PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

On the Method of Types and Approximation of Output Measures for Channels with Finite Alphabets
M. V. Burnashev
pp. 195–212

Abstract—A particular problem is considered as an example of application of the method of types to channels with infinite (continuous) alphabets.

On Filtering for a Hidden Markov Chain under Square Performance Criterion
G. K. Golubev
pp. 213–219

Abstract—An asymptotic formula for the mean-square error of the optimal filter in the problem of filtering for a hidden Markov chain with rare transitions is obtained.

Information Rate in Memoryless Channels for a Slowly Varying Markov Signal
M. S. Pinsker, V. V. Prelov, and E. C. van der Meulen
pp. 220–229

Abstract—The problem of the calculation of information rate in stationary memoryless channels with an additive noise and a slowly varying input signal is considered. Under the assumption that the input signal is a stationary Markov chain with rare transitions, it is shown that the information rate is asymptotically equivalent to the entropy of the chain and, therefore, the main term of its asymptotics does not depend on the channel noise.

Rotations of Spherical Designs
V. A. Yudin
pp. 230–236

Abstract—A part of a spherical configuration is moved along the sphere under the action of the group $SO(n)$. It is found that point arrangements thus obtained remain to be good designs. Particular cases are considered, namely, an icosahedron and minimal vectors of the lattice $E_8$.

Convergence Acceleration of Power Estimations for Markov Fields on 2D Lattices
S. I. Stasevich
pp. 237–245

Abstract—The problem of power estimation for a binary Markov field defined on a planar rectangular lattice is studied. For a given dimension of the lattice, the power of the field is considered as a function of the combinatorial interaction matrix defined at the nodes of the lattice. A method for the convergence acceleration of upper and lower power estimations of the field is proposed. Efficiency of the method is illustrated by the Fibonacci interaction, which generates the field of contour images on a rectangular lattice.

Lower Bound on the Reliability of a Network with a $2$-Connected Structure
V. P. Polesskii
pp. 246–255

Abstract—The connectedness probability of a random graph (whose edges fail independently with a given probability $q$) in the class of random graphs generated by $2$-connected multigraphs with a given number of edges and fixed values $x_1, x_2$ of the first and second components of their acyclic spectra is estimated. It is proved that the connectedness probability of a certain estimating random graph described in the paper is a lower bound for the connectedness probability of any random graph from this class for any $q$. This effectively computable bound can be used to estimate the network reliability if the network structure is a $2$-connected graph with a small number of edges.

Asymptotic Expansion of the Stationary Probability Distribution for States of a Closed Queueing Network with a Demand Transmission Channel
O. V. Ivnitskii
pp. 256–271

Abstract—A closed queueing network with multiserver nodes and several finite sources is considered where each source has its own transition matrix. Network nodes serve demands of different types. Each node has its own number of demand types. From a finite source to an arbitrary network node, from one node to another, and from an arbitrary node back to the “original” source, demands are transmitted through a multiline demand transmission channel. The service discipline at the network nodes and the discipline of choosing a demand for sending to the channel are random. Demand generation times at the sources, service times at the nodes, and transmission times in the channel are random variables, which have exponential distribution with parameters depending on the aggregate network state. For such a network, the stationary probability distribution of states is not representable in a multiplicative form. For the case where the intensity of the demand transmission in a channel is much greater than intensities of demand generation at the sources and service intensities at the nodes, a method for the asymptotic expansion of the stationary distribution is proposed and an algorithm for the computation of coefficients for arbitrarily many expansion terms is constructed.

Analysis of a Communication Network with the Adaptive ALOHA Protocol for a Finite Number of Stations under Overload
A. A. Nazarov and Yu. D. Odyshev
pp. 272–281

Abstract—A class of adaptive random-multiple-access protocols is considered, which stabilize unstable communication networks operating with the ALOHA protocol. Existence of a stationary regime is proved. The channel capacity is established. The stationary probability distribution for states of the system is found. Basic time-probabilistic parameters of the system are obtained.

Rom Rubenovich Varshamov. In Memoriam
p. 282

Letter to the Editor
A. A. Puhalskii and A. N. Rybko
p. 283