PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Complex Random Matrices and Rician Channel Capacity
T. Ratnarajah, R. Vaillancourt, and M. Alvo
pp. 1–22

Abstract—Eigenvalue densities of complex noncentral Wishart matrices are investigated to study an open problem in information theory. Specifically, the largest, smallest, and joint eigenvalue densities of complex noncentral Wishart matrices are derived. These densities are expressed in terms of complex zonal polynomials and invariant polynomials. A connection between the complex Wishart matrix theory and information theory is given. This facilitates evaluation of the most important information-theoretic measure, the so-called ergodic channel capacity. In particular, the capacity of multiple-input multiple-output (MIMO) Rician distributed channels is investigated. We consider both spatially correlated and uncorrelated MIMO Rician channels and derive exact and easily computable tight upper bound formulas for ergodic capacities. Numerical results are also given, which show how the channel correlation degrades the capacity of the communication system.

Code Bounds for Multiple Packings over a Nonbinary Finite Alphabet
V. M. Blinovsky
pp. 23–32

Abstract—The problem of constructing asymptotic bounds for multiple packings in the space of $q$-ary sequences of length $n$ is considered. For the zero rate, tightness of the expurgation bound is proved.

On the Minimum Distance of Low-Density Parity-Check Codes with Parity-Check Matrices Constructed from Permutation Matrices
A. Sridharan, M. Lentmaier, D. V. Truhachev, D. J. Costello, Jr., and K. Sh. Zigangirov
pp. 33–44

Abstract—An ensemble of codes defined by parity-check matrices composed of $M \times M$ permutation matrices is considered. This ensemble is a subensemble of the ensemble of low-density parity-check (LDPC) codes considered by Gallager [Low-Density Parity-Check Codes, Cambridge: MIT Press, 1963]. We prove that, as $M\to \infty$, the minimum distance of almost all codes in the ensemble grows linearly with $M$. We also show that in several cases the asymptotic minimum-distance-to-block-length ratio for almost all codes in the ensemble satisfies Gallager's bound.

Solution of Variational Dynamic Problems under Parametric Uncertainty
V. Yu. Tertychnyi-Dauri
pp. 45–58

Abstract—The paper deals with a number of variational dynamic problems with parameters subject to unknown smooth drift in time. Solution schemes are considered using both the classical variational method and reduction of the original problem to a conditional nonholonomic adaptive optimal control problem. In the second case, a solution is found with the help of the dynamic programming method and a specially chosen adjustment algorithm for unknown parameters.

To the Problem of Expressibility in the Algebra of Partial Boolean Functions
V. V. Tarasov
pp. 59–64

Abstract—The paper considers the problem of expressibility of total Boolean functions by superpositions over a system of partial Boolean functions. The problem is solved in terms of precomplete Boolean classes, i.e., extensions of Post classes in the algebra of partial Boolean functions.

Experimental Investigation of Forecasting Methods Based on Data Compression Algorithms
B. Ya. Ryabko and V. A. Monarev
pp. 65–69

Abstract—We suggest and experimentally investigate a method to construct forecasting algorithms based on data compression methods (or the so-called archivers). By the example of predicting currency exchange rates we show that the precision of thus obtained predictions is relatively high.