PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

$(\varepsilon,\delta)$-Entropy of Completely Ergodic Stochastic Processes
M. S. Pinsker and L. B. Sofman
pp. 251–255

Abstract—The $(\varepsilon,\delta)$-entropy of completely ergodic stochastic processes is shown to be equal to the message creation rate of these processes.

Generalized Unit-Memory Convolutional Concatenated Codes
V. V. Zyablov and S. A. Shavgulidze
pp. 256–271

Abstract—We develop and analyze a concatenated coding system with inner unit-memory convolutional codes and outer Reed–Solomon codes. We prove the existence of embedded inner code systems in which the main code and all the subcodes have optimal error-correcting properties. We investigate an inner-code decoding algorithm which allows erasures, and tradeoff relations are obtained for error and erasure probabilities. These results lead to the development of a concatenated decoding algorithm for generalized unit-memory convolutional concatenated codes and produce bounds on the decoding error exponent of this algorithm. A bound on decoding complexity of these codes is given.

On the Dual Distance of BCH Codes
V. A. Zinov'ev and S. N. Litsyn
pp. 272–277

Abstract—An upper bound is derived on the dual distance of BCH binary codes. This enables us to improve the lower bound on rational trigonometric sums in fields of characteristic 2.

Doubly Even Extremal Codes of Length 64
V. I. Yorgov
pp. 277–284

Abstract—Doubly even extremal $[64, 32, 12]$ codes are considered. We describe all such codes with automorphism of order $31$. There are $38$ inequivalent codes with this property.

Linear Ternary Quasi-perfect Codes Correcting Double Errors
I. B. Gashkov and V. M. Sidel'nikov
pp. 284–288

Abstract—Linear quasiperfect codes of length $n=1/2(3^k+1)$ are constructed with $2k$ parity-check positions and code distance $5$. Asymptotic expressions are derived for the elements of the distribution of this code.

On Minimax Signal Generation and Reception Algorithms
A. M. Chudnov
pp. 289–293

Abstract—We consider the minimax problem of generation and reception of binary semicontinuous signals with uncertain interference and Gaussian noise. We establish the existence and the properties of the least favorable interference distributions and $\varepsilon$-optimal ($\varepsilon>0$) signal generation and reception algorithms.

Bounds of Error Probability with Decision-Feedback Equalization
F. A. Taubin
pp. 294–297

Abstract—Upper and lower bounds are given on error probability when decision-feedback equalization is used in a channel with intersymbol interference. A simple procedure is proposed for computing the asymptotically exact value of the error propagation factor with weak noise.

Cluster Decompositions for Systems of Automata
S. A. Pirogov
pp. 298–303

Abstract—A method is proposed for computing the characteristics of a system of probabilistic automata with the aid of power series expansions.

Canonical Representation of Input Processes in the Dynamics of Automata
V. I. Levin
pp. 304–312

Abstract—We consider a continuous-time inertialess $(n,1)$-pole which realizes an arbitrary Boolean function $y=f(x_1,\dots, x_n)$ in response to arbitrary switching processes $x_1(t),\dots,x_n(t)$ on its inputs. It is shown that these processes always can be replaced with an equivalent combination of pulses which are linearly ordered in time and free (i.e., not assigned to particular input terminals). This essentially simplifies the identification of the response of the $(n,1)$-pole to complex input processes.

Increasing the Efficiency of Numerical Methods for Models with Repeat Calls
S. N. Stepanov
pp. 313–326

Abstract—We consider some methods of optimal computation of the probability characteristics of models with repeat calls.

Transformations of Poisson Streams and Their Application to Communication Systems
A. D. Vainshtein and A. Ya. Kreinin
pp. 326–334

Abstract—We study the correlation properties of a sequence of transformations of a Poisson stream. The $j$th transformation changes the coordinate $x_i(j)$ of the point $i$ according to $x_i(j)=x_i(j-1)+S_{ij}$, $j\geq 1$, where $S_{ij}$ are jointly independent positive random variables exponentially distributed with the parameter $\mu_j$, $x_i(0)$ is the initial coordinate of the point $i$.

INDEX
pp. 335–340

On Realizability of Finite Autocorrelation Functions
Yu. I. Abramovich and D. Z. Arov
pp. 104–106 (Russian issue)

Abstract—We give a necessary and sufficient condition for a continuous positive definite function $R(\tau)$ ($-\infty<\tau<+\infty$) to be compactly supported. A generalization to the matrix-valued and operator-valued cases is presented.

On Matrices with Nondegenerate Square Submatrices
A. K. Aydinian
pp. 106–108 (Russian issue)

Abstract—We present a method to construct triangular arrays over an arbitrary field $\operatorname{\it GF}(q)$ for which every square submatrix is nondegenerate. Rectangular submatrices of these arrays define generator matrices of MDS codes for $2\le k\le q-1$ ($k$ is the number of information symbols).