PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Existence of Linear Concatenated Binary Codes with Optimal Correcting Properties
E. L. Blokh and V. V. Zyablov
pp. 271–276

Abstract—A concatenation encoding procedure in which the first- and second-stage codes are selected independently at random is discussed. It is shown that for certain constraints on the first-stage code transmission rate many of the concatenated codes so obtained have optimal correcting properties.

Codes Correcting Errors of Large Weight in Lee Metric
L. E. Mazur
pp. 277–281

Abstract—A class of cyclic codes correcting errors of large weight in Lee metric is constructed. Negacyclic codes are also discussed, which in some cases are more efficient than the well-known Berlekamp codes.

Arithmetic Burst-Error-Correcting Codes
V. M. Gritsenko
pp. 282–291

Abstract—Methods are discussed for the synthesis of arithmetic codes detecting and correcting specified burst error configurations. The reciprocity laws for power residues in circular algebraic fields are used to construct the codes. Examples are given in the synthesis of binary and ternary code generators.

Codes for PCM Transmission
V. M. Shtein and V. A. Shuvalov
pp. 292–294

Abstract—The capacity is determined for a signal-transmission channel in pulse-code-modulation (PCM) communication systems subject to the usual constraints for this transmission mode. A necessary condition is given for the realization of codes with maximum efficiency and with specified constraints, and examples of such codes are given.

Methods of Estimating the Parameters of Stationary Stochastic Signals with a Rational Spectrum
K. O. Dzhaparidze
pp. 295–301

Abstract—The estimation of the unknown parameters of a stationary Gaussian process with a rational spectral density is discussed.

Practical Recommendations for the Spectral Analysis of Stationary Gaussian Processes
V. G. Alekseev
pp. 302–306

Abstract—Estimates obtained for the spectral density of a stationary Gaussian discrete-time stochastic process on the basis of the differential properties of the estimated spectral density are discussed. It is shown that the rejection of nonnegative weighting functions makes it possible in many situations to diminish significantly the mean-square error of estimation. Recommendations are formulated for the selection of weighting functions in accordance with the number $n$ of readings, which is assumed to be finite.

Asymptotic Properties of Least-Squares Estimates for Regression Coefficients
A. Ya. Dorogovtsev
pp. 307–313

Abstract—The asymptotic normality of least-squares estimates for the coefficients of a linear combination of stochastic functions is verified, along with the existence and convergence of the moments of the estimates. Estimates are formulated from observations of stochastic functions and a linear combination with additive “noise.” The stochastic functions and “noise” are assumed to be independent Gaussian processes.

A Model of Optimal Behavior in an Unknown Medium
A. V. Vasil'ev and A. V. Koganov
pp. 314–320

Abstract—A model of adaptation to an unknown medium in which the learning system has several actions is analyzed, where the medium yields a fixed payoff after each action. The system has a finite learning time and must maximize the sum of the payoffs in that time. The medium is not known beforehand, but a class of media is specified. The given model can be treated as a game in which the strategies are behavior algorithms for the system (which remembers the previously obtained responses of the medium) and the specification, prior to the initiation of operation of the system, of a certain medium from the admissible class of media; the latter strategy is identified with “Nature” as a player. The minimax and maximin points are investigated for the game, and a saddle point is found for a class of mixed strategies.

Asymptotic Enlargement of the States of Certain Stochastic Automata
A. R. Rotenberg
pp. 321–324

Abstract—Let a homogeneous Markov chain having a finite number of states and describing a stochastic automaton depend on a parameter $\varepsilon$ in such a way that the transition probabilities are continuous functions of $\varepsilon$ for $\varepsilon=\varepsilon_0$ and the set of states of the chain for $\varepsilon=\varepsilon_0$ decomposes into the union of $k>1$ ergodic sets $X_1,\ldots,X_k$. A family of Markov processes describing a random walk of the original Markov process on the sets $X_1,\ldots,X_k$ as $\varepsilon\to\varepsilon_0$ is constructed.

Explicit Constructions of Concentrators
G. A. Margulis
pp. 325–332

Abstract—In the solution of certain problems of switching and coding theory it is required to synthesize structures similar to what in the present article are called concentrators. While the existence of concentrators is easily proved on probabilistic grounds, their explicit construction proves difficult. The theory of group representations is used to solve the problems of the explicit construction of concentrators.

Cyclic Shift Operation for Languages
A. N. Maslov
pp. 333–338

Abstract—The closure of context-free languages and languages generated by $E$-grammars under a series of transformations specified by productions is demonstrated.

Optimum Detection of an Optical Signal
A. N. Mart'yanov and A. G. Sheremet'ev
pp. 339–340

Abstract—The dependence of the limit probability of the average error in a binary quantum communication channel on the average signal energy (number of photons) and the value of the threshold is calculated. The existence of an optimum threshold that varies discretely with the variation of the signal energy is graphically demonstrated.

Derivation of Switching Functions for the Storage Elements of a Finite Automaton with State Encoding on the Columns of a Flow Table
V. V. Sapozhnikov and Vl. V. Sapozhnikov
pp. 341–342

Abstract—A simple formula is proposed for the derivation of logic functions for the switching of storage elements of an asynchronous finite automaton with encoding of its states on the column of a flow table.

Implementation of Symmetric Functions in Homogeneous Media
E. I. Petrov
pp. 343–345

Abstract—Two variants of a homogeneous medium are discussed. In the first variant the complexity of the implementation of an arbitrary symmetric function has order $C_1n^2$, where $C_1=1/2$; in the second variant it has order $n\log_2n(1+o(1))$. Thus, a bound is obtained on the complexity that can be realized by modeling of the schema of a symmetric function in a homogeneous medium by the method of Barzdin' [Probl. Kibern., vol. 17, Nauka, Moscow, 1966, pp. 5–26].

INDEX
pp. 347–353