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Information Theory, IRE Transactions on

Issue 4 • Date July 1962

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Displaying Results 1 - 14 of 14
  • On the statistical detection problem for multiple signals

    Page(s): 274 - 280
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    The problem of detecting signals in noise is reviewed for the multiple input model, where each of the inputs can contain one of many possible signals. The detection procedure for this model becomes, in general, the testing of multiple hypotheses. Two detection criteria are examined for choosing among multiple hypotheses and it is found that, for both criteria, the decision is based on the likelihood functions for the various signals. Systems for computing likelihood ratios are examined in detail for the multiple input case. A multidimensional matched filter is considered and its relationship to the likelihood ratios is shown. Optimum signals are determined for the two-hypothesis problem. View full abstract»

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  • Learning Filters for Optimum Pattern Recognition

    Page(s): 280 - 285
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    An optimum adaptive system is obtained for the identification of pattern samples which are the sum of a fixed unknown signal, determined by the pattern of the sample, plus Gaussian noise. The system learns the unknown signals from a set of pattern samples, called learning samples, which have been identified with absolute certainty. The adaptive system is optimum in the sense that it computes the a posteriori probability of each pattern, given the sample to be recognized and the learning samples. The rate at which the probability of misrecognition of the learning system approaches the probability of misrecognition of the a posteriori probability computing system with a priori knowledge of the fixed signals is derived, for binary recognition, as a function of the number of learning samples. View full abstract»

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  • The Analysis of Certain Nonlinear Feedback Systems with Random Inputs

    Page(s): 285 - 291
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    A method is developed for the determination of the probability density function of the output of a nonlinear feedback system whose input is a random voltage of known statistical properties. The method of analysis is based upon the establishment of a mathematical model of the feedback system in such a way that the output is a Markov process. The transition probabilities of the Markov process are determined from the open-loop nonlinear characteristics of the system. From this model, the closed-loop output probability density function can be determined by the solution of an integral equation or, equivalently, by the solution of a set of simultaneous linear equations. As a consequence of the properties of stationary Markov chains, the same result can also be obtained by a process of successive matrix squaring operations. The method is then applied to a complex nonlinear feedback system, a frequency tracking loop whose function is to follow the center frequency of a narrow-band random signal in the presence of wide-band noise. In addition to the study of this system with a stationary input, a simple extension of the method is made which allows the effect of a particular time-variation of the input statistical properties to be studied. The results of a digital computer study of this system are presented and discussed. View full abstract»

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  • Efficient error-limiting variable-length codes

    Page(s): 292 - 304
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    Variable-length codes recursively defined by certain sequential machines are investigated. It is seen that the recursive definition may be used to control error propagation as well as to provide a conceptually simple decoding procedure. Furthermore, the variety of these codes is such that the theoretical minimum average code-word length can be approached quite closely for many distributions. Methods for obtaining efficient codes are discussed, and examples are given. View full abstract»

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  • Error probabilities for equicorrelated m -ary signals under phase-coherent and phase-incoherent reception

    Page(s): 305 - 314
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    Formulas for the error probabilities of equicorrelatedM-ary signals under optimum phase-coherent and phase-incoherent reception are derived in the form of previously untabulated single and double integrals. These integrals are amenable to computer evaluation for arbitraryM. Two modes of reception are considered. In the first, one ofMequal energy equiprobable signals is known to be transmitted during a symbol interval ofTseconds through a nonfading channel with additive white Gaussian noise. The receiver is assumed to be synchronized in time and frequency with the incoming signal, and reception is on a per-symbol basis. Furthermore, the cross-correlation coefficients between all the signals are equal. The probability of correct decision in both phase-coherent and phase-incoherent reception is derived exactly, as a function of the signal-to-noise ratio, the common cross-correlation coefficient, and the size of the signal setM. In the second mode of reception, the only difference is that a threshold is incorporated in the receiver. The probability of false detection and the probability of detection and correct decision are derived exactly for both phase-coherent and phase-incoherent reception as a function of the threshold level, the signal-to-noise ratio, the common cross-correlation coefficient, and the size of the signal setM. The method of reduction of multiple integrals presented here can be generalized, and may find application in other statistical studies in which the Gaussian density form is encountered under an integral. View full abstract»

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  • Statistical properties of the contours of random surfaces

    Page(s): 315 - 321
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    A random surface is a sample function of a random process{f(x, y)}depending on two real parameters. Examples of random surfaces would be: photographs or television pictures; topographic maps; atmospheric pressure charts; and the like. A number of statistical properties of the contours of such surfaces are derived. An application of the results to the problem of obtaining bounds on the information content of quantized random surfaces is outlined. View full abstract»

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  • Review of 'An Introduction to the Principles of Communication Theory' (Hancock, J. C.; 1961)

    Page(s): 331 - 332
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    Freely Available from IEEE
  • Review of 'Cybernetics, or Control and Communication in the Animal and the Machine' (Wiener, N.; 1961)

    Page(s): 332
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    Freely Available from IEEE

Aims & Scope

This Transactions ceased production in 1962. The current retitled publication is IEEE Transactions on Information Theory.

Full Aims & Scope