PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Bounds on Complexity of Trellis Decoding of Linear Block Codes
V. V. Zyablov and V. R. Sidorenko
pp. 202–207

Abstract—It is shown that the syndrome trellis [1,2] is minimal. A simple proof of the lower bound on the number of nodes of the minimal trellis is given. Asymptotic bounds on the complexity of soft maximum likelihood trellis decoding are proposed.

It is shown that virtually all codes meet the upper complexity bound. Nevertheless the block codes, constructed by termination of convolutional codes, have smaller trellis decoding complexity. The complexity is minimal if the Varshamov–Gilbert bound is tight for binary codes.

Codes Correcting Errors in the Modulus Metric, Lee Metric, and Operator Errors
V. A. Davydov
pp. 208–216

Abstract—We suggest a code construction method that yields codes correcting $t$ errors in the modulus metric with asymptotically minimum redundancy. We introduce a concept of metric homomorphism and prove the homomorphism of the transposition metric to the Lee metric and the modulus metric. New code families for the mentioned metrics are constructed.

Generalized Hamming Weights of Codes on Multi-Dimensional Quadrics
D. Yu. Nogin
pp. 217–226

Abstract—We study projective systems and linear codes corresponding to high-dimensional quadrics of hyperbolic, parabolic, and elliptic types. The generalized weight hierarchy and higher weight distribution are calculated.

Optimal Estimation of the Parameters of Normal Regression for Extended Observation Models
Yu. G. Bulychev and I. V. Burlai
pp. 227–235

Abstract—In the framework of classical normal regression theory, we solve the problem of optimal treatment of discrete measurements for the case where the observation vector includes not only the sample values of a process, but also the sample values of its derivatives of various orders. We consider the traditional problems of reconstructing the parameters of normal regression in the polynomial class and in the class of functions linear in parameters.

On the Regularity of Stochastic Processes That Are Functions of Stationary Gaussian Processes
N. P. Zabotina
pp. 236–240

Abstract—We study the regularity of a stationary process $f(x_t)$, where $x_t$ can be either a regular or a singular Gaussian process. In the case where $x_t$ is singular, sufficient conditions for the regularity of $f(x_t)$ are found.

Adaptive Control of Partially Observable Homogeneous Processes with Independent Values
V. I. Mukhin
pp. 241–246

Abstract—The concept of a normal observation process is introduced, and it is shown that if an observation process belongs to some normal class, then there exists a strategy which is adaptive in the entire class of partially observable processes with independent values. A method of adaptive strategy synthesis is described.

Asymptotic Analysis of Models with Repeated Calls in the Case of Large Losses
S. A. Stepanov
pp. 247–266

Abstract—Recurrence formulas for finding any desired number of terms in the asymptotic expansion of basic stationary characteristics of a full-available system with repeated calls into a power series in the intensity of primary calls as it tends to infinity are derived. Problems related to solution of the system of state equations for large values of intensity of primary calls are considered.

Ergodicity Properties of Queueing Networks with Group Arrivals and Group Service
D. D. Botvich and A. A. Zamyatin
pp. 267–275

Abstract—We consider queueing networks with group arrivals and group service under conditions that make it impossible to obtain explicit expressions for the stationary probabilities. The method of Lyapounov functions is used for determination of the ergodicity criterion. Also exponentially fast convergence to the stationary distribution is proved.

Bounds of Two-Terminal Network Reliability and Base Spectrum of Network Graph
V. P. Polesskii
pp. 276–288

Abstract—The base spectrum is a set of effectively computable graph parameters. Its components are the frameness and the forestness of the graph.

The significance of the base spectrum for derivation of effective bounds on the all- and two-terminal network reliability is demonstrated. Several related conjectures are formulated. For certain classes of graphs, upper bounds for two-terminal reliability are derived; these bounds confirm one of the above conjectures.

On One Extremal Property of Hamming Halfspaces
M. V. Burnashev
pp. 288–290

Abstract—In the Hamming space $E^{n}$ of binary vectors the Voronoi region ${\cal D}$ of all-zero codeword $\bf 0$ of any linear code and its shift ${\cal D} \oplus {\bf a}$ on codeword $\bf a$ are considered. It is shown that the maximum ratio of probabilities of sets ${\cal D} \oplus {\bf a}$ and ${\cal D}$ is attained when ${\cal D}$ is a Hamming halfspace.

Towards a Theory of Group Convolution
O. A. Zharov and L. S. Kazarin
pp. 291–293

Abstract—Let $G$ be a finite group. Following S. D. Berman and I. I. Grushko, we give general definitions of the $G$-spectrum and $G$-convolution that, in the case of Abelian groups $G$, coincide with the conventional definitions. We also find estimates on the computational complexity of group-theoretic convolution for non-Abelian groups in terms of degrees of irreducible representations of these groups. For a number of cases, this construction enables a time gain for some values of length of the convolved signals.

On One Approach to Modelling Intelligent Systems
V. A. Lyubetsky
pp. 294–298

Abstract—An intelligent system (IS) engendered by definite needs has behavioral motivations (of coming to a decision) that are realized in the form of goals. The activity of an IS that is directed to a specific goal runs its course in a smaller scale of time, during which the IS has one constant goal. Below we discuss this side of the activity of an IS.