PROBLEMS OF INFORMATION TRANSMISSION

A translation of *Problemy Peredachi Informatsii*

Volume 24, Number 3, July–September, 1988

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** Probabilistic Decoding of Nonbinary Majority Decodable Codes
**

V. D. Kolesnik and S. L. Portnoy

pp. 173–184

**Abstract**—Probabilistic decoding of nonbinary majority
decodable codes is considered. An optimal decoding rule is formulated and a
method of computing the check weight multipliers is described. Upper and
lower bounds are derived on the probability of decoding error in arbitrary
semicontinuous and discrete output-symmetric channels. As an example, we
consider the characteristics of majority-logic decoders in combination with
orthogonal signals in a channel with white Gaussian noise.

** Delayed Epsilon-Entropy for a Gaussian Message Corrupted by Noise
**

A. K. Gorbunov and M. S. Pinsker

pp. 185–189

**Abstract**—We introduce the notion of delayed epsilon-entropy
(rate-distortion function) for a Gaussian message corrupted by Gaussian noise
and study its properties.

** On Characterization and Existence Conditions of Codes Meeting the
Varshamov–Griesmer Bound
**

V. N. Logachev

pp. 189–204

**Abstract**—We consider the structure of anticode generator
matrices for binary linear codes meeting the Varshamov–Griesmer bound. Necessary and sufficient conditions of
existence of these codes are derived for a number of different dimensions and
code distances.

** Nonbinary Codes with Distances $4$, $5$, and $6$ of Cardinality Greater than
the BCH Codes
**

I.I. Dumer

pp. 205–214

**Abstract**—We construct linear $q$-ary codes with distances $4$, $5$,
and $6$ in which the number of check symbols for $q\gt 4$ increases with the increase
of code length more slowly than for BCH codes. Decoding algorithms are
considered.

** Nonparametric Estimation of a Linear Functional of the Regression Function
for a Given Observation Design
**

Yu. I. Pastukhova and R. Z. Khas'minskii

pp. 215–223

**Abstract**—In [*Probl. Peredachi Inf.*, 1986, vol. 22,
no. 3, pp. 43–61] we considered nonparametric estimation of a linear
functional of the regression function for a variable observation design. In this
paper, we consider the same problem for a given observation design $(t_1,\ldots,t_n)$
such that $t_1,\ldots,t_n$ are independent identically distributed random variables
with a known distribution density. We obtain a lower bound on estimation accuracy
and, under relatively light assumptions on the set of allowed regression functions,
construct an estimator that attains this bound.

** Locally Asymptotic Minimax Estimation of One Functional of an
Unknown Distribution
**

M. B. Nevel'son and I. V. Shafranskii

pp. 224–237

**Abstract**—We consider nonparametric estimation of one
functional of an unknown distribution using an independent sample from this
distribution. We construct a procedure similar to the Fisher accumulation
method, which is asymptotically optimal in the minimax sense in various
classes of loss functions.

** Some Markov Chain Functions and Associated Nonsymmetric Random Walks
with Absorbing Barriers
**

V. D. Kolesnik and B. D. Kudryashov

pp. 237–245

**Abstract**—We consider random walks controlled by an ergodic
Markov chain. For the case where the expected one-step increment is nonzero,
we obtain upper and lower bounds on the mean first-arrival time of the random
walk with absorbing barriers. These bounds are close to the bounds obtained
from Wald's identities for independent increments.

** Computing Packet Delay for Some Random Multiple Access Stack Algorithms
**

N. D. Vvedenskaya and B. S. Tsybakov

pp. 246–253

**Abstract**—Packet delays for two RMA stack algorithms are
computed and compared for the case of a feedback channel with errors. The
range of parameters when one algorithm is better than the other is
identified.

** A Comment on the Paper of Kasami, Lin, Wei, and Yamamura, “Coding for
the Binary Symmetric Broadcast Channel with Two Receivers”
**

L. A. Bassalygo and M. S. Pinsker

pp. 253–257

**Abstract**—We show that for a degrading binary symmetric
broadcast channel with two components, the representation of the code as the
direct sum of two codes of which only one is linear does not reduce the known
admissible rate region.

** On a Model of Associative Memory
**

V. V. Rykov and A. G. D'yachkov

pp. 257–260

**Abstract**—We consider the Boolean model of associative memory
using neuron networks, as proposed by Palm [*Biol. Cybern.*, 1980,
vol. 36, no. 1, pp. 19–31]. Our
previous results from the theory of disjunctive codes [*Probl. Peredachi
Inf.*, 1983, vol. 12, no. 4, pp. 229–244] are applied to derive exchange relationships
between the model parameters and the size of written information.