PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Relative Informativity and a Priori Information in the Category of Linear Information Transformers
P. V. Golubtsov
pp. 195–215

Abstract—This paper continues the study of general properties of categories of information transformers for linear stochastic information transformers. It introduces and studies the concept of relative informativity, which emerges in decision-making problems with a priori information. The problem of comparison of relative informativity leads to the notion of normal relative equivalent, which represents, in a certain sense, the maximum information that can be obtained in an experiment and provides a simple algebraic criterion for comparing relative informativity of various experiments. Many fundamental concepts of probability and statistics such as random element, distribution, joint distribution, and conditional transition distribution are defined and studied in terms of categories of information transformers. All the introduced notions are applied to the study of decision-making problems with a priori information. The proposed approach is similar to the Bayes approach in statistics. Among other results, the Bayes principle for the category of linear stochastic information transformers is derived.

The Law of Large Numbers for Capacity of Memoryless Channels with a Random Matrix of Transition Probabilities
A. S. Ambrosimov and A. N. Timashev
pp. 216–224

Abstract—We prove that the capacity of a discrete memoryless channel with a random $n\times n$ matrix of transition probabilities tends almost surely to $1-\gamma $ as $n\rightarrow \infty$, where $\gamma =0.5772\ldots\strut$ is the Euler constant.

Two-Channel Digital Complexing of Continuous Measurers
A. N. Detkov
pp. 225–227

Abstract—We analyze the efficiency of the complexing of two continuous measurers for a Gaussian–Markov stochastic process using the exact knowledge of the characteristics of the analog-to-digital converter (ADC).

Algorithms of Two-Dimensional Discrete Orthogonal Transforms Realized in Hamilton–Eisenstein Codes
V. M. Chernov
pp. 228–235

Abstract—We consider a set of algorithms of two-dimensional discrete orthogonal transforms of an $(N\times N)$ array for $N=3^r$, namely, Fourier transforms of real and complex input, discrete cosine transform. In all cases we obtain lesser multiplicative complexity compared to the known realizations. This is achieved by means of interpreting data as elements of the quaternion algebra, these elements, in turn, being represented in a form concordant with the structure of a proposed algorithm.

Orbit Partition of a Vector Space over $\operatorname{\it GF}(2)$ under the Action of the Linear-Fractional Group
A. R. Ahkiamov
pp. 236–243

Abstract—We consider the orbit partition of a vector space under the action of an automorphism group of a code. This partition allows us to describe the sets of possible detected error vectors by a minimal list of representatives. We consider a linear-fractional subgroup of the automorphism group of a quadratic residue code.

Ergodicity Properties of Stochastic Processes that are Functions of Stationary Gaussian Processes
N. P. Zabotina
pp. 244–247

Abstract—We obtain the necessary and sufficient conditions for ergodicity of the processes that are Hermitian polynomials of a stationary Gaussian process.

Markov Processes with Asymptotically Zero Drifts
M. V. Menshikov, I. M. Asymont, and R. Iasnogorodskii
pp. 248–261

Abstract—The researches of various Markov processes, in particular, of random walks in a quarter plane, showed the importance of investigating one-dimensional processes with “almost zero” mean drifts. For the first time this problem was formulated by Harris and investigated more deeply by Lamperti. The present work is devoted to the asymptotical analysis of these processes. The research method is the construction of Lyapunov functions. The obtained results essentially generate Lamperti's results.

On Application of Stochastic Processes of the Stock Theory to Modeling Computerized Information Networks
M. Ya. Postan
pp. 262–283

Abstract—We investigate a system of stochastic integral equations describing the operation of an $N$-node open network for information storage and transmission, with information flows coming from the outside. It is assumed that these flows are described by $N$ independent Levy processes with nondecreasing trajectories and drift equal to zero. A linear stochastic network of arbitrary structure, as well as models of some rather simple nonlinear networks are analyzed in detail. For these networks, we found explicit solutions to the corresponding stochastic integral equations and joint distributions of the amounts of information stored at each node. Asymptotics of some distributions is studied.

The Limiting Departure Flow in an Infinite Series of Queues
N. D. Vvedenskaya and Yu. M. Suhov
pp. 284–294

Abstract—An infinite series $ S^0, S^1, \ldots\strut$ of single servers is considered, the input of $ S^N $ being identified with the output of $ S^{N-1}$. The servers work on a “first come—first served” basis. The input of $ S^0 $ is given by a general stationary ergodic marked flow $ \xi^0 $ that forms a $G/G/1/\infty $ queue. The service time of a given customer is preserved in the course of passing from one server to another (the telegraph rule). If the service time distribution $\sigma^0$ in flow $\xi^0$ is supported on a finite number of values or, more generally, has a bounded support and an atom at the point $l^* =\sup [l:\:l\in \operatorname{supp}\sigma^0]$, we prove that the departure flow $\xi^N $ from a server $S^N$ converges as $N \to \infty$ to a limiting stationary flow $\overline {\xi}$ and specify $\overline {\xi}$. In the case where flow-$\xi^0$ service time distribution support $\operatorname{supp} \sigma^0$ is unbounded or bounded, but the point $l^*$ does not carry an atom, the flow $\xi^N$ converges (in some specific sense) to a tightly packed flow, in which the interval between arrival of two successive customers equals the service time of the first of them.