PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Capacity of the Product and Sum of Two Unmatched Broadcast Channels
A. A. El Gamal
pp. 1–16

Abstract—Assume that $p(y_1,z_1\,|\,x_1)=p(y_1\,|\,x_1)p(z_1\,|\,y_1)$ and $p(y_2,z_2\,|\,x_2)=p(z_2\,|\,x_2)p(y_2\,|\,z_2)$ are two degraded broadcast channels. A broadcast channel with transmitter $(X_1,X_2)$ and receivers $(Y_1,Y_2)$ and $(Z_1,Z_2)$ is called a product of two unmatched degraded broadcast channels. Similarly, the sum of two unmatched degraded broadcast channels is defined as a broadcast channel with transmitter $(X_1\cup X_2)$ and receivers $(Y_1\cup Y_2)$ and $(Z_1\cup Z_2)$. Unlike the original broadcast channels, neither the sum nor the product is a degraded broadcast channel. The region of the capacity is established for the following:
  (i) the product of two unmatched degraded discrete memoryless broadcast channels;
 (ii) a spectral Gaussian broadcast channel;
(iii) the sum of two unmatched degraded discrete memoryless broadcast channels.
These theorems concerning the capacity contain particular results regarding the product of discrete memoryless channels that were obtained by Poltyrev, as well as results concerning spectral Gaussian broadcast channels obtained by Hughes–Hartogs. They also demonstrate that the region of rates obtained by Hughes–Hartogs is optimal for zero overall rate.

Capacity of a Broadcast Channel with One Deterministic Component
S. I. Gelfand and M. S. Pinsker
pp. 17–25

Abstract—An internal bound is given for the capacity region of a two-output broadcast channel when there is common information. The capacity region for a broadcast channel with one deterministic component is computed. A noisy Blackwell channel is considered as an example.

Lower Bounds for the Volume of Error-Correcting Codes in Channels with Multiple Access
G. L. Katsman
pp. 25–30

Abstract—Lower bounds are derived for the volume of error-correcting codes in channels with multiple access. The case in which messages from different sources have a differing degree of protection is also considered.

On Calculation of Spectra of Stationary Random Processes on the Basis of Large Samples
V. G. Alekseev
pp. 30–35

Abstract—The article presents the results of large-scale numerical experiments aimed at computing the spectral density of a stationary random process (and its derivatives) on the basis of large samples. Both nonnegative and sign-changing weighting functions were employed to set up the spectral density estimates. In all cases, sign-changing weighting function (higher-order weighting functions) resulted in a substantial decrease in estimation error. Similar results were obtained in estimating the derivatives of the spectral density. In this case the use of higher-order weighting functions resulted in estimation errors that were many times lower.

Multiple Access with Reservation
B. S. Tsybakov and M. A. Berkovskii
pp. 35–54

Abstract—It is proposed to utilize the algorithm proposed in [B.S. Tsybakov and V.A. Mikhailov, Probl. Peredachi Inf., 1978, vol. 14, no. 4, pp. 32–59] for multiple access to a broadcast channel in conjunction with reservation. It is shown that in this manner it is possible to raise the transmission rate almost to 1 with limited delay and stable operating conditions, and without resorting to external control. In addition, new results for the algorithm from the paper cited are obtained. New definitions of the mean delay are offered.

On Stability of Binary One-Shot Switching Systems to Single Faults of Switching Elements
V. A. Garmash and L. A. Shor
pp. 55–59

Abstract—The article considers multistage one-shot switching circuits that consist of unary binary commutators and switches. Divided and nondivided unary one-shot switching circuits are constructed that are stable to single faults of any binary commutators and differ from Ofman circuits in that one binary commutator is added. Consideration is also given to divided nonunary switching circuits made up of unary binary commutators and switches with loop connections that are stable to malfunctioning of any commutator or switch.

On Some Properties of One Class of Control Systems That Operate in Stationary Random Media
V. I. Mukhin
pp. 59–65

Abstract—The article investigates the behavior of an $(A,F)$ control system in stationary random media $c(p_i,p_2,\ldots,p_k)$. Necessary and sufficient conditions are obtained which should be satisfied by a deterministic strongly connected automaton that belongs to a control system with optimum behavior. Systems with finite memory are defined, and their relationships to Ts-systems is established.

Selection-Induced Convergence to Equilibrium in a Single-Locus Autosomal Population
Yu. I. Lyubich, G. D. Maistrovskii, and Yu. G. Ol'khovskii
pp. 66–75

Abstract—The article offers a complete proof of the results announced in [Yu.I. Lyubich, G.D. Maistrovskii, and Yu.G. Ol'khovskii, Dokl. Akad. Nauk SSSR, 1976, vol. 226, no. 1, pp. 58–60].

On Bit Number Distribution upon Quantization of a Multivariate Random Variable
A. V. Trushkin
pp. 76–79

Abstract—The article considers a numerical solution algorithm for the problem of optimum distribution of a specified number of bits among the independent components of a random vector so as to obtain minimum overall quantization error for all components using the number of bits allotted for each component. Special attention is given to the case in which the minimum mean quantization error for each component, as a function of the number of bits allotted for this component, is convex.