 - 665
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1389 KB)

    A class of lower bounds for the generalized mean-square error (MSE), the probability of error, and the accuracy of domain decisions is derived. The derivation is based on the well-known properties of the functional \begin{equation} \Lambda \equiv \int _ {\mathcal{H}} - [\ln p_2 (x) - \ln p_1 (x)]p_1(x)d \gamma. \end{equation} The bounds depend on the mutual information between the channel's input ... View full abstract»

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  • Variance of Bayes estimates

    Publication Year: 1971, Page(s):665 - 669
    Cited by:  Papers (21)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (716 KB)

    This paper contains an analysis of the performance of Bayes conditional-mean parameter estimators. The main result is that on a finite parameter space such estimates exhibit a mean-square error that diminishes exponentially with the number of observations, the observations being assumed to be independent. Two situations are discussed: true parameter included in the parameter space and true paramet... View full abstract»

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  • Barankin Bounds on Parameter Estimation

    Publication Year: 1971, Page(s):669 - 676
    Cited by:  Papers (79)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1059 KB)

    The Schwarz inequality is used to derive the Barankin lower bounds on the covariance matrix of unbiased estimates of a vector parameter. The bound is applied to communications and radar problems in which the unknown parameter is embedded in a signal of known form and observed in the presence of additive white Gaussian noise. Within this context it is shown that the Barankin bound reduces to the Cr... View full abstract»

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  • Study of an integral equation arising in detection theory

    Publication Year: 1971, Page(s):677 - 686
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1451 KB)

    This paper considers the solution of a Fredholm equation occurring in detection theory problems. A solution procedure, based on solving differential equations with nonmixed boundary conditions, is described for the case when the kernel of the integral equation is known to be the output covariance of a linear finite-dimensional system excited by white noise. Solutions with discontinuities are consi... View full abstract»

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  • Deterministic approach to a class of nonparametric system identification problems

    Publication Year: 1971, Page(s):686 - 696
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1899 KB)

    In this paper a class of system identification problems of nonparametric type is considered. Specifically, given an unknown deterministic system, some basic structural aspects related to the problem of estimating its weighting function are discussed. The model adopted for the system input-output relation is general enough to cover a number of situations ranging from problems of identification of l... View full abstract»

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  • Optimal mismatched filter design for radar ranging, detection, and resolution

    Publication Year: 1971, Page(s):696 - 701
    Cited by:  Papers (33)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (864 KB)

    In a multiple-target environment a radar signal processor often uses weighting filters that are not matched to the transmitted waveform. In this paper the mean-square range-estimation error, the detection Signal-to-noise ratio (SNR), and the effects of sidelobes are expressed in terms of the impulse response of an arbitrary mismatched filter. It is desired to find that impulse response that result... View full abstract»

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  • Design of minimum-error optimal classifiers for patterns from distributions with Gaussian tails

    Publication Year: 1971, Page(s):701 - 707
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (916 KB)

    Adaptive algorithms for designing two-category linear pattern classifiers have been developed and studied in recent years. When the pattern sets are nonseparable, the adaptive algorithms do not directly minimize the number of classification errors, which is the usual goal in pattern classifier design: furthermore, they also are not minimum-error optimal, i.e., they do not generally minimize the pr... View full abstract»

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  • On decoding of Reed-Solomon codes

    Publication Year: 1971, Page(s):707 - 712
    Cited by:  Papers (22)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (869 KB)

    It is shown how nonsystematic Reed-Solomon (RS) codes encoded by means of the Chinese remainder theorem can be decoded using the Berlekamp algorithm. The Chien search and calculation of error values are not needed but are replaced by a polynomial division and added calculation in determining the syndrome. It is shown that for certain cases of low-rate RS codes, the total decoding computation may b... View full abstract»

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  • Decoding binary block codes on<tex>Q</tex>-ary output channels

    Publication Year: 1971, Page(s):713 - 718
    Cited by:  Papers (33)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (849 KB)

    This paper presents an algebraic technique for decoding binary block codes in situations where the demodulator quantizes the received signal space into<tex>Q &gt; 2</tex>regions. The method, referred to as weighted erasure decoding (WED), is applicable in principle to any block code for which a binary decoding procedure is known. View full abstract»

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  • Rate 1/2 convolutional codes with complementary generators

    Publication Year: 1971, Page(s):718 - 727
    Cited by:  Papers (21)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1383 KB)

    The structure of a class of rate<tex>\frac{1}{2}</tex>convolutional codes called complementary codes is investigated. Of special interest are properties that permit a simplified evaluation of free distance. Methods for finding the codes with largest free distance in this class are obtained. A synthesis procedure and a search procedure that result in good codes up to constraint lengths ... View full abstract»

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  • Generalization of Gallager's adaptive error control scheme

    Publication Year: 1971, Page(s):727 - 735
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1283 KB)

    One of the simplest, yet most effective schemes thus far devised for the correction of errors on compound channels is the adaptive decoding scheme invented by Gallager. In this paper we present a generalization of this scheme which, at a modest sacrifice in rate, enables the decoder to correct a burst even when the guard space following the burst contains random errors. This is accomplished with t... View full abstract»

