PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Remark on the Reliability Function of a Symmetric Channel under List Decoding
V. M. Blinovsky
pp. 85–88

Abstract—We complete the derivation of a formula for the reliability function of a $q$-ary symmetric channel under list decoding at zero rate.

On a Model and Capacity of MIMO Channels
B. S. Tsybakov
pp. 89–97

Abstract—A model of a MIMO fading channel is considered which does not assume that the discrete-time axis is divided into long intervals with a constant channel. It assumes only that there are $\ell$ possible states (or subchannels) of the channels, and at each moment both the transmitter and receiver know the channel state. The average input power in the subchannels can be different and not equal to the average input power over the full time axis. We obtain a lower bound for the capacity of the considered vector channel. Also, we consider a vector channel with one transmitting and two or more receiving antennas. We obtain optimum distributions of the average power over the subchannels and lower bounds for the channel capacity.

Generalization of a Pinsker Problem
V. V. Prelov
pp. 98–116

Abstract—A generalization of a Pinsker problem [1] on estimation of mutual information via variation is considered. We obtain some upper and lower bounds for the maximum of the absolute value of the difference between the mutual information of several random variables via variational distance between the probability distributions of these random variables. In some cases, these bounds are optimal.

On (Partial) Unit Memory Codes Based on Gabidulin Codes
A. Wachter, V. R. Sidorenko, M. Bossert, and V. V. Zyablov
pp. 117–129

Abstract—(Partial) unit memory ((P)UM) codes provide a powerful possibility to construct convolutional codes based on block codes in order to achieve a high decoding performance. In this contribution, a construction based on Gabidulin codes is considered. This construction requires a modified rank metric, the so-called sum rank metric. For the sum rank metric, the free rank distance, extended row rank distance, and its slope are defined analogous to the extended row distance in the Hamming metric. Upper bounds for the free rank distance and slope of (P)UM codes in the sum rank metric are derived, and an explicit construction of (P)UM codes based on Gabidulin codes is given.

Steiner Systems $S(v,k,k-1)$: Components and Rank
V. A. Zinoviev and D. V. Zinoviev
pp. 130–148

Abstract—For an arbitrary Steiner system $S(v,k,t)$, we introduce the concept of a component as a subset of a system which can be transformed (changed by another subset) without losing the property for the resulting system to be a Steiner system $S(v,k,t)$. Thus, a component allows one to build new Steiner systems with the same parameters as an initial system. For an arbitrary Steiner system $S(v,k,k-1)$, we provide two recursive construction methods for infinite families of components (for both a fixed and growing $k$). Examples of such components are considered for Steiner triple systems $S(v,3,2)$ and Steiner quadruple systems $S(v,4,3)$. For such systems and for a special type of so-called normal components, we find a necessary and sufficient condition for the $2$-rank of a system (i.e., its rank over $\mathbb{F}_2$) to grow under switching of a component. It is proved that for $k\ge 5$ arbitrary Steiner systems $S(v,k,k-1)$ and $S(v,k,k-2)$ have maximum possible $2$-ranks.

A Linear Algebraic Approach to Multisequence Shift-Register Synthesis
V. R. Sidorenko and G. Schmidt
pp. 149–165

Abstract—An efficient algorithm which synthesizes all shortest linear-feedback shift registers generating $K$ given sequences with possibly different lengths over a field is derived, and its correctness is proved. The proposed algorithm generalizes the Berlekamp–Massey and Feng–Tzeng algorithms and is based on Massey's ideas. The time complexity of the algorithm is $O(K\lambda N)\lesssim O(KN^2)$, where $N$ is the length of a longest sequence and $\lambda$ is the linear complexity of the sequences.

On Universal Algorithms for Adaptive Forecasting
V. V. V'yugin
pp. 166–189

Abstract—In the last decade, new methods of forecasting were developed different from traditional statistical methods. In particular, it is possible to “efficiently” predict any sequence of outcomes without using any hypothesis on the nature of a source generating it. In the present paper, a modified version of the universal forecasting algorithm is considered. The main part of the paper is devoted to algorithmic analysis of universal forecasting methods and to exploring limits of their performance.

Critical States of Strongly Interacting Many-Particle Systems on a Circle
V. A. Malyshev
pp. 190–200

Abstract—Normally, two scales are considered in multicomponent systems, namely, macro and micro scales. Moreover, it is accepted that macro variables are completely defined by micro variables. We show that in the considered particle system with strong local (Coulomb) interaction this is not always the case. Namely, information concerning some macro variables can be encoded on a scale much finer than the micro scale.

Key Masking Using Biometry
A. L. Chmora
pp. 201–215

Abstract—We construct an abstract model based on a fundamental similarity property, which takes into account parametric dependencies and reflects a specific collection of requirements. We consider a method for masking a cryptographic key using biometry, which satisfies the constructed model and guarantees an adequate practical security level.