PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 23, Number 2, April–June, 1987
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CONTENTS

Delayed Epsilon-Entropy for Small Mean-square Reproduction Error
M. S. Pinsker and A. K. Gorbunov
pp. 91–95

Abstract—We consider the calculation of epsilon-entropy without anticipation, with extrapolation and delay for the case of reproduction with nonzero mean-square error. For a stationary Gaussian sequence, we give asymptotic expressions for epsilon-entropy without anticipation, with extrapolation and delay for the case of small mean-square reproduction error.

Sample Estimate of the Entropy of a Random Vector
L. F. Kozachenko and N. N. Leonenko
pp. 95–101

Abstract—We establish conditions for asymptotic unbiasedness and consistency of a simple estimator of the unknown entropy of an absolutely continuous random vector from a sample of independent observations.

A Bound on the Distance of Unit Memory Generalized Convolutional Concatenated Codes
V. V. Zyablov and S. A. Shavgulidze
pp. 102–110

Abstract—A new class of codes are investigated, namely, binary unit-memory generalized convolutional concatenated codes. Bounds on the free distance and the construction complexity of these codes are obtained.

On the General Code Shortening Construction
V. A. Zinoviev and S. N. Litsyn
pp. 111–116

Abstract—We describe a code shortening construction, which is a generalization of the known procedures. This construction generates a number of new codes with best known parameters.

Correction of Multiple Errors by $q$-ary Codes
A. S. Dolgopolov
pp. 117–121

Abstract—We consider linear $(n,k)$-codes over $\operatorname{\it GF}(q)$ capable of correcting $t$-fold errors in the insertion, erasure, and replacement metric. It is shown that their rate does not exceed $1/2$. For $n\ge 2(k+t-1)$, a sufficient existence condition of such codes is derived. A direct construction is applied to verify this condition for $(4m,2m)$-codes and $t=1$ with $q\ge 7$ and for $(6m,2m)$-codes and $t=2$ with $q\ge 23$.

Fast Correlation Decoding of Reed–Muller Codes
Yu. D. Karyakin
pp. 121–129

Abstract—A fast correlation decoding algorithm is described for the binary Reed–Muller code. A comparative analysis of the decoding complexity of RM codes of various orders is presented.

Lower Asymptotic Bound on the Number of Linear Code Words in a Sphere of Given Radius in $\mathbb{F}_q^n$
V. M. Blinovskii
pp. 130–132

Abstract—The random coding method is applied to determine the asymptotic lower bound on the number of words of a linear code from $\mathbb{F}_q^n$, contained in a sphere of given radius. The bound is uniform relative to the center of the sphere. An upper bound is also derived on the covering radius of linear code. An upper estimate is obtained on the proportion of codes for which these bounds are valid.

Estimation of a Linear Functional from Indirect Observations
R. D. Dodunekova and R. Z. Khas'minskii
pp. 133–138

Abstract—Estimation of a linear functional of the signal $S$ is considered under various prior assumptions about $S$ for the case where we can observe only the input of two integrating filters with additive Gaussian white noise of intensity $\varepsilon^2$ and $\sigma^2$ respectively.

Identification Algorithms for Linear Systems with Correlated Input and Output Noise
A. F. Kushnir
pp. 139–150

Abstract—We consider the estimation of the parameters of the frequency characteristics of a multidimensional linear systems from observations of input and output signals, corrupted by stationary correlated noise. Estimation algorithms are proposed which, in a wide class of non-Gaussian noise, produce asymptotically normal $\sqrt{N}$-consistent estimators, where $N$ is the number of observations. The optimal form of these algorithms is determined, ensuring the lowest asymptotic covariance of the estimators. For the particular case when noise corrupts only the outputs of a multidimensional linear system and the noise spectral matrix is singular, we propose an algorithm which produces $N^{1/2+\nu}$-consistent estimators, where $0\lt\nu\leq 1/2$.

Compression of Numerical Data in Computer Data Processing Systems
B. Ya. Kavalerchik
pp. 151–156

Abstract—A variant of the combinatorial-numbering method is proposed for numerical data encoding in computer data processing systems (DPS). Coding of the common data formats in DPS is considered. The wide applications of the method in MIS are outlined.

Qualitative Methods of Analysis of Systems with Repeat Calls
S. N. Stepanov and I. I. Tsitovich
pp. 156–173

Abstract—We develop a general approach to qualitative estimation of the probability characteristics of systems with repeat calls, which are applicable over the entire range of model input parameters. The proposed method will estimate the probability characteristics in both transient and stationary modes.

BRIEF COMMUNICATIONS
(available in Russian only)

On Coding Complexity of Combinatorial Sources
V. V. Potapov
pp. 103–105 (Russian issue)

Abstract—Let $X$ be a dictionary consisting of binary words of length $n$. We show that there exists a linear one-to-one coding of $X$ with words of length $l\leq 2\log|X|+\log (n/\log|X|)$, whose program complexity equals $l$.

Note on the Construction of $\delta$-Codes
A. G. Saroukhanian
pp. 106–108 (Russian issue)

Abstract—We present constructions of two new classes of cyclic $T$-matrices, which leads to the construction of Hadamard matrices of new orders.

Remark on the Solution of Quadratic Equations over a Galois Field
V. V. Kvashennikov and V. G. Yakovlev
pp. 108–111 (Russian issue)

Abstract—We suggest a formula for the solution of quadratic equations over Galois fields $\operatorname{\it GF}(2^m)$.

A New Data Compression Method
V. N. Soldatov
pp. 111–112 (Russian issue)

Abstract—We suggest a new data compression method based on eliminating insignificant symbols from digital messages and forming data arrays of variable structure.