IEEE Transactions on Information Theory

Volume 16 Issue 6 • November 1970

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Displaying Results 1 - 25 of 31
  • Some convergence theorems for linear systems

    Publication Year: 1970, Page(s):658 - 663
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (886 KB)

    Given a probability space(Omega, S, mu);X_1, { V_n }(n = 1, 2, cdots), K-component complex-valued random variables on(Omega, S, mu), Ka positive integer, whose components have finite variance and mean zero; and two sequences of matrices{ phi_n }, { M_n }where the{ phi_n }areK times Kand the{M_n}areK_n times K, K_n View full abstract»

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  • Further decomposition of the Karhunen-Loève series representation of a stationary random process

    Publication Year: 1970, Page(s):663 - 668
    Cited by:  Papers (45)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (752 KB)

    It is shown how the Karhunen-Loève(K-L)series representation for a finite sample of a discrete random sequence, stationary to the second order, may be further decomposed into a pair of series by utilizing certain symmetry properties of the covariance matrix of the sequence. The theory is applied to the particular example of a first-order Markov sequence, the series representation o... View full abstract»

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  • Relationship between multiple and partial coherence functions

    Publication Year: 1970, Page(s):668 - 672
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (629 KB)

    Thenth-order multiple coherence between a stationary random process andnother stationary random processes is decomposed into a sum ofncomponents consisting of products of lower order partial and multiple coherence functions. An inequality is derived between partial coherence and the ratio of ordinary coherence to multiple incoherence. As a result, a coherency diagr... View full abstract»

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  • Photon counting: A problem in classical noise theory

    Publication Year: 1970, Page(s):672 - 680
    Cited by:  Papers (45)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1314 KB)

    In this paper we formulate the general problem of determining the photoelectron "counting" distribution resulting from an electromagnetic field impinging on a quantum detector. Although the detector model used was derived quantum mechanically, our treatment is wholly classical and includes all results known to date. This combination is commonly referred to as the semiclassical approach. The emphas... View full abstract»

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  • Convergence probability bounds for stochastic approximation

    Publication Year: 1970, Page(s):680 - 685
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (971 KB)

    In certain stochastic-approximation applications, sufficient conditions for mean-square and probability-one convergence are satisfied within some unknown bounded convex set, referred to as a convergence region. Globally, the conditions are not satisfied. Important examples are found in decision-directed procedures. If a convergence region were known, a reflecting barrier at the boundary would solv... View full abstract»

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  • An upper bound on the estimation error in the threshold region

    Publication Year: 1970, Page(s):692 - 699
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (999 KB)

    An upper bound on the estimation error in the threshold region (probability of threshold effect and mean-square error) is obtained for nonlinear pulse modulation systems. The problem is viewed in anN-dimensional Euclidean space. The space of all received signals is divided into two regions, corresponding to the two types of error: weak-noise approximation and threshold effect. The thres... View full abstract»

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  • New viewpoint on communication channel capabilities

    Publication Year: 1970, Page(s):712 - 716
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (824 KB)

    A channel modeling technique is described that looks at the communication problem from a new viewpoint. A quantity called unfolding capacity--the capacity of a channel as it happens to unfold--is defined. A theorem is derived that proves for the assumed channel model, a feedback scheme can be devised that for sufficiently largeN, achieves arbitrarily Iow probability of error at any rate... View full abstract»

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  • New family of single-error correcting codes

    Publication Year: 1970, Page(s):717 - 719
    Cited by:  Papers (38)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (415 KB)

    A construction is given that combines an(n, M_1, d_1)code with an(n, M_2, d_2 = [frac{1}{2}(d_1 + 1)])code to form a(2n, M_1 M_2, d_1)code. This is used to construct a new family of nongroup single-error correcting codes of all lengthsnfrom2^mto 3 ·2^{m-1} - 1, for everym geq 3. These codes have more codewords than a... View full abstract»

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  • Weight enumerator for second-order Reed-Muller codes

    Publication Year: 1970, Page(s):745 - 751
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (665 KB)

    In this paper, we establish the following result. Theorem:A_i, the number of codewords of weightiin the second-order binary Reed-Muller code of length2^mis given byA_i = 0unlessi = 2^{m-1}or2^{m-1} pm 2^{m-l-j}, for somej, 0 leq j leq [m/2], A_0 = A_{2^m} = 1, and begin{equation} begin{split} A_{2^{m-1} pm 2^{m-1-j}} = 2^... View full abstract»

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  • On the weight structure of Reed-Muller codes

    Publication Year: 1970, Page(s):752 - 759
    Cited by:  Papers (39)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1082 KB)

    The following theorem is proved. Letf(x_1,cdots, x_m)be a binary nonzero polynomial ofmvariables of degreenu. H the number of binarym-tuples(a_1,cdots, a_m)withf(a_1, cdots, a_m)= 1 is less than2^{m-nu+1}, thenfcan be reduced by an invertible affme transformation of its variables to one of the following forms. ... View full abstract»

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  • On cyclic codes that are invariant under the general linear group

    Publication Year: 1970, Page(s):760 - 769
    Cited by:  Papers (35)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1630 KB)

    Using a polynomial approach to linear codes, one derives necessary and sufficient conditions for cyclicq-ary codes to be invariant under the general linear group of substitutions over an extension field ofGF(q). The important class of polynomial codes, introduced by Kasami, Lin, and Peterson, satisfy the conditions and several new results are obtained about some of these code... View full abstract»

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  • Correction to 'Threshold characteristics of FM signals demodulated by an FM discriminator'

    Publication Year: 1970, Page(s): 769
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (84 KB)

    First Page of the Article
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  • Correction to 'Intersymbol interference and probability of error in digital systems'

    Publication Year: 1970, Page(s): 770
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (62 KB)

    First Page of the Article
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  • Note on discrimination information and variation (Corresp.)

