PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Decoding Concatenated Codes with Inner Convolutional Codes
V. V. Zyablov, J. Justesen, U. Dettmar, and U. Sorger
pp. 95–101

Abstract—We consider concatenated codes whose inner codes are unit memory (UM) or partial unit memory (PUM) convolutional codes. An algorithm of concatenated decoding for such codes is proposed, and this algorithm is proved to decode up to a lower bound for the code distance.

Binary Constant-Weight Codes Correcting Localized Errors and Defects
R. Ahlswede, L. A. Bassalygo, and M. S. Pinsker
pp. 102–104

Abstract—We establish here the asymptotically optimal transmission rate of binary constant-weight codes correcting localized errors and defects.

Separaring Systems
Yu. L. Sagalovich
pp. 105–123

Abstract—This survey is motivated by the fact that, at different times, one and the same theory of separating systems has served as an adequate research technique for such different areas of science and technology as automata synthesis, technical diagnosis, and the construction of hash functions.

On Admissible Nonparametric Estimates of the Probability Density and its Derivatives
V. G. Alekseev
pp. 124–128

Abstract—Nonparametric estimates (estimates of the Rosenblatt–Parzen type) for an unknown probability density $f(x)$ are considered. Particular attention is paid to estimates using the admissible weighting functions $K(x)$, i.e., the weighting functions which possess the properties of having Fourier transforms that are non negative and not exceeding the value $\Psi(0)$. Some examples of admissible weighting functions $K(x)$ are presented. Estimates for the functions $f(x)$ of orders $\gamma=1$ and $2$ are considered from a similar point of view.

Estimate for the Maximal Number of Messages for a Given Probability of Successful Deception
L. A. Bassalygo and M. V. Burnashev
pp. 129–134

Abstract—We investigate the asymptotic behavior of the maximal possible number of messages $M$ for large values of $Kq^{2}$, where $K$ is the number of keys and $q$ is a given probability of successful deception.

Some Information-Theoretic Problems of Discrete Data Protection
Yu. M. Shtarkov
pp. 135–144

Abstract—We consider the secrecy of discrete data, introduced by Shannon [Bell Syst. Tech. J., 28, No. 4, 656–715 (1949)]. We study the properties of certain key sets for a given probability distribution of messages, and methods for increasing the secrecy by source coding (in particular, by variable-to-fixed rate coding). We specify the statement of the randomization problem and show that sometimes, for instance, in the case of the uniform multiple substitution of letters, the randomization is inefficient.

Packet Output Time for a Strategy Which Knows the Multiplicities of Occurring Conflicts
B. S. Tsybakov
pp. 145–157

Abstract—A conflict between $k$ packets numbered by $1,\ldots,k$ is considered. Our problem is to find the optimal conflict resolution strategy minimizing the average time to the instant when the packet $1$ begins its successful transmission or maximizing the probability that this time is not greater than $x$. It is assumed that the strategy knows the multiplicity of the initial conflict $k$ as well as the multiplicities of conflicts occurring before the time when the packet $1$ achieves success. We find the optimal strategies for the cases $k=2$ and $k=3$. The problem is still open for $k\geq 4$.

Effect of an Unbalanced Random Number Generator on the Throughput of a Random Access Local Area Network
S. P. Fedortsov and N. A. Ryleeva
pp. 158–168

Abstract—A local area network with a random access of user packets is considered. Colliding packets repeat transmission with probability $p$ and postpone it with probability $1-p$. A lower bound for the algorithm throughput is derived. The bound is used for numerical evaluation of the throughput dependence on the network parameters. It is shown that the random number generator with $p\ne\frac{1}{2}$ (unbalanced generator) can be used in a network with large packet length. A comparison with other known random access algorithms for local area networks is presented.

Basic Teletrafic Model for a Party Line
V. I. Neiman
pp. 169–174

Abstract—The paper discusses a basic teletraffic model for any kind of collective telecommunication line used by subscribers (or stations) located along the line. Bus topology with communications of the stations in pairs and blocking is used as the basic teletraffic model of such a line. The Markov model describing teletraffic processes in a party line provides an explicit solution for the state probabilities of the line and, hence, for all significant traffic characteristics. Ways of extending the model for the bus with a gateway and for the ring topology, as well as for delay systems, are also discussed.

Construction of Nonbinary Codes Correcting Single Localized Errors
G. A. Kabatianskii
pp. 175–176

Abstract—For arbitrary $q$, we construct optimal codes of length $n=(q^r-1)/(q-1)$, $r=2,3,\ldots$, and size $q^{n-r}$ correcting single localized errors.

On a Telegraph-Type Equation with Non-Constant Coefficients Emerging in Randomly Accelerated Motions
M. Kelbert and E. Orsingher
pp. 177–182

Abstract—In this paper we analyze the random motion of a particle whose acceleration is the two-valued telegraph process $\{A(t),\, t\geq0\}$. We derive the third-order, hyperbolic partial differential equation governing the probability law $p=p(x,v,t)$ of the Markov vector-valued process $\{V(t), X(t),\, t\geq0\}$ ($V$ is obtained by integrating the two-valued telegraph process and $x(t)=\int\limits_0^t V(s)\,ds$ is analyzed). In particular, solutions of the form $p(x,v,t)=e^{-2\lambda t}q(x-vt,t^2/2)$ are taken into account. The general solution (in terms of the double-Fourier transform) of the equation governing $q$ is presented, and some of its properties investigated.

A Method for Obtaining the Unsteady State Probabilities in Markovian Queueing Networks
M. A. Matalytskii
pp. 182–185

Abstract—We solve the generalized system of differential equations for the state probabilities in Markovian queueing networks with various types of messages by using the method of successive approximations. The properties of the approximations obtained are studied.

New High-Rate Self-Orthogonal Convolutional Codes with Small Distance
A. E. Gheer
pp. 186–188

Abstract—We list triangle difference sets that define self-orthogonal convolutional codes with relative code rate $R=k/(k+1)$, where $k$ is any positive integer and $d_{\min}=4,5,6$. For $d_{\min}=4$, the constructed codes are either optimal or quasioptimal; for $d_{\min}=5$ and $k>11$, they are shorter than the best known codes by a factor of $1.8$ to $2.5$, and for $d_{\min}=6$ and $k\ge8$, they are shorter than the best known codes (for $k\ge9$, by a factor of $1.5$ to $1.8$).

Errata. V. M. Sidelnikov, Decoding Reed–Solomon Codes Beyond $(d-1)/2$ and Zeros of Multivariate Polynomials
p. 189