PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 34, Number 3, July–September, 1998
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CONTENTS

Error-Free Filtering of an Entropy-Singular Signal under Independent Distortions
M. S. Pinsker and V. V. Prelov
pp. 207–209

Abstract—The problem of filtering for a discrete-time stationary stochastic process $X=\{X_n\}$ from observations $Y=\{Y_n\}$ in the case of independent distortions satisfying the natural condition of dependence on the signal being estimated is considered. It is shown that for an entropy-singular process $X=\{X_n\}$ the value of $X_n$ at any time instant $n$ can be reconstructed without error from the observations $\{Y_j,\;j\leq m\}$ for any $m$.

Bounds for the E-Capacity Region of a Restricted Two-Way Channel
E. A. Haroutunian and M. E. Haroutunian
pp. 210–218

Abstract—A restricted two-way Shannon channel is studied. Outer and inner bounds for the region of rates that are achievable when error probabilities exponentially decrease with given exponents at two outputs are obtained.

Asymptotics of the Shannon and Renyi Entropies for Sums of Independent Random Variables
A. G. D'yachkov and P. A. Vilenkin
pp. 219–232

Abstract—We investigate the asymptotics as $n\to\infty$ of the Shannon and Renyi entropies for sums $\zeta_n=\xi_1+\ldots+\xi_n$, where all $\xi_i$ are independent identically distributed (i.i.d.) random variables. We consider the cases of discrete and absolutely continuous distributions of $\xi_i$. If $0\lt{\bf D}\xi_i\lt\infty$, then we find the dominant part of the asymptotics. Under the additional condition ${\bf E}|\xi_i|^N<\infty$ for an integer $N\ge3$, we construct the expansion of the entropies in powers of $n$ with the remainder term $\bar o \Bigl({n^{-\frac{N-2}{2}}}\Bigr)$. The coefficients of this expansion depend on the semi-invariants of $\xi_i$. Proofs are performed by using local limit theorems. As examples, we construct several first coefficients for Poisson, binomial, and geometric distributions. This paper improves the previous results [Fundamentalnaya Prikl. Mat., 2, No. 4, 1019–1028 (1996)].

Binary Constant-Weight Codes of Weight One Correcting Localized Errors
V. S. Lebedev
pp. 233–237

Abstract—New bounds on the maximum number of messages that can be transmitted using a constant-weight code of length $n$ and weight $1$ correcting $t$ localized errors are obtained. A connection between these codes and tournaments is established.

Minimal Codewords of the Primitive BCH Codes
Yu. Borissov and N. L. Manev
pp. 238–246

Abstract—The numbers of minimal (nonminimal) codewords of weights $10$ and $11$ in a binary double-error-correcting primitive $[n=2^m-1,n-2m,5]$ BCH code and those of weight $12$ in its extended code are found.

On Distance Regularity of Perfect Binary Codes
S. V. Avgustinovich and F. I. Solov'eva
pp. 247–249

Abstract—Perfect binary codes with distance 3 are considered. We prove that, among these codes, only Hamming codes of length 3 or 7 are distance-regular.

Pairing of Finite Modules, Duality of Linear Codes, and the MacWilliams Identities
O. A. Logachev, A. A. Sal'nikov, and V. V. Yashchenko
pp. 250–258

Abstract—The concept of the duality of codes well known in coding theory is introduced for submodules of a pair of finite modules related by a certain binary bilinear relation. Therewith, a pair of antiisomorphic complete lattices of dual submodules arises. Under certain conditions, the MacWilliams identities which connect the characteristics of a pair of mutually dual codes are proved.

Informativity in the Category of Multivalued Information Transformers
P. V. Golubtsov
pp. 259–276

Abstract—Consideration is given to the information transformers described by multivalued mappings. The paper focuses on the study of informativity. The classes of equivalent informativity are shown to form a partially ordered Abelian monoid which is isomorphic to the special family of coverings of some set. Another approach to comparing information transformers is based on the concept of the abstract problem of decision making. The concept of semantical informativity stems from this approach. It is shown that one information transformer is more informative than another one if and only if it provides a higher quality in any decision-making problem.

Closed Queueing Network with Changing Number of Request Classes at Nodes
O. V. Ivnitskii
pp. 277–289

Abstract—A closed queueing network with multiserver nodes that provide service for requests of different types, where each node may have its own number of request types, and with several finite sources with their own transition matrices is considered. Generating times at the sources and servicing times at the nodes are exponentially distributed. In the considered class of service disciplines at the nodes, a discipline is found for which the stationary probability distribution of the network states has a multiplicative form. The uniqueness of such a discipline in the considered class is proved. A particular case of this discipline is the one where the choice of a request to be serviced is equiprobable and does not depend on either the number of the request in a queue or its type.