PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 21, Number 1, January–March, 1985
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CONTENTS

Theory of Codes with Maximum Rank Distance
E. M. Gabidulin
pp. 1–12

Abstract—The article considers codes over $\operatorname{\it GF}(q^N)$. A new metric, called the rank metric, is introduced; the maximum number of coordinates of vector $\mathbf{x}=(x_1,\dots,x_n)$ that are linearly dependent over $\operatorname{\it GF}(q)$ is called its norm. For this metric a theory analogous to the theory of MDS codes is formulated. Codes with maximum rank distance are described; their spectrum is obtained; and encoding and decoding algorithms are given.

Convolutional-Block Coding in Channels with Decision Feedback
B. D. Kudryashov
pp. 12–20

Abstract—The article describes a method of transmitting information over channels with decision feedback, based on combined use of block and convolutional coding principles. A bound is obtained for the decoding error probability as a function of the length of the code constraint and the transmission rate. It is shown that the error probability decreases exponentially as the complexity of implementation of encoding and decoding increases linearly.

Coding in a Channel with Generalized Defects and Random Errors
A. V. Kuznetsov
pp. 20–25

Abstract—The author introduces a model of a channel with generalized defects and random errors, this being an aggregate consisting of a deterministic channel from a specified class $\Phi$, followed by a channel with random errors of specified multiplicity. It is assumed that the deterministic channel is known to the encoder but not to the decoder. Coding and decoding methods for such a channel are described. Lower bounds are obtained for the information-transmission rate for zero error probability, for an arbitrary set of deterministic channels $\Phi$ and arbitrary multiplicity of random errors.

Nonbinary Codes That Correct Symbol Insertions, Drop-Outs, and Substitutions
A. S. Dolgopolov
pp. 26–29

Abstract—The author constructs codes over $\operatorname{\it GF}(q)$ with length $n$ not exceeding the size of the alphabet $q$ that correct single insertions, drop-outs, and substitutions of letters in words. Bounds are given for the volume of the constructed codes. Methods of constructing short codes of maximum volume are considered.

On Sequential Estimation of Intensity of Renewal Processes
A. G. Tartakovskii
pp. 30–36

Abstract—The author considers problems of Bayesian and non-Bayesian sequential estimation of the intensity of a renewal process with a gamma distribution of the intervals between events. Sequential and nonsequential estimation procedures are compared.

On Sequential Estimation of Parameters of Diffusion Processes
V. V. Konev and S. M. Pergamenshchikov
pp. 36–46

Abstract—The authors consider the problem of estimating the linear parameters of multivariate stochastic processes described by stochastic differential equations. Sequential designs are constructed that make it possible to estimate the unknown parameters with the requisite accuracy within a finite time. Their asymptotic properties are investigated. A limiting expression that relates the duration of observations and the estimation accuracy is obtained. It is shown that the sequential estimates are asymptotically normal and that they converge with probability 1 and in the mean square.

Analysis of Losses Due to Incomplete Allowance for Correlational Structure of Gaussian Noise in Digital Signal Reception and Discrimination Algorithms
A. I. Rog and A. A. Sirota
pp. 47–51

Abstract—The authors give a method of estimating the loss that arises in the case of incomplete (or inexact) description of the covariance matrix of readings in digital signal processing with correlated noise.

Asymptotically Efficient Estimation of a Signal in Unknown Additive Noise
E. Kh. Mustafaev
pp. 51–60

Abstract—The author obtains new asymptotically efficient estimates for a signal observed in unknown symmetrical additive noise. These estimates are asymptotically efficient not only in the weak sense (in the sense of distributions), but also in the strong sense (in the sense of moments of arbitrary order).

B. S. Tsybakov and V. L. Bakirov
pp. 60–76

Abstract—The article considers a communications network employing an ALOHA random multiple-access system. A general formulation of the problem is given and three network models are proposed: with random-walk packets, with fixed routes, and a general model. The stability conditions of the network are determined. Optimization of the throughput with respect to the radius of action of the transmitters is performed.

BRIEF COMMUNICATIONS
(available in Russian only)

To Expurgated Bounds for Convolutional Codes
K. Sh. Zigangirov
pp. 102–105 (Russian issue)

Abstract—We derive new expurgated bounds on the decoding error probability for convolutional codes.

Codes for a Two-User Adder Channel
G. G. Hachatrian
pp. 105–109 (Russian issue)

Abstract—We give a method for constructing $\delta$-decodable pairs of codes for a binary two-user adder channel. We present examples of codes with prescribed $\delta$ with rates beyond the time-sharing bound.

On Codes Beyond the Gilbert Bound
V. A. Zinoviev and S. N. Litsin
pp. 109–111 (Russian issue)

Abstract—We show that for all $q\ge 46$, there exist nonlinear $q$-ary codes beyond the Gilbert bound.