PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 26, Number 3, July–September, 1990
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CONTENTS

Asymptotic Lower Bound on the Free Distance of Constant Linear Convolutional Codes with Rate $1/n_0$
V. B. Balakirsky
pp. 181–188

Abstract—A new asymptotic lower bound is obtained for the ratio of the free distance to the constraint length in the class of constant binary linear convolutional codes with rates of the form $1/n_0$. For all $n_0\ge 3$ the new bound is an improvement on the Neumann bound, but does not attain the Costello bound, which has been proved for the class of time-dependent linear convolutional codes.

Majority-Logic Decoding of Generalized Reed–Muller Codes
I. I. Grushko
pp. 189–196

Abstract—We consider the possibility of simple (i.e., when the number of checks increases as $n\log_2 n$ with code length $n$) majority-logic decoding of generalized Reed–Muller codes (GRM codes), defined as various powers of the radical of the group algebra of the group of type $(p,\dots,p)$ over a field of characteristic $p$. A simple majority-logic decoding algorithm realizing the code distance is constructed for first-order $p$-ary GRM codes and for ternary GRM codes of any order.

Covering the Hamming Space with Sets Translated by Vectors of a Linear Code
V. M. Blinovsky
pp. 196–201

Abstract—We establish an asymptotically exact bound on the cardinality of a linear code which, together with its cosets with representatives from a given set, forms a covering of the Hamming space.

Detection of a Noisy Source Moving Relative to the Receiver, with Estimation of Its Motion Parameters
G. P. Tartakovskii
pp. 202–212

Abstract—We solve the problem of optimal detection of a source of noise (interference) that moves relative to the receiver, with estimation of the minimum-distance time, the angular velocity, and the noise intensity.

Nonparametric Estimation of the Regression Function in $L^2$
G. K. Golubev and M. Nusbaum
pp. 213–225

Abstract—We consider the nonparametric estimation of the regression function in a model with independent additive Gaussian errors. Adaptive estimators are constructed for a quadratic performance criterion and their properties are analyzed.

Second-Order Asymptotic Minimax Estimation in the Presence of a Nuisance Parameter
Z. M. Landsman and B. Ya. Levit
pp. 226–244

Abstract—We consider second-order minimax estimation of the structural parameter $\theta_1$ in the presence of a nuisance parameter $\theta_2$ as the number of observations $n\to\infty$. We show that the effect of the nuisance parameter is largely determined by a “nontraditional” object in mathematical statistics—vector field $X=\partial/\partial\theta_1+J_{12}/J_{11}\partial/\partial\theta_2$, where $J_{11}$ and $J_{12}$ are elements of the inverse Fisher information matrix.

Random Multiple Access in a Channel with Binary “Success–No Success” Feedback
B. S. Tsybakov and A. N. Beloyarov
pp. 245–260

Abstract—We consider a random multiple access (RMA) algorithm for packets in a binary feedback channel. Through “success–no success” feedback, all stations learn if one of the following situations occurred in the channel: (a) a single packet was transmitted in the current window (success) or (b) no packets were transmitted or more than one packet was transmitted (no success). An RMA algorithm is proposed with rate $1/e=0.367$. Previously known algorithms had rates not exceeding $0.329$. The algorithm is generalized to the case of “empty–not empty” binary feedback.

Asymptotic Analysis of Telegraphic Message Switching Systems
F. I. Karpelevich and A. Ya. Kreinin
pp. 261–274

Abstract—Single-channel message switching systems are considered in which the transmission time is determined only by the message length and is the same at all nodes. The heavy traffic case is analyzed. It is shown that if the traffic parameter tends to 1, the sojourn time in the system is asymptotically equivalent to the waiting time in the first phase.

Probability Distribution of the Stochastic Convolution Functional of a Normal Markov Process
Yu. P. Virchenko and A. S. Mazmanishvili
pp. 275–280

Abstract—The convolution functional of a complex-valued normal Markov process is considered. An analytical expression is derived for the characteristic function of the stochastic functional. The probability density of the convolution functional is calculated numerically. General properties of the probability distribution of the convolution functional of a normal Markov process are analyzed.

Signals with Two-Level Autocorrelation
A. L. Vishnevetskii
pp. 281–285

Abstract—Let $x$ be a periodic signal with a two-level autocorrelation function. We obtain a bound on the maximum modulus of the periodic cross-correlation function of the signal $x$ with an arbitrary signal. This bound is attained for any signal $x$.

Spectral Density Estimators of a Periodically Correlated Stochastic Process
V. G. Alekseev
pp. 286–288

Abstract—We correct an error in the definition of the $r$th order weight function [V.G. Alekseev, Probl. Peredachi Inf., 24, No. 2, 31–38 (1988)] used for spectral density estimators of a periodically correlated stochastic process. It is shown that the functions $W_r(x)$, $r=2,4,6,8$, given in the cited paper satisfy the revised definition of the $r$th order weight function. Two new collections of functions $W_r(x)$, $r=2,4,\dots\strut$, are introduced, which satisfy both the original and the revised definition of the $r$th order weight function.