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Information Theory, IEEE Transactions on

Issue 5 • Date September 1973

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Displaying Results 1 - 25 of 35
  • Review of 'Synchronization Systems in Communication and Control' (Lindsey, W. C.; 1972)

    Page(s): 714 - 715
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    Freely Available from IEEE
  • Review of 'The Metaphorical Brain' (Arbib, M. A.; 1972)

    Page(s): 715 - 716
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    Freely Available from IEEE
  • Review of 'Transmission of Information by Orthogonal Functions' (Harmuth, H. F.; 1973)

    Page(s): 715 - 716
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    Freely Available from IEEE
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  • Detection of a PSK signal transmitted through a hard-limited channel

    Page(s): 623 - 630
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    This paper considers the problem of the detection of a binary phase-modulated carrier which has been transmitted along with noise through a hard-limiting repeater, corrupted by additional noise, and demodulated by cross correlation and sampling at the receiver. Three equivalent expressions are obtained for the error probability of the receiver output. Two of these expressions take the form of an infinite series involving either confluent hypergeometric functions or modified Bessel functions. A third form allows representation of the error probability in terms of Rice'sIefunction. In the special case where the signal-to-noise ratiosrho_1^2andrho_2^2at the limiter and receiver inputs are equal, the error probability is simply begin{equation} P_e = frac{1}{2} exp (-p_1^2). end{equation} Asymptotic expressions for the error probability for large and small signal-to-noise ratios are also derived. The error probability is found to be smaller than that of a linear system for all practical values of limiter and receiver input signal-to-noise ratios. The optimum repeater non-linearity is investigated and is shown to be a limiter at such signal-to-noise ratios. View full abstract»

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  • On general Gilbert bounds

    Page(s): 661 - 666
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    We define a distance measure for block codes used over memoryless channels and show that it is related to upper and lower bounds on the low-rate error probability in the same way as Hamming distance is for binary block codes used over the binary symmetric channel. We then prove general Gilbert bounds for block codes using this distance measure. Some new relationships between coding theory and rate-distortion theory are presented. View full abstract»

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  • Sequential estimation with a finite statistic

    Page(s): 631 - 635
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    A procedure is given for optimizing the sequential estimation of a random variable in the mean-square sense, with the constraint that the data must be summarized by a finite-valued statistic. This finite-valued statistic can be considered to be the memory of the processor. The estimate is constrained to be a function of the contents of the memory and the time of the estimate. An example is given to illustrate the results. View full abstract»

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  • Addresses for graphs

    Page(s): 683 - 688
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    The problem of labeling the vertices of an undirected, connected graph with binaryn-tuple addresses is considered. These addresses are to have the property that if two vertices are a distancekapart in the graph then the Hamming distance between the corresponding addresses must bekdwheredis a positive integer which is constant for the graph. Not all graphs may be so addressed. A weak characterization of addressable graphs in terms of the eigenvalues of a certain matrix associated with the graph is given. It is shown that any addressable bipartite graph may always be addressed withd = 1. For nonbipartite addressable graphs,dmust be even, and it is shown that there exist graphs requiring an arbitrarily largedfor addressing. An addressing algorithm is given which is guaranteed to address any addressable graph. View full abstract»

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  • Optimum processing for delay-vector estimation in passive signal arrays

    Page(s): 608 - 614
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    For the purpose of localizing a distant noisy target, or, conversely, calibrating a receiving array, the time delays defined by the propagation across the array of the target-generated signal wavefronts are estimated in the presence of sensor-to-sensor-independent array self-noise. The Cramér-Rao matrix bound for the vector delay estimate is derived, and used to show that either properly filtered beamformers or properly filtered systems of multiplier-correlators can be used to provide efficient estimates. The effect of suboptimally filtering the array outputs is discussed. View full abstract»

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  • Estimating a binomial parameter with finite memory

    Page(s): 636 - 643
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    This article treats the asymptotic theory of estimating a binomial parameterpwith time-invariant finite memory. The approach taken to this problem is as follows. A decision rule is a pair(t,a)in whichtfixes the transition function of a finite automaton, andais a vector of estimates ofp. Attention is restricted to automata whose transition functions allow transitions only between adjacent states. Rules(t,a)for whichtsatisfies this restriction are termed tridiagonal. For the class of prior distributions on [0,1] which have continuous density functions, we study the performance of a corresponding class of tridiagonal rules{ (t^{ast},a^{ast}) }relative to quadratic loss functions. These rules display sensitivity to the shape of the prior, and have the advantage that the Bayes estimatea^{ast}(givent^{ast}) is easily computed. Within the class of all tridiagonal rules, a particular rule(t^{ast},a^{ast})is shown, for memory size up to 30, to be locally admissible and minimax as well as locally Bayes with respect to the uniform prior. View full abstract»

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  • A note on bifix-free sequences (Corresp.)

    Page(s): 704 - 706
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    A bifix of anL-aryn-tuple is a sequence which is both a prefix and a suffix of thatn-tuple. The practical importance of bifix-free patterns is emphasized, and we devise a systematic way of generating all such sequences and determine their number. View full abstract»

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  • Justesen's construction--The low-rate case (Corresp.)

    Page(s): 711 - 713
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    By using the more general class of BCH codes, rather than RS codes as originally proposed, the results of Justesen [1] are improved for code rates below 0.07. The value ofd/nfor the new codes approaches the Varsharmov-Gilbert hound View full abstract»

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  • Testing a simple symmetric hypothesis by a finite-memory deterministic algorithm

    Page(s): 644 - 647
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    A class of finite-memory deterministic algorithms is introduced and investigated. Optimum algorithms are found for small numbers (up to 21) of states. The algorithms provide their own stopping rules. View full abstract»

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  • The nearest-neighbor rule for small samples drawn from uniform distributions (Corresp.)

