PROBLEMS OF INFORMATION TRANSMISSION

A translation of *Problemy Peredachi Informatsii*

Volume 22, Number 2, April–June, 1986

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** 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

** 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.