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  • Generalized burst-trapping codes

    Publication Year: 1971, Page(s):736 - 742
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1071 KB)

    The burst-trapping error control technique developed by Tong [1] corrects both random and burst errors adaptively. A generalization of this scheme, called generalized burst trapping (GBT), is presented here. Generalized burst-trapping codes (GBTC) also correct both random and burst errors adaptively but, in addition, are capable of correcting random errors in the guard space following a correctabl... View full abstract»

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  • Spectrum of incorrectly decoded bursts for cyclic burst error codes

    Publication Year: 1971, Page(s):742 - 748
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1169 KB)

    The enumeration of the incorrectly decoded bursts for cyclic burst error-correcting codes is reported here. The enumeration yields closed formulas for long bursts, whereas an efficient algorithm for the enumeration is given for the short bursts. The enumeration is carried out for two different decoding rules. Under the first rule, the cyclic code is a full length code, and split decodable patterns... View full abstract»

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  • Coding the binary symmetric source with a fidelity criterion (Corresp.)

    Publication Year: 1971, Page(s):749 - 751
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (446 KB)

    A procedure is defined for coding the binary symmetric first-order Markov source with the probability of error fidelity criterion. Since the rate-distortion function<tex>R(d)</tex>for this source has not yet been formulated, the coding performance provides an apparently tight upper bound for<tex>R(d)</tex>. View full abstract»

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  • Basis-restricted transformations and performance measures for spectral representations (Corresp.)

    Publication Year: 1971, Page(s):751 - 752
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (297 KB)

    This correspondence develops tools for comparative evaluation of the effectiveness of unitary transformations in signal processing applications. Performance measures for the tasks of optimal filters and optimal coding are exemplified, and measures of similarity among representations are proposed. View full abstract»

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  • A Note on the Derivation of Finite-Memory Almost-Least-Squares Recursive Filters

    Publication Year: 1971, Page(s): 753
    Request permission for commercial reuse | PDF file iconPDF (110 KB)
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  • Upper bound on the signal-to-noise ratio at the output of a threshold receiver (Corresp.)

    Publication Year: 1971, Page(s):753 - 755
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (429 KB)

    An upper bound on the signal-to-noise ratio (SNR) at the output of an estimator-correlator receiver is derived, and the nature of the transmitted signals and random channels that realize this bound is investigated. View full abstract»

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  • Geometric interpretation of admissible linear decision boundaries for two multivariate normal distributions (Corresp.)

    Publication Year: 1971, Page(s):755 - 758
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (561 KB)

    Every admissible linear decision boundary for the two-class multivariate normal recognition problem is known to be a hyperplane that is tangent to two tangent ellipsoids at their point of tangency. The ellipsoids are equiprobability surfaces for the distributions describing the classes. In this correspondence, the locus of tangent points is parameterized in a manner similar to that of Clunies-Ross... View full abstract»

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  • Entropy coding in speech and television differential PCM systems (Corresp.)

    Publication Year: 1971, Page(s):758 - 761
    Cited by:  Papers (24)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (656 KB)

    Much of the redundancy in a speech or television signal is eliminated when it is encoded into digital form by a differential pulse-code-modulation (DPCM) encoder. Additional coding of the DPCM output using entropy coding techniques (Huffman or Shannon-Fano coding) can result in a further increase in the signal-to-quantizing-noise ratio of 5.6 dB without increasing the transmission rate. View full abstract»

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  • High-rate burst-error-correcting recurrent codes (Corresp.)

    Publication Year: 1971, Page(s):761 - 765
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (833 KB)

    A bound and construction are presented for high-rate burst-error-correcting recurrent codes. The bound is an upper bound on the block length in terms of the total redundancy used in decoding, the redundancy per block, and the burst length. The construction uses a block-code parity-check matrix as the first block of the recurrent code parity-check matrix. For a block code it is typical to find that... View full abstract»

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  • A note on the decoding of double-error-correcting binary BCH codes of primitive length (Corresp.)

    Publication Year: 1971, Page(s):765 - 766
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (322 KB)

    In this correspondence a complete decoding algorithm for double-error-correcting binary BCH codes of length<tex>n = 2^m - 1</tex>is introduced. It corrects all patterns of one and two errors and all patterns of three errors that belong to cosets that have a coset leader of weight three. This algorithm is based on the step-by-step decoding algorithm introduced by Prange and the decoding... View full abstract»

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  • Pseudostep orthogonalization: A new threshold-decoding algorithm (Corresp.)

    Publication Year: 1971, Page(s):766 - 768
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (383 KB)

    In this correspondence a new decoding algorithm using majority logic is proposed. This scheme, called "pseudostep orthogonalization," is basically a hybrid version of the existing majority-logic decoding methods, namely, Reed-Massey's algorithm and Rudolph's algorithm. An example is given for the (21, 5) binary cyclic code, which can correct up to four independent errors. View full abstract»

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  • Review of 'An Introduction to Error-Correcting Codes' (Lin, S.; 1970)

    Publication Year: 1971, Page(s):768 - 769
    Request permission for commercial reuse | PDF file iconPDF (375 KB)
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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