PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 22, Number 2, April–June, 1986
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CONTENTS

New Sufficient Existence Conditions for Codes Meeting the Varshamov–Greismer Bound
V. N. Logachev
pp. 77–98

Abstract—For any value of the dimension, and for any upper bound on the weights of the code vectors, the author defines the class of generating matrices of binary linear optimal anticodes. Permissible lower bounds are obtained on the maximum number of repetitions of a column in matrices from the class introduced, and, as a consequence, new sufficient existence conditions are obtained for codes that meet the Varshamov–Greismer bound.

Zero-Error Capacity of Memoryless Channels with Weak Input Signals
V. V. Prelov
pp. 98–104

Abstract—The paper is a continuation of the study of the asymptotic behavior of the zero-error capacity of channels with weak input signals that was begun in [L.A. Bassalygo and V.V. Prelov, Probl. Peredachi Inf., 1981, vol. 17, no. 1, pp. 5–16]. Channels are considered for which the input signals assume values from an arbitrary finite-dimensional linear normed space, while the constraint on the input is specified by means of an arbitrary nonnegative function $\varphi(\cdot)$. The case in which the basic conditions of the theorems of the paper cited are not met is also considered.

New Asymptotic Lower Bounds on the Free Distance of Time-Invariant Convolutional Codes
K. Sh. Zigangirov
pp. 104–111

Abstract—It is shown that the familiar Costello bound for the free distance is valid not only for time-varying but also for time-constant convolutional codes with sufficiently “long” edges.

On Weight Spectra of Some Codes
I.E. Shparlinskii
pp. 111–116

Abstract—The author obtains new upper bounds for the number of different nonzero weights of binary linear cyclic codes, and for the number of different values of the cross-correlation function of $m$-sequences, and also an upper bound for the number of vectors in a linear cyclic code, whose weight does not exceed a specified value.

Local-Area Network with Random-Multiple-Access Stack Algorithm
B. S. Tsybakov and S. P. Fedortsov
pp. 117–125

Abstract—The authors investigate a local-area network that employs a random-multiple-access stack algorithm. The stack algorithm is generalized to the case in which the stations check the channel and transmit packets of arbitrary length. Upper and lower bounds are obtained for the maximum packet transmission rate in the network. It is shown that the maximum rate tends rapidly to 1 as the packet length increases.

Queuing Networks with Regenerating Trajectories
A. L. Tolmachev
pp. 125–132

Abstract—The author examines queuing networks with allowance for dependent durations of message servicing in subsequent stages of message routing in the networks. Under the assumption that a steady-state mode of network operation exists, the stationary distribution of the state probabilities of the network is obtained; it is of nonstandard multiplicative form. The traditional invariance of the stationary distribution is maintained for the network in question.

Robust Reconstruction of Functions by the Local-Approximation Method
A. B. Tsybakov
pp. 133–146

Abstract—The author considers a local approximation method for reconstruction of functions on the basis of observation of their values in noise. Consistency conditions for the estimates of the local approximation are given, and their rate of convergence is established. The asymptotic distribution of the estimates is determined, and it is shown that they possess the property of being robust.

Synthesis of Self-Checking Checkers for Summation Codes
A. G. Mel'nikov, V. V. Sapozhnikov, and Vl. V. Sapozhnikov
pp. 146–157

Abstract—The authors develop methods of synthesizing $(n,k)$ checkers that comprise control sums that establish whether a binary vector belongs to a code with addition. Results of application of the methods are given.

BRIEF COMMUNICATIONS
(available in Russian only)

Fast Correlation Decoding of $p$-ary Codes of Maximal Length
L. V. Kanatova, V. L. Litvinov, and L. M. Fink
pp. 98–103 (Russian issue)

Abstract—We consider a fast correlation decoding algorithm in the basis of Vilenkin–Chrestenson functions, which reduces computations over against known fast algorithms of spectral transforms.

Throughput Analysis for a Noise-Resistant Multiple Access Algorithm
G. S. Evseev and A. M. Turlikov
pp. 104–109 (Russian issue)

Abstract—We consider a synchronous random multiple access system for a broadcast channel where noise causes false conflicts. We propose an access control algorithm, which ensures information transmission with nonzero rate for any probability of a false conflict different from one.