PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Mutual Information of Several Random Variables and Its Estimation via Variation
V. V. Prelov
pp. 295–308

Abstract—We obtain some upper and lower bounds for the maximum of mutual information of several random variables via variational distance between the joint distribution of these random variables and the product of its marginal distributions. In this connection, some properties of variational distance between probability distributions of this type are derived. We show that in some special cases estimates of the maximum of mutual information obtained here are optimal or asymptotically optimal. Some results of this paper generalize the corresponding results of [1, 2, 3] to the multivariate case.

The Group of Permutation Automorphisms of a $q$-ary Hamming Code
E. V. Gorkunov
pp. 309–316

Abstract—We prove that the group of permutation automorphism of a $q$-ary Hamming code of length $n=(q^m-1)/(q-1)$ is isomorphic to the unitriangular group $\operatorname{\bf UT}_m(q)$ if the code has a parity-check matrix composed of all columns of the form $(0\ldots0\,1*\ldots*)^\mathsf{T}$. We also show that the group of permutation automorphisms of a cyclic Hamming code cannot be isomorphic to $\operatorname{\bf UT}_m(q)$. We thus show that equivalent codes can have different permutation automorphism groups.

On One Transformation of Steiner Quadruple Systems $S(v,4,3)$
V. A. Zinoviev and D. V. Zinoviev
pp. 317–332

Abstract—A transformation of Steiner quadruple systems $S(v,4,3)$ is introduced. For a given system, it allows to construct new systems of the same order, which can be nonisomorphic to the given one. The structure of Steiner systems $S(v,4,3)$ is considered. There are two different types of such systems, namely, induced and singular systems. Induced systems of $2$-rank $r$ can be constructed by the introduced transformation of Steiner systems of $2$-rank $r-1$ or less. A sufficient condition for a Steiner system $S(v,4,3)$ to be induced is obtained.

New Enumeration of Walsh Matrices
M. S. Bespalov
pp. 333–342

Abstract—The discrete Walsh transform is a linear transform defined by a Walsh matrix. Three ways to construct Walsh matrices are known, which differ by the sequence order of rows and correspond to the Paley, Walsh, and Hadamard enumerations. We propose a new enumeration of Walsh matrices and study its properties. The new enumeration is constructed as a linear rearrangement; we obtain an eigenvector basis for it and propose a convenient-to-generate fast implementation algorithm; the new enumeration possesses certain symmetry properties, which make it similar to the discrete Fourier transform.

Algebraic Codes for Network Coding
E. M. Gabidulin and M. Bossert
pp. 343–356

Abstract—The subspace metric is an object of active research in network coding. Nevertheless, little is known on codes over this metric. In the present paper, several classes of codes over subspace metric are defined and investigated, including codes with distance 2, codes with the maximal distance, and constant-distance constant-dimension codes. Also, Gilbert-type bounds are presented.

Graph-Based Convolutional and Block LDPC Codes
I. E. Bocharova, B. D. Kudryashov, and R. V. Satyukov
pp. 357–377

Abstract—We consider regular block and convolutional LDPC codes determined by parity-check matrices with rows of a fixed weight and columns of weight 2. Such codes can be described by graphs, and the minimum distance of a code coincides with the girth of the corresponding graph. We consider a description of such codes in the form of tail-biting convolutional codes. Long codes are constructed from short ones using the “voltage graph” method. On this way we construct new codes, find a compact description for many known optimal codes, and thus simplify the coding for such codes. We obtain an asymptotic lower bound on the girth of the corresponding graphs. We also present tables of codes.

On Signal Reconstruction in White Noise Using Dictionaries
G. K. Golubev
pp. 378–392

Abstract—Assume that we observe a Gaussian vector $Y=X\beta +\sigma\xi$, where $X$ is a known $p\times n$ matrix with $p\ge n$, $\beta\in \mathbb{R}^n$ is an unknown vector, and $\xi\in \mathbb{R}^n$ is a standard Gaussian white noise. The problem is to reconstruct $X\beta$ from observations $Y$, provided that $\beta$ is a sparse vector.

Superpositions of Continuous Functions Defined on a Baire Space
S. S. Marchenkov and S. I. Krivospitsky
pp. 393–399

Abstract—We consider uniformly continuous functions on a Baire space and introduce the notion of a continuity modulus of a function. We formulate a condition on the growth of the continuity modulus $\varphi$ guaranteeing that superpositions of $n$-ary functions with continuity modulus $\varphi$ do not exhaust all $(n+1)$-ary functions with continuity modulus $\varphi$ for any $n$. Moreover, negating this property leads to the inverse effect.

Parameter Estimation for Product-Form Distributions of Queueing Networks
G. Sh. Tsitsiashvili and M. A. Osipova
pp. 400–405

Abstract—Basic parameters of a queueing network are its routing matrix, arrival flow rate, and service rates at network nodes. To estimate these parameters, one has to solve a system of balance equations. In turn, a product-form limiting distribution of the number of customers at the network nodes is defined through loading factors. Therefore, in the paper we propose to estimate loading factors through estimates of the limiting distribution based on observations of the number of customers at the nodes. This makes it possible to avoid solving a system of balance equations. This algorithm is realized for Jackson networks: classical, in a random environment, with blocked transitions.

The International Dobrushin Prize
pp. 406–409

INDEX
pp. 410–414