    Publication Year: 1970, Page(s):771 - 773
    Cited by:  Papers (28)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (454 KB)

    First Page of the Article
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  • On a mean-square approximation problem (Corresp.)

    Publication Year: 1970, Page(s):776 - 778
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (516 KB)

    This correspondence is concerned with the problem of choosing an approximation for the random variable obtained by operating on a stochastic processx(t)with a zero-memory non-linearity followed by a linear transformation. It is desired to approximate the nonlinearity with a simpler function and two different criteria are considered for selecting this approximation, viz., the mean-square... View full abstract»

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  • Block filtering in amplitude-continuous time-discrete channels (Corresp.)

    Publication Year: 1970, Page(s):782 - 786
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (894 KB)

    A linear amplitude-continuous (LAC) block filter is a real-valued rectangular matrix transformationAof a vector of real-valued zero-mean signal samples with covariance matrixR_x, such thattr(A R_x A ^ T)is invariant withA. The matrixAadds redundancy to the signal by having more rows than columns. A special class of LAC filters, called orthogon... View full abstract»

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  • Unification of linear information feedback schemes for additive white Gaussian noise channels (Corresp.)

    Publication Year: 1970, Page(s):786 - 789
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (710 KB)

    For the transmission of a Gaussian information source over an additive white Gaussian noise channel, several noiseless-feedback linear estimation schemes are shown to be the same in the sense that they not only achieve the rate-distortion bound on the minimum attainable mean-square error, but also possess identical system parameters. Moreover, Butman's noiseless-linear-feedback scheme for the tran... View full abstract»

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  • Decoding of circulant codes (Corresp.)

    Publication Year: 1970, Page(s):797 - 802
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (946 KB)

    Many of the best random error-correcting group codes known (cyclic or not) can be reduced to echelon canonical form, in which the parity matrix is mainly or entirely composed of one or several circulants. This correspondence deals with simple and efficients methods for coding and decoding such codes, called quasi-cyclic in recent literature. The main result is that when the parity matrixC View full abstract»

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  • Review of 'The Sciences of the Artificial' (Simon, H. A.; 1969)

    Publication Year: 1970, Page(s):803 - 804
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    Freely Available from IEEE
  • Constructive encoder for multiple burst correction of binary convolutional codes (Corresp.)

    Publication Year: 1970, Page(s):792 - 793
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (328 KB)

    A class of multiple burst convolution codes generated by encoders that are constructed using a single digital "building block" is given. The number of identical small sections used in the encoder depends upon the degree of error correction desired. View full abstract»

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  • Threshold noise analysis of FM signals for a general baseband signal modulation and its application to the case of sinusoidal modulation (Corresp.)

    Publication Year: 1970, Page(s):778 - 781
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (528 KB)

    This paper analyzes the threshold characteristic of FM signals. An exact solution, obtained previously [1] for Gaussian base-band modulation, is generalized in order to obtain the autocorrelation function of the output signal plus noise of an FM discriminator for the case of more general baseband signals. For an application of the general results, sinusoidal modulation is analyzed in detail. It is... View full abstract»

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  • Estimation with finite memory

    Publication Year: 1970, Page(s):685 - 691
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (896 KB)

    A finite-state model for sequential minimum-mean-square-error estimation of a random variable in additive noise is analyzed to determine the dependence of optimum performance and structure on the memory size of the estimator. Necessary conditions for determining the structure of the optimum finite-state estimator are derived for arbitrary statistics. Numerical results are presented for Gaussian st... View full abstract»

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  • Synthesis of multivariate Gaussian random processes with a preassigned covariance (Corresp.)

    Publication Year: 1970, Page(s):773 - 776
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (632 KB)

    Evaluation of complex systems in a laboratory environment requires the generation of inputs to the system sensors that are representative of the operational environment. It is therefore necessary to synthesize input test signals that reflect the mutual dependencies found in situ. For multivariate Gaussian inputs, algorithms are derived allowing 1) the transformation of dependent Gaussian random va... View full abstract»

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  • Design of radar signals and receivers subject to implementation errors

    Publication Year: 1970, Page(s):707 - 711
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (712 KB)

    The problem of designing finite-pulse-train radar signals and receivers to maximize the detectability of targets in the presence of clutter has recently been solved. In practice, the performance of these optimum signal-receiver pairs is often degraded seriously by implementation errors. The purpose of this paper is to present an iterative procedure for designing signal-receiver pairs, which takes ... View full abstract»

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  • Use of a sequential decoder to analyze convolutional code structure (Corresp.)

    Publication Year: 1970, Page(s):793 - 795
    Cited by:  Papers (16)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (584 KB)

    An existing sequential decoding program can be easily modified to enumerate the number of low-weight codewords in a convolutional code, where weight is defined either over a decoding constraint length or "free." We tabulated several good rate one-half constraint-length 49 systematic codes that were obtained quickly with this procedure. 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