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<tex>(\Omega, S, \mu)</tex>;<tex>X_1, \{ V_n \}(n = 1, 2, \cdots), K</tex>-component complex-valued random variables on<tex>(\Omega, S, \mu), K</tex>a positive integer, whose components have finite variance and mean zero; and two sequences of matrices<tex>\{ \phi_n \}, \{ M_n \}</tex>where the<tex>\{ \phi_n \}</tex&g... 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 (47)
    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 of whi... 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)

    The<tex>n</tex>th-order multiple coherence between a stationary random process and<tex>n</tex>other stationary random processes is decomposed into a sum of<tex>n</tex>components 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 incoher... 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 (43)
    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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  • 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 (881 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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  • 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 an<tex>N</tex>-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 effec... View full abstract»

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  • Modified digital correlator and its estimation errors

    Publication Year: 1970, Page(s):699 - 706
    Cited by:  Papers (33)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1118 KB)

    The method of using auxiliary random noise to unbias the output of the multilevel digital correlator is investigated. It is shown that any random noise satisfying certain conditions may be used. The uniformly distributed noise that has been used previously in the polarity-coincidence correlator is a special case. Discretely distributed auxiliary noise, although not satisfying the conditions, has t... 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 (702 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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  • 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 large<tex>N</tex>, achieves arbitrarily Iow probability of error... 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 any ... View full abstract»

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  • Convolutional codes I: Algebraic structure

    Publication Year: 1970, Page(s):720 - 738
    Cited by:  Papers (410)  |  Patents (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (3434 KB)

    A convolutional encoder is defined as any constant linear sequential circuit. The associated code is the set of all output sequences resulting from any set of input sequences beginning at any time. Encoders are called equivalent if they generate the same code. The invariant factor theorem is used to determine when a convolutional encoder has a feedback-free inverse, and the minimum delay of any in... View full abstract»

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  • Generalized threshold decoding of convolutional codes

    Publication Year: 1970, Page(s):739 - 745
    Cited by:  Papers (1)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (876 KB)

    A one-step threshold decoding method previously presented for cyclic block codes is shown to apply generally to linear convolutional codes. It is further shown that this method generalizes in a natural way to allow decoding of the received sequence in its unquantized analog form. 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 (24)
    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}... 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 (41)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1082 KB)

    The following theorem is proved. Let<tex>f(x_1,\cdots, x_m)</tex>be a binary nonzero polynomial of<tex>m</tex>variables of degree<tex>\nu</tex>. H the number of binary<tex>m</tex>-tuples<tex>(a_1,\cdots, a_m)</tex>with<tex>f(a_1, \cdots, a_m)</tex>= 1 is less than<tex>2^{m-\nu+1}</tex>, then<tex>f</tex>... 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 (36)
    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 cyclic<tex>q</tex>-ary codes to be invariant under the general linear group of substitutions over an extension field of<tex>GF(q)</tex>. The important class of polynomial codes, introduced by Kasami, Lin, and Peterson, satisfy the conditions and several new results are obtained ... 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
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  • Correction to 'Intersymbol interference and probability of error in digital systems'

    Publication Year: 1970, Page(s): 770
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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 | PDF file iconPDF (454 KB)
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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 (621 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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  • 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 process<tex>x(t)</tex>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... 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 (519 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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  • 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 transformation<tex>A</tex>of a vector of real-valued zero-mean signal samples with covariance matrix<tex>R_x</tex>, such that<tex>tr(A R_x A ^ T)</tex>is invariant with<tex>A</tex>. The matrix<tex>A</tex>adds redundancy to the signal by having more rows t... 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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  • Optimum linear feedback scheme for matching colored Gaussian sources with white Gaussian channels (Corresp.)

    Publication Year: 1970, Page(s):789 - 791
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (519 KB)

    Linear preemphasis and deemphasis filters are found for matching a class of colored Gaussian sources and wide-band additive white Gaussian-noise channels by the utilization of noiseless feedbacks. These filters are optimum in the sense that they give an overall mean-square error that corresponds to the rate-distortion bound. 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