PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 6, Number 1, January–March, 1970
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CONTENTS

Codes with Generalized Majority Decoding and Convolutional Codes
S. D. Berman and A. B. Yudanina
pp. 1–12

Abstract—Tensor operations on codes with majority decoding leading to codes with generalized orthogonalization are considered, and corresponding convolutional codes with complete orthogonalization are constructed.

Transmission Capacity with Zero Error and Erasure
M. S. Pinsker and A. Yu. Sheverdyaev
pp. 13–17

Abstract—A definition of transmission capacity $C^0_{\text{er}}$ with zero error and erasure is introduced and it is shown that for a sufficiently extensive class of channels (which includes, for example, a completely asymmetric binary channel) the capacity $C^0_{\text{er}}$ coincides with the usual capacity $C$.

Error Probability in Transmission over a Gaussian Channel with Noiseless Feedback
Nguyen Dang Te
pp. 18–25

Abstract—Transmission over a discrete Gaussian channel with white and nonwhite noise and with complete feedback is considered. The upper limits of the optimum error probability are obtained when transmitting $\tau^l$ messages ($\tau$ is the transmission length), whose exponential terms are the same as the exponential term of the optimum error probability in transmission of two messages.

Asymptotic Error Probability for Transmission over a Channel with White Gaussian Noise and Instantaneous Noiseless Feedback
A. G. D'yachkov
pp. 26–36

Abstract—This paper describes the transmission of information which takes on a finite number of equiprobable values and which is independent of the noise in the communication channel, over a channel with continuous time and instantaneous (complete) noiseless feedback. The additive noise in the communication channel is defined by means of a generalized random process, called white Gaussian noise. The exponent of the error probability (the reliability function) for such transmission is calculated.

On the Theory of Cyclic Arithmetic Codes
pp. 37–42

Abstract—The author proposes new cyclic arithmetic codes with a large distance, namely, AN-codes with $$A=(2^{\text{lcm}(e_ip_i^{m_i-1})}-1)/B,\quad\text{where}\quad B=\prod\limits^i_{i-1}p_i^{m_i}$$ and $e_i$ is the exponent of $2$ mod $p_i$. A detailed study is made of the cases $B=p_1p_2$ and $B=p^m$, for which estimates of the arithmetic distance and efficiency of the codes are obtained.

Ya. Z. Tsypkin and G. K. Kel'mans
pp. 43–49

Abstract—We consider the problem of classifying situations when there is no a priori information on their probability characteristics. Using the proposed adaptive Bayes procedure, optimal iterative algorithms are obtained for estimating Bayes decision rules. As an example we solve the problem of constructing a Neyman–Pearson receiver.

Use of Equidistant Codes for State Assignment in an Automaton
pp. 50–60

Abstract—Special codes for increasing the structural reliability of a finite automaton are constructed. The subject of the investigation is equidistant codes, and in particular, codes yielded by Hadamard matrices. An upper bound is established for the number of internal elements (storage elements) of a noiseproof automaton.

Invariant Measures of Certain Markov Operators Describing a Homogeneous Random Medium
L. N. Vasershtein and A. M. Leontovich
pp. 61–69

Abstract—We are given a lamp in a row of lamps stretching to infinity on either side; if the lamp and an immediate neighbor are burning at a given instant, it will continue to burn at the next instant; otherwise, it will burn only with probability θ. We show in this paper that, discounting the trivial case of “all lamps burning,” there is not more than one invariant measure on the space of states of this random medium.

The Stability of Stochastic Difference Systems
V. M. Konstantinov
pp. 70–75

Abstract—This paper is devoted to problems in the stability of stochastic difference schemes. Conditions are given for $p$-stability and the probability stability of the trivial solution of the equations describing difference systems. A basis is provided for the possibility of linearizing such systems. A number of examples are considered.

A Single-Channel Queueing System with Limited Queueing, Several Input Flows, and Arbitrary Servicing Time
D. G. Mikhalev
pp. 76–84

Abstract—We consider a single-channel queueing system in which there are several input flows with relative servicing priorities and a limited number of queueing positions. The servicing time distribution is assumed to be arbitrary. Recurrence relations are obtained for finding the system-state probabilities. We find the mean waiting time and the mean number of requests in each type of queue. A computational algorithm is found for determining the probability of loss for each type of request.

Some Properties of Infinite Prefix Codes
Al. A. Markov
pp. 85–87

Abstract—Four conditions for completeness of a finite prefix code are considered, and it is shown that no two of these conditions are equivalent in the class of infinite prefix codes.

The Distribution of the Largest Values in the Realization of Random Processes with Discrete Time
Ya. A. Fomin
pp. 88–92

Abstract—An expression is given for the distribution of the duration of intervals between peaks of a stationary normal-random process in terms of the limiting distribution of its absolute maximum for large intervals. A general expression is determined for the probability density of the largest values in realizations of random processes with discrete time (random sequences); an approximation of this expression, based on the properties of multiply connected Markov chains, is given. As an example the distribution of the largest values in realizations of a stationary Rayleigh sequence is calculated approximately.