PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Error Probability Exponent for a Feedback System with the Use of a Concatenated Code
L. F. Zhigulin and V. V. Zyablov
pp. 1–6

Abstract—A system with (noiseless) feedback and advanced correction based on a concatenated code is analyzed. An upper bound is derived for the error probability in the system and for the average code combination length for a given concatenated code decoding algorithm in the case of a memoryless channel.

Block Transmission of a Weak Signal in a Memoryless Channel
M. V. Burnashev
pp. 7–14

Abstract—A scheme related to [J.P.M. Schalkwijk and T. Kailath, IEEE Trans. Inf. Theory, 1966, vol. 12, no. 2, pp. 172–182; J.P.M. Schalkwijk, IEEE Trans. Inf. Theory, 1966, vol. 12, no. 2, pp. 183–189; 1968, vol. 14, no. 2, pp. 324–331; K.Sh. Zigangirov, Probl. Peredachi Inf., 1967, vol. 3, no. 2, pp. 98–101] is formulated for the transmission of binary messages in a discrete-time memoryless channel with complete feedback, asymptotically optimizing the transmission rate for a weak input signal. The capacity is calculated for a channel with “almost smooth” noise.

Construction of Single-Error-Correcting Nonbinary Arithmetic Codes
V. N. Dyn'kin and B. N. Kimel'fel'd
pp. 15–18

Abstract—The authors solve the problem of determining a fundamental characteristic of a single-error-correcting AN-code, namely the quantity $M_r(A,3)$, which is defined as the minimum positive integer, the weight of whose product by $A$ in the base $r$ number system is less than $3$. The proposed method can be used for any $r$. Expressions are given for the computation of $M_r(A,3)$ when $r=5,7,11$, and $8$.

Optimization of Concatenated Decoding Algorithms
V. V. Zyablov
pp. 19–24

Abstract—The correcting properties of concatenated and iterative codes implemented in various algorithms for their concatenated decoding are investigated. An assessment of the correcting properties (multiplicity of reliably corrected errors) is obtained by the analysis of a game situation with the channel and the decoder as players. The losses of the channel in this case are estimated in terms of the multiplicity of the error sets, and the losses of the decoder are estimated in terms of the number of decoding trials. A minimax strategy is found for a fixed number of decoding attempts.

Matrix Algorithm for the Synthesis of Minimal Encoding Networks for Linear Convolutional Codes
V. P. Zarovnyi
pp. 25–31

Abstract—An algorithm for the synthesis of minimal-memory encoding networks on a code matrix or on the transfer function of a linear convolutional (recurrent) code is described. The operation of the algorithm is illustrated by examples. The results are extended to a broader class of convolutional codes.

Asymptotic Behavior of the Linear Prognosis Error for a Class of Stochastic Processes
A. L. Genis
pp. 32–42

Abstract—Estimates are obtained for the quantities $\delta_T(\tau)=\sigma^2_T(\tau)-\sigma^2(\tau)$ and $J(\xi^\infty_0,\xi^{-T}_{-\infty}\,|\,\xi^0_{-T})$ [where $\sigma^2_T(\tau)$ is the error of prognosis from an earlier $T$ to a future $\tau$] for a certain class of stochastic processes. It turns out that these quantities decay according to a power law.

Optimal Coherent and Incoherent Diversity Reception in Channels with Fluctuation and Concentrated Noise Disturbances
A. A. Sikarev
pp. 43–49

Abstract—Algorithms are obtained for coherent diversity reception and for incoherent diversity reception with coherent multipath addition in systems optimal under the simultaneous action of fluctuation and concentrated noise disturbances that can be approximated by a quasi-deterministic noise model. The potential noise immunity of the systems and the possibilities for the suppression of concentrated noise are analyzed.

Estimation of the Spectrum of a Gaussian Stochastic Process on the Basis of a Realization of the Process with Omissions
V. G. Alekseev and Yu. A. Savitskii
pp. 50–54

Abstract—The investigated problem is to formulate an estimate of the spectral density $f(\lambda)$ ($|\lambda|\le\pi$) of a stationary Gaussian stochastic process $\xi_k$, $k=\ldots,-1,0,1,\ldots\strut$, on the basis of a realization of the process in which every sequence of $m$ observations is followed by $p$ omissions. An asymptotically (with unbounded growth of the volume of the realization) unbiased and consistent estimate is formulated for the value of the function $f(\lambda)$ at a point $\lambda_0$, where $|\lambda_0|\ne k\pi/(m+p)$, for the case $m>p\ge 1$. The estimate of $f(\lambda_0)$ is given in a form suitable for computation by means of the rapid Fourier transformation method.

Upper Bound for the Power of an Automaton State Code
Yu. L. Sagalovich
pp. 55–63

Abstract—An upper bound on the power of an automaton state code is obtained on the basis of two race models for $q$-stable delay elements. The upper and lower bounds on the power of the automaton state code are compared with the corresponding bounds for ordinary noise-immune block codes, and some new problems are discussed.

Complexity of an Optimum Nonblocking Switching Network without Reconnections
L. A. Bassalygo and M. S. Pinsker
pp. 64–66

Abstract—A method is proposed for the synthesis of an asymptotically optimum nonblocking switching network.

Distribution of the Number of Requests in a Queueing System with “Warm-up”
Yu. I. Ryzhikov
pp. 67–74

Abstract—A method is proposed for calculating the stationary probabilities of the states of an $M|G|1$ queueing system in which a request entering the unoccupied system has a service time distribution $\Phi(\tau)$ and in all other cases has a service time distribution $F(\tau)$.

A Two-Pattern Recognition Problem for a Noisy Channel, Solvable by Extensive Game Theory
V. F. Nesteruk and N. N. Porfir'eva
pp. 75–79

Abstract—The two-pattern recognition problem with the possibility of a null situation is investigated. The problem is stated in an extensive game context; the optimal strategies of the observation system are determined, a recognition criterion is found, and the role of the null situation is assessed.

Bounded-Density Burst-Error-Correcting Codes
I. M. Boyarinov
pp. 80–83

Abstract—Linear and, in particular, cyclic codes correcting single burst errors with a bounded number of nonzero components are investigated. As a result of the study linear codes are constructed that correct arbitrary burst errors of length $b$ or less and have asymptotically minimum redundancy.

Quantum-Mechanical Approach to Optical Image Reconstruction
V. V. Mityugov and V. P. Morozov
pp. 84–87

Abstract—A unified quantum-mechanical approach to problems in the reconstruction of images is described in the formalism of linear canonical transformations of field variables.