PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

On Code Distances for a Class of Group Codes
K. Buzási, A. Pethő, and P. Lakatos
pp. 149–156

Abstract—The article considers group codes of group $G$, this being the direct product of second-order cyclic groups over field $K$, whose characteristic is different from $2$. The code distances of the codes in question are investigated as a function of their dimension and of the number $n$. Assume that for code $I$ we have $KG=I\oplus\bar{I}$. On the basis of Berman's hypothesis, for $\dim\bar{I}\leq q(n,k)$ (where $q(n,k)=\sum\limits^k_{i=1} C_n^i$) the code distance of the code does not exceed $2^k$. It is shown in the paper that Berman's bound is exact for $n\le 4$, but it becomes more and more crude as $n$ increases. Explicit formulas are given for the numbers that refine this bound.

On Optimal Bit Allocation Algorithm for Quantizing a Random Vector
A. V. Trushkin
pp. 156–161

Abstract—It is shown that the use of the allocation algorithm for a specified number of bits for quantizing independent components of a random vector, known earlier for the case of convex functions of minimum mean quantization error for individual components, can ensure minimum overall mean quantization error for all components even in the convex case, if some condition of quasiconvexity is satisfied with respect to the result of this algorithm. In the opposite situation, the resultant solution simplifies the search for the optimal allocation in terms of a dynamic programming algorithm.

Estimation of Mean Error for a Discrete Successive-Approximation Scheme
V. N. Koshelev
pp. 161–171

Abstract—The article investigates coding of discrete memoryless sources by the successive-approximation method. A coding theorem is proved and a generalized Omura bound [IEEE Trans. Inf. Theory, 1973, vol. 19, no. 4, pp. 490–497] is derived for the mean error of the last step of the approximations. The results are applied to a special narrow class of additive approximation schemes. The question of investigating the complexity of the latter is raised.

On Properties of the Statistical Estimate of the Entropy of a Random Vector with a Probability Density
A. V. Ivanov and M. N. Rozhkova
pp. 171–178

Abstract—The article considers one statistical estimate of the entropy of a random vector possessing a probability density. It is shown that this estimate is consistent, and an assertion regarding the rate of convergence of the moments of the estimate to zero is obtained.

Optimum Compensation for Structurally Deterministic Noise
A. S. Kotousov
pp. 178–182

Abstract—The article takes up the problem of asymptotically optimal filtering of the information parameter of a signal that is received in noise and structurally deterministic interference that is functionally related to a random parameter. Optimal compensation algorithms for intense interference are investigated.

Estimation of Square-Integrable Density on the Basis of a Sequence of Observations
S. Yu. Efroimovich and M. S. Pinsker
pp. 182–196

Abstract—We consider nonparametric estimation of the spectral density. It is assumed that the correlation coefficients satisfy the inequality $\sum\limits^{\infty}_{j=-\infty}a_j\theta^2_j\leq Q$, $a_j\geq 0$, $Q>0$. Asymptotically exact estimates for the minimax mean-square risk are obtained. A consistent and asymptotically efficient linear estimation plan is constructed.

Asymptotic Power of Statistical Criteria for Counting Processes
Yu. N. Lin'kov
pp. 196–205

Abstract—The article obtains the asymptotic behavior of the error probabilities of the maximum-likelihood criteria with asymptotic level $\alpha\in(0,1)$ in the case of discrimination of two counting processes with continuous compensators. Asymptotically locally most powerful criteria for testing the simple hypothesis against the complex parametric alternative are obtained.

Asymptotically Optimal Switching Circuits
L. A. Bassalygo
pp. 206–211

Abstract—The constants for some asymptotically optimal switching circuits are more precisely determined.

Asymptotic Analysis of a Complete Communication Network with a Large Number of Points and Bypass Routes
V. V. Marbukh
pp. 212–216

Abstract—The article obtains asymptotic values as $n\to\infty$ of some characteristics of a complete communication network with $N$ points and bypass routes. In particular, it is shown that for certain parameter values and $n\to\infty$ there is a “phase transition of Van der Waals type” in the network. The approach is based on the “hypothesis of conservation of chaos” in the network as $n\to\infty$.