PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 16, Number 2, April–June, 1980
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CONTENTS

Asymptotic Behavior of the Capacity of a Continuous Channel with Large Smooth Noise
V. V. Prelov
pp. 81–92

Abstract—The article investigates the asymptotic behavior of the capacity of a memoryless channel with independent additive noise, under the assumption that the average signal power of the input tends to zero. It is assumed that the distribution density of the noise is a smooth function. It is shown that the order of the asymptotic form of the capacity depends strongly on whether there exists a set of nonzero measure on which the distribution density of the noise becomes zero. If there is no such set, the order of the asymptotic form depends on the rate of decrease of the noise distribution density at infinity.

Lower Bound for Ensemble-Average Error Probability for a Discrete Memoryless Channel
A. G. D'yachkov
pp. 93–98

Abstract—The article obtains a lower asymptotic bound for the average error probability over a standard ensemble of codes for the case of decoding using a list of fixed length $L\ge 1$ for a discrete memoryless channel. For all coding rates, this bound establishes the optimality of the exponent of the familiar Gallager upper bound [E.G. Gallager, Information Theory and Reliable Communication, Wiley, 1968].

Bounds on Volume of Linear Codes with Unequal Information-Symbol Protection
G. L. Katsman
pp. 99–105

Abstract—Linear codes with unequal information-symbol protection are investigated. Upper and lower bounds for the volume of these codes are derived.

Distribution of Weights of Irreducible Cyclic Codes and Strongly Regular Graphs
S. M. Dodunekov and V. I. Yorgov
pp. 105–110

Abstract—Irreducible cyclic codes are considered. Some known results are proved by a new method. The number of vectors of weight $2$ in the dual code of an irreducible cyclic code is computed, and it is shown that projected irreducible cyclic codes exist. The associated strongly regular graphs are new.

On Error Burst Correction Using Binomial Codes
G. L. Tauglikh
pp. 111–120

Abstract—Classes of binary cyclic and linear binomial codes are constructed. A simple decoding algorithm for linear binomial codes is considered; it is based on successive application of majority decoding algorithms for cyclic binomial codes. It is shown that linear binomial codes are not inferior in terms of their parameters to many known error-burst-correcting codes, with the exception of optimal codes.

Optimal Filtering of Square-Integrable Signals in Gaussian Noise
M. S. Pinsker
pp. 120–133

Abstract—Expressions are considered for the optimal mean-square error $\delta^2$ of restoration of signals from $\mathrm L_2(0,T)$ in Gaussian noise $\xi_1(t)$; the exact asymptotic form of $\delta^2$ is obtained for the case in which $\xi_1(t)=\varepsilon\xi(t)$, $\varepsilon^2\to 0$, while $\theta(t)\in\mathfrak{A}$, $\mathfrak{A}$ is an ellipsoid in $\mathrm L_2(0,T)$, and also when $T\to\infty$. It is shown that the linear estimates are asymptotically optimal.

Resolution of a Conflict of Known Multiplicity
B. S. Tsybakov
pp. 134–144

Abstract—The problem of resolving a conflict of known multiplicity $k$ is considered. Recursive conflict-resolution strategy is proposed and investigated. It is shown that this strategy is optimal for $k=2$ and $k=3$. A comparison is made with the conflict-resolution algorithm of [B.S. Tsybakov and V.A. Mikhailov, Probl. Peredachi Inf., 1978, vol. 14, no. 4, pp. 32–59].

Switching Systems with Allowance for Repeated Calls
G. I. Falin
pp. 145–151

Abstract—The article considers an extensive class of queueing systems with repeated calls that incorporate non-full-access arrangements, various communications networks, and so forth. For systems of this type, general asymptotic formulas are obtained for the fundamental probability characteristics under low system load, and a number of general qualitative properties of the servicing process are established.

Convergence to Equilibrium in a Polylocus Polyallele Population with Additive Selection
L. A. Kun and Yu. I. Lyubich
pp. 152–161

Abstract—The article considers an infinite panmix autosomal population with discrete nonoverlapping generations that is haploid on the gamete level and diploid on the zygote level. In the population there is additive selection with respect to any number of autosomal loci with any number of alleles at each locus; there are no mutations. It is shown that if the fitnesses at each locus are positive, then the population tends to equilibrium regardless of its initial state. This had been established earlier only for two diallele loci with preference of heterozygotes at each one [S. Karlin and M.W. Feldman, J. Appl. Probab., 1970, no. 7, pp. 262–271].

BRIEF COMMUNICATIONS
(available in Russian only)

On a Construction of Linear Codes with Unequal Protection of Information Symbols
I. M. Boyarinov
pp. 103–107 (Russian issue)

Abstract—A construction based on the combination of generator matrices of codes is proposed and analyzed, which allows us to construct new linear codes with unequal information-symbol protection. In this set of codes, a class of asymptotically optimal codes is found.

Capacity of an Arbitrary Channel with Defects
S. I. Gelfand and M. S. Pinsker
pp. 108–109 (Russian issue)

Abstract—An expression for the capacity of a channel with defects is given.