PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Information Rates in Certain Stationary Non-Gaussian Channels in Weak-Signal Transmission
M. S. Pinsker, V. V. Prelov, and E. C. van der Meulen
pp. 1–13

Abstract—Let $\xi=\{\xi_j\}$ and $\zeta=\{\zeta_j\}$ be independent discrete-time second-order stationary processes obtained by means of an invertible linear transformation $L$ from a stationary entropy-regular process $X= \{X_j\}$ and a sequence of i.i.d.\ random variables $Z=\{Z_j\}$ such that $\xi=LX$ and $\zeta=LZ$. Under the assumption that the Fisher information $J(Z_1)$ exists and some additional assumptions on the properties of the linear transformation $L$ and on the density function of $Z_1$, it is shown that the following equality for the information rate $\overline{I}(\varepsilon\xi; \varepsilon\xi+\zeta)$ holds: $\overline{I}(\varepsilon\xi; \varepsilon\xi+\zeta)=\displaystyle\frac{1}{2}J(Z_1)(\operatorname{var}X_1)\varepsilon^2+ o(\varepsilon^2),\: \varepsilon\to 0$. This result is a generalization of the corresponding results of [M. S. Pinsker et al., IEEE Trans. Inf. Theory, 41, No. 6, 1877–1888 (1995); M. S. Pinsker and V. V. Prelov, Probl. Peredachi Inf., 30, No. 4, 3–11 (1994) ], where $\zeta$ was assumed to be Gaussian.

Sections of the Del Pezzo Surfaces and Generalized Weights
M. I. Boguslavsky
pp. 14–24

Abstract—We analyze sections of split Del Pezzo surfaces and compute generalized Hamming weights of the corresponding algebraic-geometric codes.

Implementation of Convolutional Decoding Algorithms in CDMA Systems
D. K. Zigangirov, S. A. Popov, and V. V. Chepyzhov
pp. 25–38

Abstract—On the basis of the Qualcomm standard, the efficiency of sequential decoding in code-division multiple-access systems (CDMA) is investigated.

Detection and Reception of a Sequence of Signals Distorted by a Random Interference and Independent Noise
S. V. Pazizin
pp. 39–47

Abstract—Within the framework of a “signal—interference—noise” model, we consider the problem of recognizing two signals from a sequence of vector observations. The asymptotical normality of the log-likelihood ratio is demonstrated, and asymptotically sufficient statistics are found at a small (signal + interference)/noise ratio for an isolated observation. As an example, we consider the case where the interference is a time delay of the signal appearance.

Minimax Detection of a Signal for Besov Bodies and Balls
Yu. I. Ingster and I. A. Suslina
pp. 48–59

Abstract—We consider an asymptotical minimax problem of detection of a signal from functional sets corresponding to the Besov balls $B_{p,q}^\sigma(C)$ or Besov bodies $\Theta_{p,q}^s(C)$ with a remote $L_2$-ball, the signal being observed in the Gaussian white noise of intensity $\varepsilon\gt0,\:\sigma\gt0,\:s=\sigma-1/p+1/2\gt0$. For the case of Besov bodies, for $q\geq p$ or $\min(p,q)\geq2$, asymptotically exact estimates of the minimax probability of the detection errors are obtained, while for other cases and Besov balls, asymptotically exact conditions of the minimax distinguishability are found.

Optimum Discretization of Weak-Signal Observations under Constraints on the Quantization Rate
I. M. Arbekov
pp. 60–66

Abstract—The paper investigates the problem of determining the optimum procedure of discretization of weak-signal observations in Gaussian noises under constraints on the rate of data quantization. The optimization is carried out with respect to the value of the asymptotical relative efficiency (ARE) of the likelihood-ratio criteria on the binary-symbol space and on the initial-data space. We find the conditions for the relationship between the powers of the determinate and stochastic components of the signal, in order that the single-digit discretization under the proper choice of the threshold be optimum.

On Optimal Behavior of Finite Automata in a Random Medium
A. V. Kolnogorov
pp. 67–75

Abstract—We propose a solution of the “multi-armed bandit” problem in the minimax formulation with the use of finite automata with constant structure and known fixed number of states.

Estimation of the Randomness of Figure Overlap
N. B. Vasil'ev and A. M. Leontovich
pp. 76–96

Abstract—The problems considered in the paper arose as grounds for one of the methods of determining to what extent a configuration of biological objects (cells) observed in a field of vision is random. Estimates for the variance of the intersection area for cells of a given shape randomly placed in a field of vision are presented. For this, several geometric theorems of isoperimetric type are proved. Estimates for arbitrary moments of figure-intersection areas are also obtained. Based on them, the central limit theorem is proved under some additional assumptions (figures are assumed to be small and round enough).