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IEEE Transactions on Information Theory

Issue 1 • January 1969

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Displaying Results 1 - 25 of 42
  • On the deflection of a quadratic-linear test statistic

    Publication Year: 1969, Page(s):16 - 21
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (840 KB)

    The deflection of a bounded quadratic-linear test statistic is considered for the following binary detection problem. HypothesisH_{1}--received waveform is a sample function from a random process with known covariance and mean functions, but unknown probability distributions, versusH_{2}--received waveform is a sample function from a Gaussian process (noise) having known cova... View full abstract»

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  • Minimum bandwidth of M signals with specified code or correlation matrix

    Publication Year: 1969, Page(s):38 - 48
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1221 KB)

    The minimum bandwidth ofMreal equi-energy signals is derived for the cases of either a specified code or a specified correlation matrix. The definition of bandwidth is in terms of the ratio of the energy passed by a linear time-invariant filter to the input energy, and incorporates a great variety of definitions. In one instance, the signals are time limited; in a second, a weighted int... View full abstract»

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  • The asymptotic error probability for transmission of orthogonal signals over the generalized incoherent channel

    Publication Year: 1969, Page(s):48 - 52
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (688 KB)

    The probability of error for the transmission of one ofM-orthogonal, equally likely, equal-energy signals over the white Gaussian noise channel is known. For large values ofTit is shown that this result is asymptotically equivalent to the error probability for the same signal set transmitted over a different channel, termed here the generalized incoherent channel of order View full abstract»

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  • Improving communication reliability by use of an intermittent feedback channel

    Publication Year: 1969, Page(s):52 - 60
    Cited by:  Papers (52)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1162 KB)

    This paper describes and analyzes a feedback communication scheme where the feedback channel is used only to inform the transmitter, at specified times (prior to a final decision), which message the receiver considers most likely. The feedback information is used by the transmitter to modify its transmission according to a rule known also to the receiver. When orthogonal signals are used and only ... View full abstract»

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  • Optimal communication systems with noiseless feedback for a binary source and white Gaussian channel

    Publication Year: 1969, Page(s):61 - 66
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (818 KB)

    The sequential and nonsequential feedback systems for a binary source, first proposed by Turin, are considered. It is shown that in both cases the optimal signals belong to the familypm A (y)[1 + exp (pm y)]^{-1}, whereA(y)is arbitrary. In the sequential scheme the bound on transmission rate is achieved for anyP_{e}by all members of this family, and in the nonseque... View full abstract»

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  • An application of rate-distortion theory to a converse to the coding theorem

    Publication Year: 1969, Page(s):66 - 71
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (783 KB)

    A lower bound to the information rateR(D)for a discrete memoryless source with a fidelity criterion is presented for the case in which the distortion matrix contains the same set of entries, perhaps permuted, in each column. A necessary and sufficient condition forR(D)to equal this bound is given. In particular, if the smallest column element is zero and occurs once in each r... View full abstract»

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  • Generalized threshold decoding and the Reed- Solomon codes

    Publication Year: 1969, Page(s):78 - 81
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (610 KB)

    A necessary condition for the existence of a set ofJorthogonal parity check equations is developed, and it is demonstrated that, except for the trivial codes, the Reed-Solomon codes are notL-step orthogonalizable. Massey's concept of threshold decoding is generalized, and it is demonstrated that the Reed-Solomon codes are completely threshold decodable. Since every BCH code i... View full abstract»

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  • New binary coding results by circulants

    Publication Year: 1969, Page(s):81 - 92
    Cited by:  Papers (82)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1898 KB)

    The Introduction contains a new circulant echelon canonical form for the perfect(23,12)Golay code and some tentative conclusions are suggested. Section I gives an account of the properties of circulant matricesA, and a number of lemmas that make it possible to determine the minimum weight of codes generated by the rows of a matrix of the form|E|A|. In Section II, i... View full abstract»

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  • Matrix approach to synchronization recovery for binary cyclic codes

    Publication Year: 1969, Page(s):93 - 101
    Cited by:  Papers (8)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1040 KB)

    The problem of detecting and correcting loss of synchronization for binary cyclic codes is examined. The method used is to form a coset code from tho given(n, k)cyclic code by adding a suitablenvector to each cyclic code word before transmission. Unlike some other techniques, the length of the code wordnis not altered. A code word may be represented in at least two... View full abstract»

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  • A family of codes for the correction of substitution and synchronization errors

    Publication Year: 1969, Page(s):102 - 106
    Cited by:  Papers (24)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (855 KB)

    Binary block codes are constructed that are capable of correcting, in everyt geq 3consecutive words, either one substitution error in each one of, at the most,t-2words, or one synchronization error (but not both). In order to decode any one word, the decoder needs to wait for the reception of, at the most, the nextt-1words. View full abstract»

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  • Correction of synchronization errors with burst-error-correcting cyclic codes

    Publication Year: 1969, Page(s):106 - 109
    Cited by:  Papers (9)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (615 KB)

    It is shown that every linear cyclicb-burst-error-correcting code over any finite field can be modified to correct up to(b-2)symbols of synchronization slippage without additional redundancy, while maintaining its additive error-correcting capability in the absence of synchronization errors. For codes that are interleaved to a degreem, the synchronization error-cor... View full abstract»

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  • A class of high-speed decoders for linear cyclic binary codes

    Publication Year: 1969, Page(s):113 - 117
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (689 KB)

