PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Bounds on Volume of Error-Correcting Codes in a Broadcast Channel (Generalized Blackwell Channel)
L. A. Bassalygo and M. S. Pinsker
pp. 163–174

Abstract—Bounds of Varshamov–Gilbert type are obtained for the volume of error-correcting codes in broadcast channels in which one of the components is deterministic.

On Extremal Polynomials Used in Bounds of Code Volume
V. M. Sidel'nikov
pp. 174–186

Abstract—Delsarte [Philips Res. Rep., 1972, vol. 27, pp. 272–289] found a method of obtaining upper bounds for the volume of a code with specified code distance. The bound obtained via this method is defined by polynomial $H(x)$ that possesses certain particular properties. In this paper it is shown that the polynomials given in [V.I. Levenshtein, Proc. 7th All-Union Conf. on Coding Theory and Information Transmission, vol. 2, Moscow–Vilnius, 1978, pp. 103–108] are extremal for Delsarte’s method.

Hierarchical Coding of Discrete Sources
V. N. Koshelev
pp. 186–203

Abstract—The author proves a generalization of the source coding theorem to the case in which the same message must be represented in the form of several copies with different error levels.

Generalized $\delta$-Codes and Construction of Hadamard Matrices
S. S. Agayan and A. G. Sarukhanyan
pp. 203–211

Abstract—The article investigates the problem of constructing Hadamard matrices on the basis of codes. Recursive formulas are obtained for constructing generalized $\delta$-codes which are used as a basis, in particular, for constructing $T$-matrices and Baumert–Hall arrays of new orders.

Second-Order Asymptotically Minimax Estimates for the Mean of a Normal Population
P. E. Berkhin and B. Ya. Levit
pp. 212–229

Abstract—The paper considers the classical problem of estimating a multidimensional parameter against a background of additive Gaussian noise. The first nontrivial term of the asymptotic expansion of the minimax risk of the estimate of a parameter belonging to bounded region $G\subset\mathbb{R}^k$ with piecewise-smooth boundary is investigated. Its relationship to the first eigenvalue of the Dirichlet problem in $G$ for some elliptic differential operator is established. The form of the second-order asymptotically minimax estimate is given.

Random Multiple-Access Stack Algorithm
B. S. Tsybakov and N. D. Vvedenskaya
pp. 230–243

Abstract—The article proposes an easy-to-implement algorithm for random multiple access of packets to a broadcast channel. The algorithm requires that the transmitting/receiving station follow the state of the channel only in the period from the instant of sending its packet until its successful transmission. It is shown that the algorithm results in finite average delays for transmission at rates less than $0.384$. Results of simulation of the access system are given.

On the Optimal Strategy for Activation of a Servicing Device in One Class of Systems with Group Servicing
L. B. Boguslavskii and E. A. Fainberg
pp. 243–253

Abstract—The article considers a system with several limited queues for requests and one servicing device that operates in accordance with the following principle: switch on; service all accumulated requests at once; switch off. Servicing of requests produces revenue, while activation of the device creates overhead. The structure of the optimal activation strategy for the device that maximizes the average revenue per unit time is determined.

On the Redundancy of Linear Cyclic Codes with Permutational Decoding
V. S. Kugurakov
pp. 108–110 (Russian issue)

Abstract—We obtain several lower bounds on the redundancy of linear cyclic codes that correct independent additive errors using permutational decoding.