PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 14, Number 1, January–March, 1978
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CONTENTS

On Bounds for Packings on a Sphere and in Space
G. A. Kabatyanskii and V. I. Levenshtein
pp. 1–17

Abstract—A method is proposed for obtaining bounds for packings in metric spaces, the method being based on the use of zonal spherical functions associated with a motion group of the space. For the maximum number $M(n,\theta)$ of points of a unit sphere of $n$-dimensional Euclidean space at an angular distance of not less than $\theta$ from one another, the method is used to obtain an upper bound that is better than the available ones for any fixed $\theta$ ($0<\theta<\pi/2$) and $n\to\infty$. This bound yields a new asymptotic upper bound for $\delta_n$, namely, the maximum packing density of an $n$-dimensional Euclidean space by equal balls.

Variable-Length Convolutional Coding of a Sequence of Independent Binary Symbols
V. N. Koshelev
pp. 17–25

Abstract—The article examines the application of convolutional coding methods to the problem of compression of data produced by a binary memoryless source. As compared to a convolutional coding arrangement with a constant compression factor, a variable-compression-factor arrangement has a more reliable and stable sequential decoding procedure. For coding arrangements with a variable generating sequence, bounds are obtained for the first two moments of the number of vertices of a free-type code that can be checked by the decoding device for one message edge.

Estimation of Spectrum Parameters of Random Processes on the Basis of Observations in Noise
K. O. Dzhaparidze and G. I. Marr
pp. 26–35

Abstract—The case is considered in which the observed process is the sum of two independent stationary random processes, namely, the signal that is of interest and distortion noise, under the assumption that both processes are Gaussian. The paper considers the problem of testing the hypothesis that noise is present in the available observation data; a method is proposed for obtaining asymptotically effective estimates of the unknown spectral-density parameters of the signal and the unknown intensity of “white noise.”

On Asymptotic Optimality of Recursive Estimates
M. B. Nevel'son
pp. 35–49

Abstract—The article considers the problem of nonparametric estimation of a functional of an unknown distribution on the basis of independent observations if this functional is the solution of some system of equations. Under broad conditions, recursive estimates of stochastic-approximation type are set up that are locally asymptotically minimax in the class of loss functions that increase not more rapidly than a power law.

Analysis of Measurement Accuracy for the Coordinates of the Center of Gravity of an Optical Image
P. A. Bakut, I. N. Troitskii, and N. D. Ustinov
pp. 49–54

Abstract—The measurement accuracy for the coordinates of the center of gravity of an optical image is investigated with allowance for the quality of post-detector processing, for the case in which the received light signal passes through a turbulent atmosphere.

Some Properties of Boolean Differentials and of Activities of Arguments of Boolean Functions
Sh. E. Bozoyan
pp. 54–62

Abstract—The concept of the derivative of a Boolean function with respect to an ensemble of arguments is introduced, and a number of properties are established. Some properties of activities of arguments of Boolean functions are also established. The concept of activity of elements of functional schemes is also introduced; it is employed in the structural theory of circuit reliability.

Estimates of Information Cost of Computing Boolean Functions in Combination Circuits
A. P. Goryashko and A. S. Nemirovskii
pp. 63–70

Abstract—A new measure of the complexity of Boolean functions is introduced, this being defined by the quantity of information transmitted over all the channels of a circuit that computes a Boolean vector-valued function. Upper and lower bounds for this complexity measure are obtained.

Note on Fast Multiplication of Polynomials over Galois Fields
L. A. Bassalygo
pp. 71–72

Abstract—It is noted that multiplication of polynomials over Galois fields virtually coincides with ordinary multiplication of natural numbers.

Bounds on the Convergence Rate in Limiting Theorems for an $M|G|1|\infty$ System under Heavy Traffic
Ya. G. Genis
pp. 72–76

Abstract—The author determines the error involved in replacing the real distribution functions for the dwell time in the system, the waiting time for servicing to begin, and the queue length in the steady state by limiting distribution functions. A system without priorities and a system with absolute and relative priorities are considered.

BOOK REVIEWS

E. L. Blokh and V. V. Zyablov. Generalized Concatenated Codes
Reviewed by G. Sh. Poltyrev
pp. 77–78