PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Error Exponents for Product Convolutional Codes
C. Medina, V. R. Sidorenko, and V. V. Zyablov
pp. 167–182

Abstract—An upper bound on the error probability (first error event) of product convolutional codes over a memoryless binary symmetric channel, and the resulting error exponent are derived. The error exponent is estimated for two decoding procedures. It is shown that, for both decoding methods, the error probability exponentially decreasing with the constraint length of product convolutional codes can be attained with nonexponentially increasing decoding complexity. Both estimated error exponents are similar to those for woven convolutional codes with outer and inner warp.

A Different Approach to Finding the Capacity of a Gaussian Vector Channel
B. S. Tsybakov
pp. 183–196

Abstract—The paper considers a Gaussian multiple-input multiple-output (MIMO) discretetime vector channel with memory. The problem is to find the capacity of such a channel. It is known that the capacity of Gaussian vector channels with memory was given in [1: Brandenburg, L.H. and Wyner, A.D., Bell Syst. Tech. J., 1974, vol. 53, no. 5, pp. 745–778.]. In the present paper, we show a different approach, which uses another definition of the capacity. For a channel with $n=2$ inputs and outputs, this approach gives an expression for the capacity which is different from that in [1]. The paper shows what the dependence of input signal components should be to give this capacity. A multidimensional water-filling interpretation works for the optimum vector input signal power distribution but cannot work for the description of the input component dependences. For the case of $n\ge 3$ inputs and outputs, we give a lower bound on the channel capacity.

The Grey–Rankin Bound for Nonbinary Codes
L. A. Bassalygo, S. M. Dodunekov, V. A. Zinoviev, and T. Helleseth
pp. 197–203

Abstract—The Grey–Rankin bound for nonbinary codes is obtained. Examples of codes meeting this bound are given.

A New Class of Nonlinear $Q$-ary Codes
S. A. Stepanov
pp. 204–216

Abstract—In this paper we construct two new families of nonlinear $q$-ary codes derived from the corresponding families of modified Butson–Hadamard matrices. These codes have very easy construction and decoding procedures, and their parameters are rather close to the Plotkin bound.

Classification of Steiner Quadruple Systems of Order 16 and Rank 14
V. A. Zinoviev and D. V. Zinoviev
pp. 217–229

Abstract—All $708\,103$ nonisomorphic Steiner systems $S(16,4,3)$ of order $16$ and rank $14$ over $\mathbb{F}_2$ are enumerated. Among them there are exactly $1059$ homogeneous systems. It is shown that all the $708\,103$ Steiner systems can be obtained by the general doubling construction presented in the paper.

On Fragments of Words
V. K. Leont’ev and S. A. Mukhina
pp. 230–233

Abstract—We find a precise value of the function $F_N(m,n,k)$, which is the number of binary words of length $N$ and weight $m$ that contain an arbitrary word of length $n$ and weight $k$ as a fragment. As a consequence, we obtain a known result on the number of binary words of length $N$ that contain a fixed word of length $n$ as a fragment.

Limit Dynamics for Stochastic Models of Data Exchange in Parallel Computation Networks
A. G. Malyshkin
pp. 234–250

Abstract—We study limit dynamics of a system of interacting particles, which is one of possible models for the parallel and distributed computation process. For a rather wide class of multi-particle interactions, we prove that the stochastic process describing the configuration of a particle system weakly converges in the fluid-dynamic limit to a deterministic process, which is a solution of a certain partial differential equation.

Distribution of Investments in the Stock Market, Information Types, and Algorithmic Complexity
V. V. V’yugin and V. P. Maslov
pp. 251–261

Abstract—For a simplest mathematical model of a stock market, the problem of optimal distribution of investments among different securities (stocks, bonds, etc.) is considered. Our results, which are obtained in terms of algorithmic complexity, allow to discuss heuristically the properties of sufficiently complex security portfolios in the conditions of daily changing return rates. All considerations are given in the combinatorial framework and do not use any probabilistic models.

Letter to the Editor (Remark on “Recursive Aggregation of Estimators by the Mirror Descent Algorithm with Averaging” Published in Probl. Peredachi Inf., 2005, no. 4)
A. B. Juditsky, A. V. Nazin, A. B. Tsybakov, and N. Vayatis
p. 262