PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Ordering of Information Criteria for Discrimination of Probability Distributions
A. A. Amosov and V. V. Kolpakov
pp. 245–250

Abstract—The authors introduce an axiom system that characterizes so-called divergences, i.e., a class of information measures for discriminating probability distributions with specified properties. A general analytic form for the functional in in question is given. A number of inequalities are established between the most widely used information criteria for discriminating probability distributions, these being linear functions of the divergences.

Data Transmission over a Discrete Channel with Feedback. Random Transmission Time
M. V. Burnashev
pp. 250–265

Abstract—Asymptotically optimal limits are obtained for the mean transmission time for specified error probability and the number of possible messages. As a corollary of these results, the author gives an optimal reliability function for the channel in question (with noiseless feedback and a Markov instant of decision-making).

On One General Bound for Code Volume
E. M. Gabidulin and V. R. Sidorenko
pp. 266–269

Abstract—An inequality if obtained that yields an upper bound on the volume of a code with specified distance for any metric.

On One Approach to the Decoding of Bose–Chaudhuri–Hocquingham Codes
E. F. Skvortsov and Yu. V. Sulimov
pp. 270–277

Abstract—As applied to the decoding of Bose–Chaudhuri–Hocquingham codes, the authors consider methods of solving a system of linear equations with Hankel matrix of coefficients for the unknown polynomials that result from division in accordance with Euclid’s algorithm and are generated from the determining elements of this system. The method is compared with other available methods in terms of the amount of computation involved and complexity of implementation.

On Bounds on the Number of Code Words in Binary Arithmetic Codes
G. A. Kabatyanskii
pp. 277–283

Abstract—Improvements are obtained for the asymptotic bounds for binary arithmetic codes (analogous to the Hamming and Gilbert bounds). It is shown that there exist many different classes of $AN$-codes on which the limit of “exhaustion” (Gilbert bound) is achieved for arithmetic codes. A similar result is obtained for additive truncated cyclic codes.

Cyclic Code that Corrects Double Bursts of Arithmetic Errors
G. L. Tauglich
pp. 284–289

Abstract—A class of cyclic $AN$-codes that correct double bursts of arithmetic errors is proposed. These codes are analogs of Bahl–Chien codes. A simple decoding algorithm is examined.

On Optimum Generators of Convolutional Codes with Rate $R=1/2$
I. N. Karbovskii and G. M. Karbovskaya
pp. 290–296

Abstract—Results are given of a search for optimum (with respect to $d_{\min}$) generators of convolutional codes for a rate $R=1/2$, up to a code limitation $n=30$, and principles for setting up search algorithms are described.

Sequences of Maximum Length as Automaton State Codes
Yu. L. Sagalovich
pp. 296–299

Abstract—It is shown that sequences of maximum length over an arbitrary finite field are an automaton state code for one model of hazards in multipositional delay elements of automata.

One-Dimensional Automaton Networks with Monotonic Local Interaction
G. A. Gal'perin
pp. 299–310

Abstract—The behavior of strings that are infinite in both directions and consist of identical finite automata is investigated. The states of a finite number of adjacent automata provide the input for each automaton. The states of a finite number of adjacent automata provide the input for each automaton. Monotonic interaction of automata is considered. An effective means of predicting the following two aspects of the behavior of such systems is given; a) are they “wash-out” systems and b) how do the states of systems of automata with long initial files vary as $t\to\infty$.

Loopless Decomposition of Probabilistic Automata
A. Kh. Giorgadze, G. E. Yakobson, and L. V. Burshtein
pp. 310–315

Abstract—Probabilistic automata are represented as a Bernoulli generator and corresponding deterministic automaton in series. Necessary and sufficient conditions for loopless decomposition of probabilistic automata are found. If the decomposition in question holds for the deterministic part of the automaton.

Isthmus Structure in a Summary Matroid
V. P. Polesskii
pp. 315–322

Abstract—A summary matroid of the form $M^k=M+\ldots+M$ ($k$ times) is considered, where $M$ is an arbitrary matroid on finite set $E$. Subset $F\subset E$ on which equality is attained in the Nash–Williams formula for determining the rank of matroid-sum $M^k$ is called a $k$-extremal subset. The article investigates the class of $k$-extremal sets of matroid $M$.

Formalization of the Problem of Complexity of Code Specification
L. A. Bassalygo
pp. 322–324

Abstract—The article offers one possible rigorous formulation of the problem of simple specification of an asymptotically good sequence of codes and a corresponding interpretation of the results of Gilbert, Varshamov, and Zyablov.

Determination of Cyclic Representatives of Cyclic Codes
A. P. Kurdyukov
pp. 325–326

Abstract—In this paper we offer an algorithm for finding cyclic representatives of cyclic codes over $GF(p)$.

INDEX
pp. 327–333