PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Correcting Codes with an Additional Property
L. A. Bassalygo
pp. 1–5

Abstract—An inductive method of constructing correcting codes with additional properties, based on Bose–Chaudhuri codes, is proposed.

Bounds of the Minimal Error Probability on Checking a Finite or Countable Number of Hypotheses
I. Vajda
pp. 6–14

Abstract—Upper and lower bounds are constructed for the minimum error probability of the determination of a parameter assuming a finite or countable set of values. The bounds are simply expressed in terms of a function introduced in the paper, which has properties similar to the Shannon entropy. The properties of the function are investigated.

The Correction of Triple Errors in Bose–Chaudhuri Codes over the Field $\mathit{GF}(3)$
M. V. Matveeva
pp. 15–21

Abstract—A class of ternary Bose–Chaudhuri codes correcting three and detecting four errors is considered. For this class of ternary codes a decoding method is proposed which has certain advantages over the usual method of decoding for $p$-ary codes. As opposed to the usual decoding method where in the case of three errors we invariably arrive at an equation of the third degree, in a number of cases the proposed method leads to quadratic equations from which the locations of certain errors are found in explicit form. Examples are given. A decoding scheme is presented.

The Problem of Automatic Correction of Grouped Errors on Magnetic Tape
V. S. Lapin
pp. 22–26

Abstract—A method is proposed of correcting error bursts in a multidigit transmission system for parallel data transmission. The method is based on specially obtained cyclic codes correcting periodic error bursts. The method is efficient for correcting errors on magnetic tape.

Noise Stability of a Class of Wideband Systems for the Transmission of Discrete Information with Signal Fading
D. D. Nasledov and A. A. Sikarev
pp. 27–34

Abstract—This paper considers the noise stability of wideband systems for the transmission of discrete information with separate processing of the orthogonal components of the received signal in a channel with fading and additive fluctuation noise. Expressions are obtained for the error probability and a comparative analysis is performed of the noise stability of different variants of realization of these systems depending on the degree of correlation of the fading of the signal components.

Some Properties of $m$-ary Communication Systems with Coding
Yu. P. Pyatoshin
pp. 35–40

Abstract—A channel with $m$ equidistant signals ($m\ge2$) in the presence of additive white Gaussian noise is considered. It is assumed that when coding is used the transmitter power, the quantity of information transmitted, and the transmission time are kept the same as without coding, that is, no additional energy or time is used on the transmission of redundant symbols. Curves are constructed showing for what values of the signal/noise ratio and transmission rate transmission with an arbitrarily small error probability is possible. Some asymptotic expressions are obtained showing that with increasing $m$ the system improves extremely slowly. Thus, for example, the system with $m=2^{20}$ signals is potentially no better than a binary system.

Capacity of a Randomized Channel with Feedback and Matching of the Source
I. A. Ovseevich
pp. 41–46

Abstract—An expression is obtained for the capacity of a Gaussian randomized channel with feedback with limiting of the mean input signal power in time and given spectral density of the additive noise and fading probability density. It is proved that by linear encoding and decoding of the signal combined with permutation of the spectral components of the message together with permutation of its time segments along such a channel, it is possible to transmit messages forming a Gaussian random process so that the resulting mean square error is minimal.

Controllable Markov Processes and Stefan’s Problem
B. I. Grigelionis and A. N. Shiryaev
pp. 47–57

Abstract—The properties of the “cost” $s(x)$ are investigated for controllable Markov processes with continuous time. We obtain a new (integral) form of the recurrence equations satisfied by the “cost” $s(x)$, and find conditions for which $s(x)$ is the solution of a generalized Stefan problem.

Priority Organization in Queueing Systems Using a Model of the Collective Behavior of Automata
V. I. Varshavskii, M. V. Meleshina, and M. L. Tsetlin
pp. 58–60

Abstract—A queueing system with waiting is considered. The arriving Poisson streams have different exponential service times. A system of priorities without interruption is organized directly on the channels without prior knowledge of the incoming stream characteristics. Results obtained by simulation on a computer show that the quality of operation of the proposed system is fairly close to the operating quality of a system with priorities whose probability characteristics are shown in advance.

Optimal Detection of a Quantum Signal
P. A. Bakut and S. S. Shchurov
pp. 61–65

Abstract—The problem of synthesizing an optimal method of detecting a quantum signal is formulated, and for the simplest case the detection characteristics of the quantum field source are obtained.

A Hypothesis on Bose–Chaudhuri Codes
V. K. Leont'ev
pp. 66–68

Abstract—It is shown that Bose–Chaudhuri codes correcting $t$ errors are not quasi-perfect for blocks of length $n=2^m-1$ if $2\lt t\lt \sqrt{n}/\lg n$ and $m\ge 7$.

Determination of the Distribution of Overshoot Durations of the Phase Cosine of a Normal Stationary Random Process by a Time Discretization Method
B. R. Levin and Ya. A. Fomin
pp. 68–70

Abstract—The method of time discretization of random processes [B.R. Levin and Ya.A. Fomin, Radiotekhnika, 1965, vol. 20, no. 10, pp. 1–8] is used to obtain a general expression for an independent and single-valued approximation of the distribution of overshoot durations of the phase cosine of a normal stationary random process above a given level, and also the mean value and variance of this distribution. Results are presented of a single-valued approximation of the distribution of duration of the phase cosine above the levels $z=-1.0,\: -0.5,\: 0,\: 0.5,\: 1.0$.

Some Local Stability Criteria of Power Regulation in a Group of Radio Stations
V. L. Stefanyuk
pp. 71–72

Abstract—This paper presents the results of an investigation of some local criteria for the regulation of power which ensure the stability of the choice of powers in a group of radio stations creating mutual interference, subject to the condition that each radio station knows only the local information about the state of the group.

Multidimensional Probability Density of a Signal Which is Phase (Frequency) Modulated by a Random Process
V. I. Vladimirov
pp. 72–75

Abstract—The $n$-dimensional probability density of a signal phase (frequency) modulated by a random process is determined. As an example an expression is given for the two-dimensional probability density of a signal phase modulated by a stationary normal random process or by a harmonic oscillation with random initial phase in the interval $(0,2\pi)$.

The Search for Extremal Paths on a Finite Graph
A. Ya. Tolchan
pp. 75–80

Abstract—A relief is considered as a set of extremal paths on a finite graph (possibly a multigraph with loops). Conditions are formulated by which the relief may be constructed by a simple computational procedure. Corresponding algorithms and examples of their application are given.

Representation of Relative Phase Telegraphy Signals
Yu. G. Tratas
pp. 80–83

Abstract—A method is demonstrated which permits the signals of relative phase telegraphy to be represented as signals obtained by the usual method of manipulation, that is, the method in which only one message symbol corresponds to each signal emitted by the transmitter. The optimal receiver circuits following from this representation are presented.