PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Optimum Transmission of a Gaussian Message over a Channel with White Gaussian Noise and Feedback
I. A. Ovseevich
pp. 191–199

Abstract—The article deals with messages which form a Gaussian random process and are such that their epsilon-entropy per unit time does not exceed the capacity of a channel with white Gaussian noise and complete feedback; linear methods of encoding and decoding such that the reproduction error does not exceed $\varepsilon^2$ are discussed.

Optimum Filtration of Quantum Variables with a Quadratic Quality Criterion
B. A. Grishanin and R. L. Stratonovich
pp. 200–206

Abstract—The authors consider the quantum generalization of the problem of optimum estimation of a sequence of random variables in terms of the criterion of minimum mean-square error. For the Gaussian case it is shown that the optimum filtration algorithm for the observed sequence is linear and an explicit form of this algorithm is found; it coincides with the corresponding nonquantum result.

A New Class of Linear Correcting Codes
V. D. Goppa
pp. 207–212

Abstract—A class of binary error-correcting codes is described. Each code in the class is specified by some polynomial in $GF(2^m)$. If the degree $t$ of the polynomial is known, the following estimate can be obtained for the code parameters: $n\le 2^m$, $k\ge n-mt$, $d\ge 2t+1$. The codes described are in general noncyclic. The only cyclic codes in the class in question is the Bose–Chaudhuri–Hoquingham (BCH) code. All the basic properties of the BCH code are evidently the result of the fact that it belongs to this class of codes and not to the class of cyclic codes. For all the codes of the class in question, therefore, there exists a decoding scheme analogous to Peterson’s algorithm for BCH codes. The codes are constructed by identifying the initial space of binary vectors with some set of rational functions.

Weight Spectrum for Certain Classes of Cyclic Correcting Codes
S. Sh. Oganesyan and V. G. Yagdzhyan
pp. 213–218

Abstract—The article offers finite formulas for the weight spectra of two infinite classes of binary cyclic codes.

Cyclic Codes which Correct Arithmetic Errors
G. M. Tenengol'ts and V. N. Dyn'kin
pp. 219–222

Abstract—A method is proposed for finding the cyclic representatives of a cyclic code which corrects arithmetic errors. A formula is obtained for the code distance of one class of cyclic codes which are more efficient than the familiar Mandelbaum codes.

Memoryless Channels with Synchronization Errors: the General Case
S. Z. Stambler
pp. 223–229

Abstract—Shannon’s theorems are proved for general memoryless channels with synchronization errors.

Nonlinear Transformations of Gaussian Processes
Yu. M. Ryzhov
pp. 230–237

Abstract—The article considers nonlinear transformations of Gaussian process $\xi(t)$ which have the form $\int\limits_0^Tf(\xi(t))\,dt$. It is shown that for a certain class of Gaussian processes, $\xi(t)$ can specify the function $\mathbf I(x)=\int\limits_0^T\delta(x+\xi(t))\,dt$, where $\delta(x)$ is the Dirac delta function. The properties of $\mathbf I(x)$ are studied.

A Natural Discrete Model of a Drawing, Certain of Its Asymptotic Properties, and Prediction of the Slave-Scan Process
V. G. Polyakov
pp. 238–245

Abstract—The author studies an ensemble of drawings as a discrete source of signals which are obtained by scanning along lines. The quantized function of a discrete argument which describes the lines in the drawing is taken to be the angle of inclination of the tangent to the line as a function of the arc length; this corresponds to an approximation of the lines in the drawings by broken lines in the discrete model which consist of links of fixed length, where each link is oriented along some one of $N$ fixed directions. The author analyzes the combined effect of the parameter $N$ and of the statistic of the initial drawings on the distribution of the transition probabilities of the source and the average number of readings. The theoretical level is established for the reduction of signal volume by predicting whether the direction of the preceding step will be preserved in the next step of the scan.

A One-Line Queueing System with a Limited Number of Waiting Places and Priorities
P. P. Bocharov
pp. 246–252

Abstract—A one-line queueing system with two incoming Poisson flows of demands is analyzed. The service times of the demands in both flows are arbitrarily distributed. The system has $r\lt\infty$ waiting places. The case is considered in which, when demands are serviced out of turn, a relative priority is established in the system, and when a demand is placed in the queue, an absolute priority is established. The system is analyzed by using line Markov processes. For a given system an algorithm is obtained for the stationary probability distribution of the system; it amounts to the solution of a nonhomogeneous system of $r+1$ linear algebraic equations.

Capacity of a Discrete-Time Gaussian Channel with a Filter
B. S. Tsybakov
pp. 253–256

Abstract—A discrete-time channel with a filter and Gaussian additive noise is considered. The capacity of the channel is found on the basis of the “nonstationary” definition.

Method of Expanding Polynomials in a Finite Field
V. N. Dyn'kin and D. A. Agaronov
pp. 257–260

Abstract—Problems of reducibility of polynomials in the field $GF(2)$ are discussed.

Error and Erasure Probability in Receiving Signals with Unknown Phase
V. A. Morozov
pp. 261–263

Abstract—Approximate (asymptotic expressions are obtained for the error and erasure probabilities in “null-zone” reception of binary orthogonal signals of unknown phase against a background of Gaussian noise.

One Method of Coding Information
Yu. L. Lesin
pp. 264–265

Abstract—A method of encoding large volumes of information by two numbers is proposed. The basis of the method is a mechanical analog. The resultant numbers preserve some integral quality of the transformed volumes of information.

Approximation of Continuous Distributions by a Mixture of Erlang Distributions
N. I. Mal'tseva
pp. 266–268

Abstract—The article considers the problem in which a single-channel system services flows for which the intervals between demands are mutually independent and identically distributed with arbitrary density function. The problem is solved by approximating an arbitrary distribution by a mixture of Erlang distributions.

Single-Channel Communications Systems
G. P. Zakharov, A. V. Nebeev and V. P. Revel's
pp. 269–272

Abstract—The article considers single-channel communications systems of finite reliability with absolute message priorities. The generalized criterion for the communications quality is taken to be the probability of transmission at the proper time. The concept of the law of information “aging” is introduced. A combined discussion of two random and independent processes, information “aging” and transmission, is used to obtain analytic expressions for the probability of transmission at the proper time of messages of arbitrary priority.

Study of Multichannel Information Transmission Systems by the Method of Optimizing the Strategy of the Distributing Device
A. V. Nebeev and V. P. Revel's
pp. 273–276

Abstract—The authors propose a mathematical model which yields the basic qualitative characteristics of multichannel systems whose channels are nonuniform in reliability and capacity and which are used to transmit information subject to aging.

Nonergodicity of Uniform Threshold Networks for Small Self-Excitation
L. G. Mityushin
pp. 277–280

Abstract—The article considers the behavior of networks composed of elements which are capable of spontaneous excitation. It is shown that the network is nonergodic for small self-excitation probabilities if and only if the inequality $p\ge N/2+1$ holds, where $p$ is the threshold and $N$ is the number of inputs for a network element.