CONTENTS                  

Optimal Filtering of a Gaussian Signal Against a Background of Almost Gaussian Noise
M. S. Pinsker and V. V. Prelov
pp. 295–311

Abstract—An asymptotic expression as $\varepsilon\to 0$ is derived for the mean-square error of the optimal nonlinear filtering of a discrete-time stationary Gaussian process $X=\{X_j\}$ from the observations $Y=\{Y_j\}$ under the assumption that the observed process $Y$ is the sum $Y_j=X_j+N_j+\varepsilon Z_j$, $j=0,\pm1,\ldots\strut$, where the stationary processes $X=\{X_j\}$, $N=\{N_j\}$, and $Z=\{Z_j\}$ are mutually independent and, moreover, $N$ and $X$ are Gaussian processes having spectral densities and $Z$ is an entropy-regular second-order process. It is also shown that the optimal linear filter reconstructing the signal $X$ from the observations $X+N$ (i.e., when the weak additional noise $\varepsilon Z$ is missing) is asymptotically optimal. If $\varepsilon Z$ is an entropy-singular process, then the mean-square error of the optimal filtering does not depend on $Z$ ($\{Z_j\}$ can be correctly reconstructed from the observations $\{Y_j\}$).

Weighted Voting in Multichannel Systems of Discrete Signal Transmission
Yu. A. Zuyev and S. K. Ivanov
pp. 312–324

Abstract—We consider the problem of improving the reliability of binary signal transmission by duplicating information channels and using a procedure of weighted voting at the receiver for reconstruction of the symbol transmitted. Quantitative estimates for such a reconstruction error probability are obtained. The properties of the simple-majority decision are considered separately.

A Simple Proof of the Main Inequalities for Fundamental Parameters of Codes in Polynomial Association Schemes
V. I. Levenshtein
pp. 325–336

Abstract—$P$- and $Q$-polynomial association schemes are considered. A simple proof of seven main inequalities for such code parameters as the minimum distance, the dual distance, the number of distances, the external distance, and the covering radius is given. This proof is based on using the annihilating and dual-annihilating polynomials for codes and orthogonality conditions for polynomial systems which are adjacent to systems $P$ and $Q$. All of these inequalities, some of which are new, are attained in some cases.

On Sequential Classification of Autoregressive Processes with Unknown Variance of Noise
A. A. Dmitrienko and V. V. Konev
pp. 337–347

Abstract—The problem of guaranteed discrimination of a finite number of hypotheses for an autoregressive process from direct and indirect observations (with an additive noise) is considered. Under each hypothesis, the autoregressive parameters are assumed to be known, whereas the variances of the process noise and interference in the observation channel may take arbitrary values. Sequential procedures of classification with a guaranteed probability of the correct decision are proposed. Asymptotic formulas for duration of the procedures are obtained.

On the Synthesis of Circuits Using Unreliable Generalized Contacts
V. V. Tarasov
pp. 348–352

Abstract—We consider the algebra of unreliable generalized contacts (switches) and present necessary and sufficient conditions for implementation of the contacts with desired reliability.

Fast Calculation of the Riemann Zeta Function $\zeta(s)$ for Integer Values of the Argument $s$
E. A. Karatsuba
pp. 353–362

Abstract—We suggest an algorithm for fast calculation of the Riemann zeta function for integer values of the argument, which is based on the method for fast calculation of Siegel's $E$-functions. The computational complexity is near to optimal.

The Best Possible Bounds for Full Rank Probability of a Random Submatroid
V. P. Polesskii
pp. 363–379

Abstract—We give a new proof of (the sharpest at present) attainable and effectively computable lower bounds for full rank probability of a random submatroid, which were previously obtained by the author. The proof reveals the nature of these bounds and involves majorization theory methods of deriving inequalities in constructing such bounds. The comparison of the obtained bounds with other attainable ones for the characteristic under estimation is given.

Using Ideas and Methods of Information Theory in Analyzing the Flexibility of the Language of Ants and Their Aptitude to Add and Subtract Small Numbers
Zh. I. Reznikova and B. Ya. Ryabko
pp. 380–387

Abstract—During experiments, ants had to transmit information on the number of one of 40 “branches” with a feeding-tray in order to get food. However, the feeding-tray appeared considerably more often on two previously chosen branches than on all the others. It turned out that ants, first, could reconstruct their communication system when it was necessary to coordinate message lengths with the frequency of their occurrence, and second, could add and subtract small numbers while transmitting information about the feeding-tray number.