PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Zero-Error Capacity of Continuous Memoryless Channels with a Small Input Signal
L. A. Bassalygo and V. V. Prelov
pp. 1–9

Abstract—We examine a continuous memoryless channel given by an arbitrary transition function $Q(x,B)$, $x\in X$, $B\in\mathscr{Y}$, whose signal space at the input is a $k$-dimensional Euclidean space $\mathbb{R}^k$, while the signal space at the output is an arbitrary measurable space $(Y,\mathscr{Y})$. The asymptotic behavior of the zero-error capacity of such a channel under the assumption that the input signal power tends to zero is investigated.

Study of the Second-Order Properties of the Estimates of the Signal Parameter in White Gaussian Noise. Estimate of Maximum a posteriori Density
M. V. Burnashev
pp. 10–18

Abstract—Asymptotic expansion of the maximum a posteriori density estimate is investigated, with analysis of its distribution function in the problem of estimation of an unknown parameter $\theta_0$ from observation of diffusion process $X_t$ defined by the stochastic differential $$ dX_t=S_t(\theta_0)\,dt+dW_t,\quad t\in[0,T],\quad \theta_0\in\Theta, $$ where $W_t$ is a standard Wiener process and $S_t(\theta)$ is a known function.

Sequential Testing of Composite Hypotheses with Dependent Nonstationary Observations
A. G. Tartakovskii
pp. 18–28

Abstract—The article considers sequential tests of two composite hypotheses for nonhomogeneous dependent processes. The properties of Wald's sequential rule are investigated for the case of normal observations. The distribution of the test length, the mean test length, and in some particular cases the upper bound on the mean test length are obtained.

Recognition of Normal Sets with Unknown and Different Means and Variances
Ya. A. Fomin and G. R. Tarlovskii
pp. 28–32

Abstract—An adaptive algorithm is developed for recognition of normal sets with unknown and different means and variances, which is based on utilization of classified training samples to form estimates of unknown parameters. The confidence of the recognition and the volumes of training and checking samples required for its support are estimated from the result of a statistical experiment using the Monte Carlo method.

Error Bounds for the Method of Minimization of Empirical Risk
A. B. Tsybakov
pp. 33–42

Abstract—New nonasymptotic upper bounds are obtained for the probability of deviation of the minimum empirical risk from the minimum average risk in a class of problems that includes signal identification against an additive noise background under conditions of a priori uncertainty, as well as certain other pattern-recognition problems.

On Consistency of Bayesian Parameter Estimation
A. I. Yashin
pp. 42–49

Abstract—The consistency problem is investigated for estimates of the conditional expectation types for random variables with a countable set of values according to observations of random processes in discrete time. Necessary and sufficient conditions for strong consistency are obtained in terms of the characteristics of the likelihood ratio of certain special probability measures. It is shown that the more detailed characterization of observed random processes makes it possible to obtain the consistency condition in terms of their probability characteristics. Consistency conditions are given for parameter estimates obtained from observations of the paths of a Markov chain and a Gaussian process.

Stationary Distributions of Time-Homogeneous Markov Processes Modeling Message-Switching Communication Networks
A. N. Rybko
pp. 49–63

Abstract—The article focuses on stationary distributions of time-homogeneous Markov processes modeling message-switching communication networks. Necessary conditions are derived for the existence of a stationary distribution and a construction is given which simplifies the proof of their sufficiency. Working formulas are proposed for calculating the stationary distribution as the sum of a series.

Upper Bound for the Capacity of a Random Multiple Access System
V. A. Mikhailov and B. S. Tsybakov
pp. 63–67

Abstract—It is shown that the normalized capacity of a system of synchronized random multiple access is less than 0.587 packets per unit time.

Asymptotic Analysis of a Class of Channel-Switching Networks
G. I. Falin
pp. 67–71

Abstract—Communication networks are discussed with a positive flow rate of calls between any pair of points connected by at least one direct path. An asymptotic expansion of the mean blocking probability is derived for any heavily loaded network of such kind.

To the Analysis of Self-Assembly Processes with Interacting Bonds
M. L. Tai
pp. 72–76

Abstract—A mathematical model of self-assembly processes with interacting bonds is analyzed. Concepts describing such processes are introduced. Differential equations that describe the concentration of bonds are derived. Theorems about the quadrature representation of bond concentration and about the conservation of a state of chaos in self-assembly processes are proved which greatly simplify the determination of the dependence of the process state on time, initial conditions, and dynamic properties of bonds.

Lower Bound on the Complexity of Discrimination of Two Statistical Hypotheses
K. Sh. Zigangirov
pp. 108–112 (Russian issue)

Abstract—The problem of discrimination of two statistical hypotheses by a finite-complexity automaton is considered. A lower bound on the automaton complexity is obtained, which depends on the required values of the first- and second-kind error probabilities.