PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 6, Number 2, April–June, 1970
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CONTENTS

New Results in the Theory of Simultaneous Optimum Detection and Estimation of Signals in Noise
D. Middleton and R. Esposito
pp. 93–106

Abstract—Earlier work of the authors [IEEE Trans. Inf. Theory, 1968, vol. 14, no. 3, pp. 434–444] is extended to the sequential or adaptive decision-making processes involving optimum signal detection and extraction, when exact knowledge as to the signal’s presence is unavailable at any given stage. In particular, the uncoupled cases are developed, and extension to the coupled cases is considered. These problems are typical of many “multidecision” situations occurring in adaptive processing, unsupervised learning, and pattern recognition. Explicit development of the theory here is restricted to time-invariant parameters and deterministic signal waveforms. An improved approach to the single-decision problem of joint detection and estimation is also given, and illustrated by an example of coherent signal detection, and amplitude estimation, in which optimum and sub-optimum performance is compared. Various distinctions between different classes of estimators that are possible in the adaptive case are explicitly discussed, including their convergence properties. The paper concludes with a summary of the results obtained and suggestions for future work.

Comments on Automata in Random Media
M. E. Hellman and T. M. Cover
pp. 107–114

Abstract—In this paper several approaches are presented to the problem of optimizing the design of a finite automaton for the hypothesis testing problem and the related two-armed bandit problem. It is noted that the two-armed bandit formulation is equivalent to a fundamental question raised by Tsetlin and his colleagues concerning the unknown optimal design of automata in random media. A solution of this problem is given by appropriate application of other work which is presented in condensed and unified form here. Closely related problems involving Markov switching hypotheses and multiple hypotheses remain unsolved.

Retention and Maximization of Information in Data Reduction
I. Vajda
pp. 115–121

Abstract—This paper considers the following problem: to minimize, with respect to a class of reductions satisfying some requirements as regards “capacities,” etc., the Bayesian or average risk which increases in data reduction, or to find a simple criterion allowing us to decide whether the drop in the quality of the solution for a given reduction is permissible. The paper offers an estimate of the increase in the average risk due to data reduction in terms of the average number of observations and the generalized Shannon entropy of individual observations.

Asymptotic Behavior of the Capacity of a Continuous Channel with a Large Amount of Noise
V. V. Prelov
pp. 122–135

Abstract—We consider a channel with independent additive noise, whose output signal $\eta=\xi+\zeta$, where $\xi$ is the input signal and $\zeta$ is the noise. Assuming that the average power of the input signal tends to zero $M|\xi|^2\leq\varepsilon\to 0$, and with certain conditions imposed on the distribution density of the noise $\zeta$, we determine the asymptotic behavior of the channel capacity. We also obtain the form of the asymptotically optimum distribution at the channel input.

Low-Capacity Channels and Symbol-by-Symbol Transmission
R. Z. Khas'minskii
pp. 136–143

Abstract—Symbol-by-symbol transmission over channels with large amounts of additive noise and feedback is considered. The asymptotically optimum transmission method is constructed for the case of fairly regular noise.

G. Tartara
pp. 144–147

Abstract—In this note we consider the efficiency of channel use in asynchronous address systems with many outputs, when binary code words are used as addresses of various output subchannels.

Encoding and Decoding Cyclic Code Groups
N. Abramson
pp. 148–154

Abstract—In this paper we show that the product of two cyclic codes with block lengths relatively prime can be described in terms of two interlaced codes. Using this description we provide an improved characterization of the generating polynomial of the product code in terms of the generating polynomials of the two original codes. We then show that the product code and seven other codes related to the product code (called a code group) can all be obtained from four canonical polynomials which may be calculated using the Euclidean Algorithm. These results then lead to simple encoder realizations for cyclic code groups and to a decoding algorithm, called cascade decoding.

Analysis of a Decision-Directed Receiver for a Markov Sequence with Unknown Transition Probabilities
S. C. Schwartz and L. D. Davisson
pp. 155–158

Abstract—In many applications, such as in video transmission, the data can be modeled as a Markov sequence and the performance of the detector improved through incorporation of the transition probabilities into the threshold. The difficulty in implementation is that the transition probabilities are often unknown or known imprecisely. In this paper, a decision-directed receiver (DDR) is analyzed which estimates these transition probabilities. This is an extension of recently reported work where the data consisted of an independent sequence with unknown priors.

Upper Bounds for the Error Probability for Channels with Feedback
K. Sh. Zigangirov
pp. 159–163

Abstract—The author derives upper bounds for the attainable error probability in block transmission over binary symmetrical and Gaussian channels with feedback.

Lower Bounds for the Reliability of Block Codes in Binary Channels with Noisy Feedback
V. N. Koshelev
pp. 164–168

Abstract—The author compares the reliability of information transmission in a repeat-request scheme and in a scheme with control feedback, assuming that the capacity of the reverse channel is restricted.

One Method of Describing Random Fields with a Discrete Argument
M. B. Averintsev
pp. 169–175

Abstract—The article considers a method of describing a random field by using conditional probabilities written in the form of exponents similar to the Gibbs distributions of statistical physics. It is shown that this method is applicable to Markov fields with positive conditional probabilities.

Optimum Noncoherent Reception in Channels with Fluctuation and Concentrated Noise
A. A. Sikarev
pp. 176–184

Abstract—The author obtains and analyzes the decision rules for one-shot noncoherent reception in discrete-information transmission systems; the rules are optimum under the action of fluctuation noise and concentrated interference which can be approximated by the interfering-signal model. Primary attention is given to the case of Rayleigh fading of signal and noise. Expressions are obtained for the error probability, and the noise stability of such systems is compared with that of a system which is optimum for a channel with only normal fluctuation noise.

Error-Correcting Codes in Channels with Relative Phase Manipulation
A. E. Neifakh
pp. 185–190

Abstract—The article proposes a method of analysis which makes it possible to allow for the effect of error multiplication in RPM and to select derivative codes whose correcting capacity can be effectively used in communications channels. Encoding and decoding procedures are developed for derivative codes, which are of approximately the same degree of complexity as the corresponding procedures for cyclic codes. Conditions are determined under which the code corrects the same number of single errors and of combinations of double adjacent errors.