    A general method is proposed for decoding any cyclic binary code at extremely high speed using only modulo2adders and threshold elements, and the decoders may be designed for maximum-likelihood decoding. The number of decoding cycles is a fraction of the number of digits in the code word. View full abstract»

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  • Quasi-self-reciprocal polynomials and potentially large minimum distance BCH codes

    Publication Year: 1969, Page(s):118 - 121
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (655 KB)

    We consider the problem of determining which irreducible polynomials with coefficients in a finite fieldGF(q)are quasi-self-reciprocal. Our characterization of these polynomials is in terms of a set of positive integers,Dq.Dqhas applications to certain BCH codes. This work determines those codes (as specified byn, the length of the code, and not byk... View full abstract»

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  • Minimum distance estimates of the performance of sequential decoders

    Publication Year: 1969, Page(s):128 - 140
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1881 KB)

    In the past, criteria for predicting the performance of individual codes with sequential decoding have been intuitive. In this paper, simple tests are derived that allow easy determination of the performance on the BSC (binary symmetric channel) of a given binary convolutional code decoded with a modified version of the Fano algorithm. A "distance-guaranteed computational cutoff rate,"R_{dgco... View full abstract»

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  • An upper bound on moments of sequential decoding effort

    Publication Year: 1969, Page(s):140 - 149
    Cited by:  Papers (25)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1217 KB)

    In this paper we derive an infinite tree code ensemble upper bound on thenuth(nu leq 1)moments of the computational effort connected with sequential decoding governed by the Fano footnote[1]{algorithm}. It is shown that thenuth moment of the effort per decoded branch is hounded by a constant, provided the transmission rateR_{0}satisfies inequality (2), T... View full abstract»

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  • Error-propagation properties of uniform codes

    Publication Year: 1969, Page(s):152 - 161
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1618 KB)

    The problem of error propagation in uniform codes is investigated using the concept of parity-parallelogram submatrices and the threshold-decoding algorithm. A set of optimum orthogonalization rules is presented and it is shown that if these rules are incorporated into the decoder, then sufficient conditions can be found for the return of the decoder to correct operation following a decoding error... View full abstract»

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  • Correction to 'A Statistical Theory of Reverberation and Similar First-Order Scattered Fields. Parts I and II'

    Publication Year: 1969, Page(s):161 - 162
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (248 KB)

    First Page of the Article
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  • An upper bound onk/nfor affine-invariant codes with fixedd/n(Corresp.)

    Publication Year: 1969, Page(s):174 - 176
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (442 KB)

    An upper bound on the transmission ratiok/nfor binary cyclic codes whose extended codes are invariant under the affine group of permutations, is presented. As a consequence, the transmission ratiok/nof any affine-invariant code with a fixedd(minimum weight)/nis shown to approach zero as the code length n increases. This is an extension of the Lin and Wel... View full abstract»

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  • Threshold decoding selected rate one-half and one-third convolutional codes (Corresp.)

    Publication Year: 1969, Page(s):179 - 184
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (673 KB)

    The results of a search for threshold decoding equations are presented for a selection of different length, ratefrac{1}{2}andfrac{1}{3}convolutional codes. The decoders corresponding to these equations are simulated on a computer in order to perform an error analysis. Error analysis for seven ratefrac{1}{2}codes (lengths span the range fromn = 4to22... View full abstract»

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  • The equivalence of L-step orthogonalization and a Reed decoding procedure (Corresp.)

    Publication Year: 1969, Page(s):184 - 186
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (447 KB)

    This correspondence shows the formal equivalence between Massey's decoding scheme called threshold decoding involvingL-step orthogonalizable codes and Reed's decoding scheme originally conceived for the Muller codes. Upon examining these two decoding algorithms it is shown that each can be described in terms of a decoding logic circuit. The formal equivalence of the algorithms is proved... View full abstract»

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  • Correction of two erasure bursts (Corresp.)

    Publication Year: 1969, Page(s):186 - 187
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (303 KB)

    First Page of the Article
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  • Review of 'Introduction to Fourier Optics' (Goodman, J. W.; 1968)

    Publication Year: 1969, Page(s): 191
    Request permission for commercial reuse | PDF file iconPDF (163 KB)
    Freely Available from IEEE
  • A survey of progress in coding theory in the Soviet Union

    Publication Year: 1969, Page(s):197 - 244
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (7323 KB)

    Described in this report are the results of a comprehensive technical survey of all published Soviet literature in coding theory and its applications--over400papers and books appearing before March 1967. The purpose of this report is to draw attention to this important collection of technical results, which are not well known in the West, and to summarize the significant contributions. ... View full abstract»

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  • A feedback decoding scheme for linear convolutional codes (Corresp.)

    Publication Year: 1969, Page(s):189 - 190
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (264 KB)

    A decoding scheme, with feedback, for linear convolutional codes is given. The scheme when applied to linear nonsystematic convolutional codes requires no post-decoding processing involving memory to retrieve the information sequences. This implies that no additional errors occur that are due only to the information retrieving process. View full abstract»

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  • Shift-register synthesis and BCH decoding

    Publication Year: 1969, Page(s):122 - 127
    Cited by:  Papers (853)  |  Patents (36)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1000 KB)

    It is shown in this paper that the iterative algorithm introduced by Berlekamp for decoding BCH codes actually provides a general solution to the problem of synthesizing the shortest linear feedback shift register capable of generating a prescribed finite sequence of digits. The shift-register approach leads to a simple proof of the validity of the algorithm as well as providing additional insight... 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
Prakash Narayan 

Department of Electrical and Computer Engineering