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Information Theory, Transactions of the IRE Professional Group on

Issue 4 • Date September 1954

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Displaying Results 1 - 18 of 18
  • Preface

    Page(s): 1
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  • Binary coding

    Page(s): 23 - 28
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  • Error-free Coding

    Page(s): 29 - 37
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  • Information, organization and systems

    Page(s): 64 - 66
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  • Simulation of self-organizing systems by digital computer

    Page(s): 76 - 84
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    A general discussion of ideas and definitions relating to self-organizing systems and their synthesis is given, together with remarks concerning their simulation by digital computer. Synthesis and simulation of an actual system is then described. This system, initially randomly organized within wide limits, organizes itself to perform a simple prescribed task. View full abstract»

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  • A study of ergodicity and redundancy based on intersymbol correlation of finite range

    Page(s): 85 - 92
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    Some of the basic concepts of information theory are critically reviewed in the light of a generalized formulation of the theory of Markoff's chains, in which the initial and final states are sequences of symbols of different lengths, and occurrence of symbols is governed by inter-symbol correlation probability of finite range. In particular, the conditions of ergodicity and the structure of "ergodic subsets" of sequences of arbitrary length are carefully discussed. A mathematical method is developed to determine the "range" and "strength" of inter-symbol correlation. A brief summary of the content is given at the end of Section 1. View full abstract»

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  • Multivariate information transmission

    Page(s): 93 - 111
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    A multivariate analysis based on transmitted information is presented. It is shown that sample transmitted information provides a simple method for measuring and testing association in multidimensional contingency tables. Relations with analysis of variance are pointed out, and statistical tests are described. View full abstract»

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  • Modern statistical approaches to reception in communication theory

    Page(s): 119 - 145
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    When reception in the theory of communication is recognized as a problem in statistical inference, system design and system analysis appear as the counterparts of designing and evaluating statistical tests. This paper discusses the optimum properties of designs based on statistical decision theory from the risk point of view, and from that of information theory. Connections between risk and information loss are established, which result in a unified theory of system design. This includes Minimax methods capable in principle of handling all degrees of a priori knowledge of signal and noise statistics, new methods for comparing actual and ideal systems for the same purpose, and new interpretations of previously used formulations as special cases of the more general theory. Both detection and extraction of signals in noise are considered, the former as a problem of testing statistical hypotheses and the latter as one of estimating parameters. Formulation of the general reception problem as a decision operation is followed by a summary of statistical decision theory from the risk point of view, with some examples of Bayes and Minimax tests and optimum classes of decision rules. Applications to detection show the optimum nature of likelihood ratio receivers as a class, and indicate methods for defining the minimum detectable signal and for comparing system performance. As an illustration, curves of Bayes and Minimax risk are given for detection of a pulsed carrier in noise. Applications to extraction show the nature of optimum extraction and the roles of the mean square error and maximum likelihood criteria from the more general point of view of risk theory. Conditions under which information loss is an extremum in detection and extraction are established, and information loss itself as a criterion of performance is compared with that of the risk measure. View full abstract»

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  • A non-linear prediction theory

    Page(s): 146 - 162
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  • The theory of signal detectability

    Page(s): 171 - 212
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    The problem of signal detectability treated in this paper is the following: Suppose an observer is given a voltage varying with time during a prescribed observation interval and is asked to decide whether its source is noise or is signal plus noise. What method should the observer use to make this decision, and what receiver is a realization of that method? After giving a discussion of theoretical aspects of this problem, the paper presents specific derivations of the optimum receiver for a number of cases of practical interest. The receiver whose output is the value of the likelihood ratio of the input voltage over the observation interval is the answer to the second question no matter which of the various optimum methods current in the literature is employed including the Neyman - Pearson observer, Siegert's ideal observer, and Woodward and Davies' "observer." An optimum observer required to give a yes or no answer simply chooses an operating level and concludes that the receiver input arose from signal plus noise only when this level is exceeded by the output of his likelihood ratio receiver. Associated with each such operating level are conditional probabilities that the answer is a false alarm and the conditional probability of detection. Graphs of these quantities called receiver operating characteristic, or ROC, curves are convenient for evaluating a receiver. If the detection problem is changed by varying, for example, the signal power, then a family of ROC curves is generated. Such things as betting curves can easily be obtained from such a family. The operating level to be used in a particular situation must be chosen by the observer. His choice will depend on such factors as the permissable false alarm rate, a priori probabilities, and relative importance of errors. With these theoretical aspects serving as an introduction, attention is devoted to the derivation of explicit formulas for likelihood ratio, and for probability of detection and probability - of false alarm, for a number of particular cases. Stationary, band-limited, white Gaussian noise is assumed. The seven special cases which are presented were chosen from the simplest problems in signal detection which closely represent practical situations. Two of the cases form a basis for the best available approximation to the important problem of finding probability of detection when the starting time of the signal, signal frequency, or both, are unknown. Furthermore, in these two cases uncertainty in the signal can be varied, and a quantitative relationship between uncertainty and ability to detect signals is presented for these two rather general cases. The variety of examples presented should serve to suggest methods for attacking other simple signal detection problems and to give insight into problems too complicated to allow a direct solution. View full abstract»

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  • The human use of information--I: Signal detection for the case of the signal known exactly

    Page(s): 213 - 221
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    A theory of visual detection is developed, based on the model provided by the theory of signal detectability,2 and, more generally, by the theory of statistical decision. Two experiments are reported which test some predictions of the theory for the case of the signal-known-exactly. These experiments demonstrate that the human observer tends toward optimum behavior, where optimum behavior is defined as that behavior which maximizes the expected gain from the decision. Their results show the proportion of correct detections to be dependent upon the proportion of false alarms; they indicate that neural activity is a power function of signal intensity. The data also demand a re-evaluation of the threshhold concept. Predictions are made for the data obtained using two different methods of response, forced-choice end yes-no, and the internal consistency of the theory is demonstrated. The predictions of the theory are compared with contrasting predictions of conventional sensory theory; the data are also related to conventional theory. View full abstract»

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  • The human use of information--II: Signal detection for the case of an unknown signal parameter

    Page(s): 222 - 227
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    Two specific cases of signal detection involving uncertainty in the frequency of a sound signal are compared with the case of the signal-known-exactly. In the first case the signal is either of two known frequencies; in the second case the signal is any frequency within a given range. It is suggested that detection behavior that is optimal for the three cases requires a deal mechanism: a combination of a wide-open receiver end a panoramic receiver. Evidence is presented that supports the existence of such a mechanism. Estimates of the bandwidth end seen-rate of the receiver are included. View full abstract»

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Aims & Scope

This Transactions ceased production in 1954. The current retitled publication is IEEE Transactions on Information Theory.

Full Aims & Scope