PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Fast Decoding Algorithms for First-Order Reed–Muller codes
S. N. Litsyn and O. I. Shekhovtsov
pp. 87–91

Abstract—The authors propose a decoding algorithm for first-order Reed–Muller codes that requires a linear number of operations in relation to code length.

Decoding for a Noiseless Channel with Two Users
G. G. Khachatrian
pp. 91–96

Abstract—The author proposes an easy-to-implement decoding algorithm for linear uniquely decodable code pairs.

Two Decyclical Lengthening Methods for Block Codes
V. Yu. Krachkovsky
pp. 97–105

Abstract—The author proposes two lengthening methods for block codes that are variants of the constructs of decyclical lengthening. Their use makes it possible to construct new block codes with parameters that are better than the available ones. Suitable examples are given. By lengthening Hamming codes of length $2^m-1$ by $2m$ symbols, the author constructs a class of codes with minimum distance $7$ and redundancy $3m$.

On Optimal Filtering of a Function of Many Variables in White Gaussian Noise
M. Nusbaum
pp. 105–111

Abstract—The author considers asymptotic expressions for the optimum mean-square error $\delta^2$ of reproducing signals in white Gaussian noise over $\mathbb R^k$, when the signal belongs to the class of smooth periodic functions of many variables. By using the familiar general result for ellipsoids in Hilbert spaces, the author calculates the corresponding rates and constants in the example under consideration.

Quantum Estimation Theory for a Markov Message
A. Ya. Gorodetskii
pp. 112–118

Abstract—The problem of estimating messages transmitted by a photon signal is considered from the standpoint of quantum mechanics as a problem of measuring the average count rate of discrete signals at the detector output. It is shown that, within the framework of correlation theory, the problem can be reduced to filtration of a Markov message in white noise.

On Efficient Solution of the Interpolation Problem on the Basis of Observations of Jump Processes
V. M. Khmetov and A. I. Yashin
pp. 119–130

Abstract—The authors investigate the problem of interpolating a process with piecewise-continuous trajectories on the basis of observations of a multivariate point process. Equations are derived for the estimates and errors of direct and inverse interpolation in the case of conditionally Gaussian observation scheme.

Random Multiple Access of Packets to a Channel with Errors
N. D. Vvedenskaya and B. S. Tsybakov
pp. 131–146

Abstract—The article investigates the noise immunity of one multiple-access method, namely the stack algorithm. For this an infinite system of linear-algebraic equations for the conditional mean session length is considered. The region of transmission rates such that the system remains stable is determined. The boundaries of the region depend on the error probabilities.

Packet Switching in a Channel without Feedback
B. S. Tsybakov and N. B. Likhanov
pp. 147–161

Abstract—The authors consider transmission of packets from $M$ transmitters to one common receiver over a channel without feedback. Undesirable superpositions of packets (i.e., conflicts) may occur in the channel. It is assumed that the transmitters do not know the packet propagation time to the receiver. The problem of determining the system capacity region $\mathfrak R$ is considered. It is shown that region $\mathfrak R$ coincides with the ergodicity region of an ALOHA system with feedback. A switching matrix that yields any rates from $\mathfrak R$ is obtained. Generalizations of the problem are given. A similar system with equal rates for all transmitters was considered earlier by J.L. Massey [IEEE Int. Symp. on Inf. Theory (Les Arcs, 1982), IEEE, New York, 1982, p. 101].

Estimation of A Posteriori Probability in Problems of Pattern Recognition and Prediction
E. F. Yurkov
pp. 162–169

Abstract—In relation to problems of patterns recognition and prediction, the author proposes a method of estimation of the a posteriori probability; in contrast to the existing methods, this method avoids the stage of estimation of multivariate distributions. The property of consistency of the estimate is investigated. An example of the use of the method in a prediction problem is given.

Upper Bounds for the Risk in the Problem of Recognition of Two Classes
N. G. Cherkashin
pp. 169–176

Abstract—Lower bounds are obtained for the risk in the problem of recognition of two classes, under conditions in which the parameters of the conditional densities are unknown but there are classified samples of finite size $N$. It is shown that, under certain general conditions of regularity, the risk converges at a rate not greater than $N^{-1}$.

Converse Coding Theorem for a Gaussian Source with Side Information
S. I. Gelfand and M. S. Pinsker
pp. 101–106 (Russian issue)

Abstract—We consider the problem of coding of correlated Gaussian memoryless sources.

On Estimation of Information-Type Measures
O. Gulyás and G. Légrády
pp. 106–108 (Russian issue)

Abstract—We will prove an estimate for information-type measures from a certain class, which includes, in particular, the Kolmogorov distance, Bhattacharya distance, and symmetric Pearson criterion. Applied statistics is easily computed even in a multidimensional case. We will prove the consistency of the estimate.

Perfect Constant-Weight Codes and Steiner Systems
G. L. Movsisian
pp. 109–112 (Russian issue)

Abstract—We obtain a necessary existence condition for Steiner systems. We show nonexistence of some Steiner systems, as well as a connection between Steiner systems and perfect constant-weight codes.