PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 1, Number 2, April–June, 1965
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CONTENTS

Some Cyclic Codes and a Scheme for Decoding by a Majority of Tests
V. D. Kolesnik and E. T. Mironchikov
pp. 1–11

Abstract—Cyclic codes permitting majority decoding are considered. A geometrical interpretation of majority decoding based on finite projective geometry is introduced. The use of this geometrical model facilitates the discovery of codes (similar to the Bose–Chaudhuri codes) with simple decoding schemes.

Evaluation of $\varepsilon$-Entropy of Random Variables for Small $\varepsilon$
Yu. N. Lin'kov
pp. 12–18

Abstract—An expression for the $\varepsilon$-entropy $H_\varepsilon(\xi)$ is derived for an $n$-dimensional random variable $\xi$ whose density distribution satisfies rather general conditions. An asymptotic expression for $H_\varepsilon(\xi)$ as $\varepsilon\to0$ is obtained for the case when the accuracy of transmission is given by a loss function $\rho(x,y)$ satisfying some weak conditions. Specific cases are examined.

A Method for Increasing the Reliability of Finite Automata
Yu. L. Sagalovich
pp. 19–25

Abstract—This article presents a method for increasing the reliability of finite automata by using noise-resistant codes and a state assignment that eliminates critical hazards for the case of automata with failure-resistant memory elements.

Asymptotic Properties of the Behavior of Elementary Automata in a Game
V. A. Volkonskii
pp. 26–39

Abstract—The game for automata outlined in [M.L. Tsetlin, Uspekhi Mat. Nauk, 1963, vol. 18, no. 4, pp. 3–28] can be described by a Markov chain whose states are the sets of states of all of the automata in the game. The behavior of simple automata with deep memories can be described approximately by a Markov chain whose states are the sets of outputs (and not states) of the players. This makes it possible to investigate analytically the asymptotic properties of specific games for automata, which we will demonstrate with reference to a game of two automata and a Goore game [V.A. Borovikov and V.I. Bryzgalov, Avtomat. Telemekh., 1965, vol. 26, no. 4, pp. 683–687].

Some Examples of Simulation of the Collective Behavior of Automata
S. L. Ginzburg and M. L. Tsetlin
pp. 40–46

Abstract—Problems associated with the reliability of the collective behavior of automata in a symmetric game are investigated. Simulation of the game-playing behavior of automata is used to solve the problem of distributing computer resources (in an elementary situation).

On the Synthesis of Microprogram Automata
V. G. Lazarev
pp. 47–59

Abstract—The class of microprogram automata is defined. The use of the language of algorithmic logical schemes (ALS) to write down the operation conditions of a microprogram automaton is proposed. Various realizations of ALS by microprogram automata are considered. A matrix method of combining identical ALS operators based on the compression of the state matrix of the automaton is described.

A Method for Assigning the Internal States of Asynchronous Finite Automata with Pulse-Potential Memory Elements
E. I. Peil
pp. 60–65

Abstract—The author consider a method for assigning the internal states of any asynchronous automaton with pulse-potential memory elements by using successive decomposition of automata. The method proposed makes it possible to eliminate inadmissible competition between internal elements and to weaken the relationship between the variables of logical converters.

Some Qualitative Investigations of Partial Access Circuits
Ya. Ya. Sedol and M. A. Shneps
pp. 66–71

Abstract—The paper deals with the choice of optimal partial access circuits depending on the intensity $\lambda$ of the calling rate for a given number of lines. Proved are certain principles, based on the loss probability as a function of $\lambda$ as $\lambda\to0$ and of $\lambda^{-1}$ as $\lambda\to\infty$, according to which the optimal partial access circuit should be chosen.

Optimal Connecting Structures in Information Systems
V. V. Kiryukhin
pp. 72–76

Abstract—The problem of distributing a limited number of identical communication channels in a system so as to maximize the reliability of the system as a whole is considered. The problem is formulated as a problem of nonlinear programming and is solved by known methods. Ranges of values of the system parameters are indicated in which one or other connecting structure is preferred.

On the Quantity of Information Processed by a Nonlinear System with Internal Noise
A. V. Skorokhod
pp. 77–83

Abstract—We investigate a random signal $x(t)$ passing through a system such that at the output there is obtained a process $y(t)$ related to $x(t)$ by a differential equation. The differential operator contains a term which depends on the internal noise of the system. It is assumed that this noise is Gaussian white noise, and the differential operator is a general nonlinear operator. Under the assumption that $x(t)$ is a Gaussian process, an expression is found for the quantity of information in the process $y(t)$ relative to $x(t)$. For the case when the relation between $x(t)$ and $y(t)$ is stationary, a rather simple expression for the rate of transmission is found.

A Topological Estimate of the Memory Capacity of a Multicycle Circuit
S. V. Makarov
pp. 83–86

Abstract—The author presents a method that, in a number of cases, makes it possible to obtain a nontrivial upper bound for the memory capacity of a multicycle system when only the circuit connection graph is known and the actual elements at the vertices of the graph are not.