PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 2, Number 2, April–June, 1966
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CONTENTS

Optimal Coding in the Case of Unknown and Changing Message Statistics
B. M. Fitingof
pp. 1–7

Abstract—A coding method is proposed which is independent of the message probabilities and permits a compression of the messages corresponding to their redundancy, without a knowledge of the statistical laws responsible for this redundancy. Sufficient conditions are formulated for optimality of coding in this sense. It is pointed out how results of this kind may be generalized to a noisy channel, in the sense of obtaining optimal methods of transmitting over such channel messages which are independent of the statistics of the message source.

Estimate of the Complexity of Sequential Decoding of Random Tree Codes
V. N. Koshelev
pp. 8–20

Abstract—An algorithm of a modification of sequential decoding is described, and estimates are obtained characterizing the complexity and reliability of the method.

On the Convolution of Information in a Classical Probability Scheme
A. Yu. Lev, D. P. Mil'man, and V. D. Mil'man
pp. 21–28

Abstract—Two problems are considered connected with the transformation of information by a finite memoryless automaton with $n$ inputs and $l$ outputs ($l\lt n$). Properties of the input alphabet are indicated which give the minimum information dispersion. Simple rules are found for the approximate solution of the problem of minimizing the information dispersion with an estimate of the error.

Arithmetic Codes with Determination of the Place of Error
pp. 29–32

Abstract—This paper investigates the possibility of using the correcting ability of arithmetic separable codes generated by two simple moduli to determine the position of an erroneous group of digits of a message. Estimates are obtained for the length of a group, the number of errors occurring in it, and the number of information digits of the code. Numerical results are given.

Zero-Sum Games for Two Asymptotically Optimal Sequences of Automata
V. I. Krinskii
pp. 33–41

Abstract—The author considers zero-sum games for two automata whose memory grows without limit. It is proved that for a relatively large class of asymptotically optimal sequences of automata, the limiting payoff always lies between the upper and lower values of the game. Inside these limits, the payoff depends only weakly on the matrix of the game and is determined primarily by the structures of the playing automata.

Noise-Resistant State Assignment Method for Asynchronous Finite Automata
Yu. L. Sagalovich
pp. 42–47

Abstract—The author presents a method for assigning the internal states of an asynchronous finite automaton so as to stabilize the automaton relative to failures and critical competition between internal elements. The method allows for the logical structure of the automaton and is effective when the number of input signals is small.

Photon Channels with Small Occupation Numbers
L. B. Levitin
pp. 48–56

Abstract—We consider a photon channel in which the transmitter sets the average occupation numbers of the field oscillators, while the receiver records a certain portion of the photons emitted by the transmitter. If the average numbers of photons recorded are peak- or average-limited, and are also small compared to unity, then the transmission capacity may be calculated to asymptotic accuracy for quite general conditions based on the transition probabilities, but independent of their specific form. It is demonstrated that, contrary to general opinion, fluctuations in the numbers of photons plays a minor role in the case of small occupation numbers, and the transmission capacity tends toward that of the ideal channel.

Statistical Properties of Polarization Parameters of Radio Signals and Noise
A. P. Rodimov
pp. 57–62

Abstract—To estimate the noise stability of communication systems in which polarized manipulation of signals is used, it is necessary to know the statistical structure of partially polarized waves. Probability density distributions are obtained for the geometric parameters of the polarization ellipse of a quasimonochromatic partially polarized wave for a circular and linear basis of representation of this wave. It is shown that for practical applications the more convenient one to use is the density distribution obtained from the circular basis of representation.

An Inverse Problem in Information Theory
V. Ya. Rozenberg and N. A. Rubichev
pp. 63–64

Abstract—Within the framework of an arbitrary preassigned probability distribution which ensures the maximum entropy, a problem on the determination of a set of constraints is investigated.

An Estimate of $d_{\min}$ for Cyclic Codes
V. I. Korzhik
p. 65

Abstract—An upper bound for $d_{\min}$ based on the properties of the generating polynomial is found. This may be useful for improving Bose–Chaudhuri estimates.

The Calculation of the Loss Probability in Schemes Constructed from Complete Access Groups
G. L. Ionin and Ya. Ya. Rachevskii
pp. 66–69

Abstract—We consider symmetric schemes with losses constructed from complete access groups, in the case of the arrival of a simple stream and of an Engset stream with an exponential serving law. We apply to the expressions for the loss probability some combinatorial relations which considerably simplify their form, permitting them to be computed on a digital computer. Numerical examples are given.