    Page(s): 697 - 699
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    It is shown in the classification problem, when independent samples are taken from uniform distributions, that for small sample sizes the probability of misclassification when using the nearest-neighbor rule is "close" to its asymptotic value. It is also shown that when using this rule the probability of classification in many cases is close to its Bayes optimum even for small sample sizes. Moreover, if one is restricted to a small sample size from one population, it is shown that it is not necessary to "make up" this deficiency by taking a large sample from the other population; best results may be obtained when both sample sizes are small. View full abstract»

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  • Dual product codes for correction of multiple low-density burst errors

    Page(s): 672 - 677
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    In many communication channels noise disturbances occur in the form of low-density bursts. Codes capable of correcting multiple bursts of low density are efficient tools of error control for such channels. One such class of codes is presented ia this paper. This Class of codes can be decoded by simple majority logic. The approach is to use codes which are the duals of product codes whose component codes are majority-logic-decodable cyclic codes. View full abstract»

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  • Convergence of the edited nearest neighbor (Corresp.)

    Page(s): 696 - 697
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    The editedknearest neighbor rule (k-NNR) consists of 1) eliminating those samples from the data which are not classified correctly by thek-NNR and the remainder of the data, and 2) using the NNR with the samples which remain from 1) to classify new observations. Wilson has shown that this rule has an asymptotic probability of error which is better than that of thek-NNR. A key step in his development is showing the convergence of the edited nearest neighbor. His lengthy argument is replaced here by a somewhat simpler one which uses an intuitive fact about the editing procedure. View full abstract»

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  • On the error matrix in optimal linear filtering of stationary processes

    Page(s): 593 - 599
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    The error covariance matrix corresponding to optimal linear causal filtering of second-order stationary processes in additive noise is considered. Formulas expressing this error matrix in terms of the optimal transfer function are established, and in the nonsingular case the optimal transfer function is expressed in terms of the spectral densities. These are straightforward generalizations of previously published scalar results, and the derivation is similarly based on Hardy space theory. Explicit bounds on the minimal error (i.e., the trace of the optimal error covariance matrix) are obtained for filtering in white noise. Furthermore, an explicit expression for the error covariance matrix is derived for the case of transmitting the same signal over several white-noise channels. View full abstract»

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  • An estimate of the upper bound on error probability for maximum-likelihood sequence estimation on channels having a finite-duration pulse response (Corresp.)

    Page(s): 699 - 702
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    An estimate of an upper bound on performance in terms of probability of error is developed for maximum-likelihood sequence estimation over channels for which only the pulse response energy and duration are known. This bound is evaluated for channels with a pulse response duration up to 10 signaling intervals, and the related minimum-distance channel codes are presented. View full abstract»

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  • Simple nonstatistical television compression system

    Page(s): 648 - 652
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    A television system is proposed which sends a succession of high-bandwidth and low-bandwidth pictures over a channel. If flicker is avoided, the eye judges picture quality from successive presentations of the pictures by taking an average. It appears that an exchange can be effected between the power in the high-frequency components and the actual duration of these components. Using only successive high-bandwidth and low-bandwidth pictures, a 1.5:1 compression ratio can be achieved, accompanied by a small drop in subjective quality. Using a "high-frequency boost circuit" to get a compression ratio up to 2.75:1 still gives satisfactory picture quality. Experiments using movie pictures in place of the previously mentioned stills show that high compression ratios are possible. View full abstract»

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  • Short-time spectral and autocorrelation analysis in the Walsh domain

    Page(s): 615 - 623
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    A short-time dyadic autocorrelation function (dacf) and a short-time Walsh energy spectrum of the first kind are defined in the Walsh-Fourier domain. The "natural" choice of the short-time functions does not lead to a Walsh-Fourier transform pair (dyadic Wiener-Khintchine theorem), and thus a second kind of short-time dacf and short-time Walsh energy spectrum are defined as the Walsh-Fourier transforms of the first kind. This leads to a meaningful and convenient Walsh transform pair between the first short-time Walsh energy spectrum and the second short-time dacf. The measurement procedures for both kinds of functions are discussed, and the mean values of these short-time functions are shown to be related to the corresponding long-time functions. View full abstract»

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  • A representation theorem and its applications to spherically-invariant random processes

    Page(s): 600 - 608
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    Thenth-order characteristic functions (cf) of spherically-invariant random processes (sirp) with zero means are defined as cf, which are functions ofnth-order quadratic forms of arbitrary positive definite matricesp. Everynth-order spherically-invariant characteristic function (sicf) is represented as a weighted Lebesgue-Stieltjes integral transform of an arbitrary univariate probability distribution functionF(cdot)on[0,infty). Furthermore, everynth-order sicf has a corresponding spherically-invariant probability density (sipd). Then we show that everynth-order sicf (or sipd) is a random mixture of anth-order Gaussian cf [or probability density]. The randomization is performed onnu^2 rho, wherenuis a random variable (tv) specified by theF(cdot)function. Examples of sirp are given. Relations to previously known results are discussed. Various expectation properties of Gaussian random processes are valid for sirp. Related conditional expectation, mean-square estimation, semMndependence, martingale, and closure properties are given. Finally, the form of the unit threshold likelihood ratio receiver in the detection of a known deterministic signal in additive sirp noise is shown to be a correlation receiver or a matched filter. The associated false-alarm and detection probabilities are expressed in closed forms. 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
Frank R. Kschischang

Department of Electrical and Computer Engineering