PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Sequential Decoding in a Continuous Channel
K. Sh. Zigangirov, M. S. Pinsker, and B. S. Tsybakov
pp. 1–10

Abstract—A memoryless channel discrete in time and continuous in amplitude is considered. Sequential decoding procedures for this channel are proposed and discussed. The Gaussian channel is studied in detail for the cases of polyphase, binary, and random Gaussian coding.

Shannon’s Theorems for Channels with Synchronization Errors
R. L. Dobrushin
pp. 11–26

Abstract—A memoryless channel with synchronization errors is defined as a channel in which each input symbol independently of other symbols is transformed into a word of random (including also zero) length, and at the output of the channel the ordinal number of the input symbol from which the given output symbol was obtained is unknown. For such channels Shannon’s theorem on transmission rates for which noise stable coding methods exist, is formulated and proved.

Estimation of the Fidelity of Transmission of Discrete Messages over Channels with Bursts of Errors or Erasures
O. V. Popov, V. Ya. Turin, and B. M. Igel'nik
pp. 27–36

Abstract—The lower bound of the probability of an incorrect decoding or erasure of a message transmitted with a given block length over a channel with bursts of errors or erasures, is expressed in terms of the probability of damage by bursts of a different number of symbols. Formulas are deduced for estimating the distribution of these probabilities by a model of an error source which agrees with experimental data relating to a standard telephone channel. The possibility of using the formulas obtained for estimating the probabilities of occurrence of different numbers of errors in a block of given length is indicated.

Power Regulation in a Group of Radio Stations
V. L. Stefanyuk and M. L. Tsetlin
pp. 37–43

Abstract—A descriptive investigation is made of a group of radio stations creating mutual interference. The study of the possible modes of operation of the radio stations of the group leads to the consideration of a matrix with positive diagonal and negative nondiagonal elements. It is shown that the vector of the attainable noise/signal ratios must belong to a certain infinitely connected $\Lambda^n$-domain which is not identical with the positive orthant of the corresponding space. Local stability of power regulation is established, this being a necessary condition for the stability of the choice of some (attainable) vector of the noise/signal ratios by means of an independent power regulation carried out by each transmitter.

Bounds of the Probability and of the Number of Correctable Errors for Nonblock Codes
M. S. Pinsker
pp. 44–55

Abstract—Upper bounds are derived for the number of correctable errors for nonblock codes. Explicit expressions are given for the upper limits of the power of a code as the decoding delay $\tau\to\infty$ for the case where a fixed number $t$ of errors may occur in the interval $\tau$, and for the case where the number of errors $t=\alpha\tau$ increases linearly with $\tau$. These bounds are similar to the Hamming and Elias bounds for block codes. The upper limit of the error probability is also calculated for nonblock transmission over a binary symmetric memoryless channel: the exponential term of this limit is the same as the exponential term for block codes of length $\tau$. It is shown that for transmission rates tending to zero, the exponential term of the error probability converges to the exponential term of the error probability for block transmission at zero rate. It is shown that many estimates also remain valid when feedback is present.

Arithmetic Codes with Correction of Multiple Errors
I. L. Erosh and S. L. Erosh
pp. 56–63

Abstract—The use of arithmetic correcting codes in a system consisting of a communication channel and a digital computer makes it possible to detect or correct errors arising in any section of this system, both in the communication channel and in the information processors, and this affords the possibility of considerably reducing the number of encoders and decoders. The universality of arithmetic codes is due to this. Methods of finding such codes with code distance equal to three are described in the literature. An extremely inefficient inspection process may be used for finding codes with a large distance. In this paper a method of synthesizing arithmetic codes with any code distance is presented. Several theorems enabling this synthesis to be realized are stated. An upper bound is given for arithmetic codes similar to Hamming’s upper bound for group codes.

Games of Automata Possessing Different Activities
A. V. Butrimenko
pp. 64–69

Abstract—Games of automata are considered. It is assumed that the automata engage in a game with different probabilities. A method of local organization of the game is indicated in which the whole group, however, behaves suitably.

Evaluation of Methods of Formal Investigation of Texts in Dead Languages
Yu. A. Shreider
pp. 70–78

Abstract—An account is given of the principles for automatic decipherment of historical documents which are used by the VINITI group under the leadership of M.A. Probst. The author considers problems of dividing texts into blocks, classification of morphemes into auxiliary and root morphemes by means of the variational principle, and establishment of correspondences between related languages.

The Quantum Distribution of the Envelope of a Quasi-Harmonic Signal in Gaussian Noise
R. L. Stratonovich
pp. 79–80

Abstract—The characteristic function of the square of the envelope of the quantum quasi-harmonic signal $x(t)$ is found by double integration in the $x$-representation according to the function $\varphi\sqrt\lambda=\operatorname{Sp}(e^{-\beta\mathrm{H}}\rho)$.

Cycles of an Algorithm for the Synthesis of Irreducible Polynomials over the Field $\mathit{GF}(2)$
G. A. Garakov
pp. 81–82

Abstract—A study is made of the problem of cycles in the algorithm for the synthesis of irreducible polynomials over the field $\mathit{GF}(2)$ proposed by R.R. Varshamov. A test is also proposed to check for a primitive root with respect to the modulus of a Mersenne prime $n=2^m-1$, requiring less calculation than the usual test.