PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Mathematical Analysis of Algebraic Sequential Coding
K. Sh. Zigangirov
pp. 1–10

Abstract—A statistical analysis of the properties of algebraic sequential decoders is performed. It is shown that for nonbinary alphabets these decoders provide a gain in decoding complexity over classical sequential decoders and Viterbi decoders.

Bounds for Codes with Separately Localized Errors
L. A. Bassalygo, S. I. Gelfand, and M. S. Pinsker
pp. 11–17

Abstract—This is a continuation of an earlier paper [L.A. Bassalygo et al., IEEE Trans. Inf. Theory, 37, no. 3, 880–884 (1991)] in which codes that correct partially localized errors were studied. The situation was examined in which $l$ positions (of $n$) in which errors (not more than $t$) are possible are known in coding while the remaining positions ($n-l$) are error-free. Here we permit the presence of errors in those positions.

Soft-Decision Maximum-Likelihood Decoding of Partial-Unit-Memory Codes
V. V. Zyablov and V. R. Sidorenko
pp. 18–22

Abstract—A method is proposed for soft-decision maximum-likelihood decoding of partial- and total-unit-memory codes. The proposed algorithm has an exponential complexity gain over the Viterbi algorithm at rates greater than $0.5$.

Characteristics of Systems Based on CPFSK Signals and Convolutional Codes
V. V. Zyablov, N. A. Ugrelidze, and S. A. Shavgulidze
pp. 23–32

Abstract—Code-signal systems based on convolutional codes and continuous-phase frequency-shift-keyed signals are studied. The codes are defined over the ring of integers. The characteristics of the constructed systems are tabulated. Error-probability bounds for some systems and the results of computer modeling are provided.

New Lower Bounds for Minimum Distance of Linear Quasi-Cyclic and Almost Linear Cyclic Codes
V. V. Chepyzhov
pp. 33–44

Abstract—New lower bounds are derived for the minimum distance of linear $(np,kp)$ quasi-cyclic codes over arbitrary fields $\operatorname{\it GF}(q)$ for transmission rate $R=k/n$ and for almost linear cyclic codes of length $p$ over nonprime fields $\operatorname{\it GF}(q^n)$ for transmission rate $R=k/n$, where $p$ is any prime number. It is not assumed that $q$ is a primitive root modulo $p$. This result makes it possible to establish the asymptotic attainability of the corresponding Gilbert–Varshamov bounds by quasi-cyclic and almost linear cyclic codes with the indicated characteristics for almost all prime numbers $p$.

Nonparametric Estimation of Smooth Probability Densities in L₂
G. K. Golubev
pp. 44–54

Abstract—The author examines the problem of nonparametric estimation of probability density by the sampling of random variables with a square-law quality test and in the absence of a priori information on the smoothness of the density to be estimated.

Approximations in Sequential Rules for Discrimination of Complex Hypotheses and Their Precision in the Problem of Signal Detection from Postdetector Data
A. G. Tartakovskii and I. A. Ivanova
pp. 55–65

Abstract—Exact formulas are derived for the performance characteristic and average duration of Wald's sequential rule for discrimination of complex hypotheses that take into account threshold jumps by the logarithm of the probability ratio. Approximations of the characteristics of Wald's rule and the asymptotically minimax sequential rule are provided and compared. The accuracy of the found approximations in limiting situations is illustrated by the example of detection of a Gaussian signal from the results of preliminary processing.

Convergence of Stochastic-Approximation Procedures in the Case of a Regression Equation with Several Roots
V. A. Lazarev
pp. 66–78

Abstract—It is shown that the Robbins–Monro stochastic-approximation procedure cannot converge to the root $\widetilde x$ of the regression equation $R(x)=0$ if at least one eigenvalue of the matrix $(\partial R/\partial x)(\widetilde x)$ has a positive real part. A similar result is obtained for the Kiefer–Wolfowitz procedure.

Blocked RMA Stack Algorithm for a Network with a Finite Number of Stations
B. S. Tsybakov and V. B. Faingol'd
pp. 79–86

Abstract—A network with a finite number of stations and a stack algorithm for random multiple access are examined. A condition for network stability and the average packet delay are found.

An Access Algorithm for a Communication Channel
B. S. Tsybakov and S. P. Fedortsov
pp. 86–99

Abstract—A multiple-access system with a finite number of stations is examined. The stations of the system are numbered, and their number is assumed to be known. An efficient access algorithm which allows for conflicts and ensures their resolution with the aid of the station numbers is proposed. The average packet delay at a station with a given number is analyzed. It is shown that the delay is smaller than that of a random-multiple-access stack algorithm.