PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 24, Number 3, July–September, 1988
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CONTENTS

Probabilistic Decoding of Nonbinary Majority Decodable Codes
V. D. Kolesnik and S. L. Portnoy
pp. 173–184

Abstract—Probabilistic decoding of nonbinary majority decodable codes is considered. An optimal decoding rule is formulated and a method of computing the check weight multipliers is described. Upper and lower bounds are derived on the probability of decoding error in arbitrary semicontinuous and discrete output-symmetric channels. As an example, we consider the characteristics of majority-logic decoders in combination with orthogonal signals in a channel with white Gaussian noise.

Delayed Epsilon-Entropy for a Gaussian Message Corrupted by Noise
A. K. Gorbunov and M. S. Pinsker
pp. 185–189

Abstract—We introduce the notion of delayed epsilon-entropy (rate-distortion function) for a Gaussian message corrupted by Gaussian noise and study its properties.

On Characterization and Existence Conditions of Codes Meeting the Varshamov–Griesmer Bound
V. N. Logachev
pp. 189–204

Abstract—We consider the structure of anticode generator matrices for binary linear codes meeting the Varshamov–Griesmer bound. Necessary and sufficient conditions of existence of these codes are derived for a number of different dimensions and code distances.

Nonbinary Codes with Distances $4$, $5$, and $6$ of Cardinality Greater than the BCH Codes
I.I. Dumer
pp. 205–214

Abstract—We construct linear $q$-ary codes with distances $4$, $5$, and $6$ in which the number of check symbols for $q\gt 4$ increases with the increase of code length more slowly than for BCH codes. Decoding algorithms are considered.

Nonparametric Estimation of a Linear Functional of the Regression Function for a Given Observation Design
Yu. I. Pastukhova and R. Z. Khas'minskii
pp. 215–223

Abstract—In [Probl. Peredachi Inf., 1986, vol. 22, no. 3, pp. 43–61] we considered nonparametric estimation of a linear functional of the regression function for a variable observation design. In this paper, we consider the same problem for a given observation design $(t_1,\ldots,t_n)$ such that $t_1,\ldots,t_n$ are independent identically distributed random variables with a known distribution density. We obtain a lower bound on estimation accuracy and, under relatively light assumptions on the set of allowed regression functions, construct an estimator that attains this bound.

Locally Asymptotic Minimax Estimation of One Functional of an Unknown Distribution
M. B. Nevel'son and I. V. Shafranskii
pp. 224–237

Abstract—We consider nonparametric estimation of one functional of an unknown distribution using an independent sample from this distribution. We construct a procedure similar to the Fisher accumulation method, which is asymptotically optimal in the minimax sense in various classes of loss functions.

Some Markov Chain Functions and Associated Nonsymmetric Random Walks with Absorbing Barriers
V. D. Kolesnik and B. D. Kudryashov
pp. 237–245

Abstract—We consider random walks controlled by an ergodic Markov chain. For the case where the expected one-step increment is nonzero, we obtain upper and lower bounds on the mean first-arrival time of the random walk with absorbing barriers. These bounds are close to the bounds obtained from Wald's identities for independent increments.

Computing Packet Delay for Some Random Multiple Access Stack Algorithms
N. D. Vvedenskaya and B. S. Tsybakov
pp. 246–253

Abstract—Packet delays for two RMA stack algorithms are computed and compared for the case of a feedback channel with errors. The range of parameters when one algorithm is better than the other is identified.

A Comment on the Paper of Kasami, Lin, Wei, and Yamamura, “Coding for the Binary Symmetric Broadcast Channel with Two Receivers”
L. A. Bassalygo and M. S. Pinsker
pp. 253–257

Abstract—We show that for a degrading binary symmetric broadcast channel with two components, the representation of the code as the direct sum of two codes of which only one is linear does not reduce the known admissible rate region.

On a Model of Associative Memory
V. V. Rykov and A. G. D'yachkov
pp. 257–260

Abstract—We consider the Boolean model of associative memory using neuron networks, as proposed by Palm [Biol. Cybern., 1980, vol. 36, no. 1, pp. 19–31]. Our previous results from the theory of disjunctive codes [Probl. Peredachi Inf., 1983, vol. 12, no. 4, pp. 229–244] are applied to derive exchange relationships between the model parameters and the size of written information.