PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 10, Number 1, January–March, 1974
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CONTENTS

Linear Transmission of Nonstationary Gaussian Messages in a Gaussian Channel with Feedback
I. A. Ovseevich and M. S. Pinsker
pp. 1–5

Abstract—A linear scheme is formulated for the transmission of an arbitrary Gaussian message in a Gaussian channel with full feedback, and the optimality of the scheme is proved for the case of white noise in the channel.

Uniformly Packed Codes
L. A. Bassalygo, G. V. Zaitsev, and V. A. Zinov'ev
pp. 6–9

Abstract—The concept of uniformly packed codes is generalized. Necessary conditions for their existence are deduced (in particular, an analog of Lloyd’s theorem for perfect codes), and the weight spectrum of such codes is given. Several families of uniformly packed codes are described, and the results of a computer search for such codes are given.

Decoding Complexity of Low-Density Codes for Transmission in a Channel with Erasures
V. V. Zyablov and M. S. Pinsker
pp. 10–21

Abstract—It is proved that low density codes of length $n$ exist with a decoding that corrects all erasures up to multiplicity $\alpha n$ with a complexity of order $n\ln n$. It is shown that the ratio of $\alpha n$ to the code distance corresponding to the Varshamov–Gilbert bound has a lower bound varying from 0.33 to 0.66 as the transmission rate is increased from 0 to 1.

Evaluation of the Minimum Distances of Cyclic AN Codes
pp. 22–25

Abstract—The weight spectra of certain cyclic codes are determined, the results illustrate the measure of complexity of future research in this area.

Burst-Error-Correcting Codes for Data Transmission and Arithmetic Operations
G. L. Tauglikh and G. M. Tenengol'ts
pp. 26–30

Abstract—Burst-error-correcting codes are described for data transmission and for the execution of arithmetic operations. The codes have a significantly lower redundancy than the Fire codes and their arithmetic analogs.

Estimation of a Signal Parameter in Gaussian White Noise
I. A. Ibragimov and R. Z. Khas'minskii
pp. 31–46

Abstract—The asymptotic properties of the maximum-likelihood estimator (MLE), truncated MLE, and Bayes estimators of a one-dimensional parameter are investigated for the transmission of a continuous signal in a channel with Gaussian white noise. The conditions are determined under which the consistency and asymptotic efficiency of these estimators (i.e., in the terminology of Kotel'nikov [Theory of Potential Noise Immunity, Moscow–Leningrad, Gosenergoizdat, 1956 (in Russian)], the absence of anomaly) are guaranteed. The results obtained in this connection may be regarded as a mathematically rigorous expression of the assertion in the book cited that anomaly is absent if the noise is sufficiently small and different branches of the signal curve do not pass too close to one another. Frequency modulation is studied in closer detail. In particular, an exponentially exact bound is found for the width of the band in which a consistent estimate of the parameter is obtainable, i.e., anomaly is absent, for a given transmission time.

Estimates of a Periodic-Signal Parameter against a White Noise Background
M. B. Nevel'son
pp. 47–57

Abstract—Simple recursive estimators are discussed for a parameter of a periodic signal transmitted in an additive channel with Gaussian white noise. Sufficient conditions arc given for these estimators to be consistent and asymptotically efficient.

Optimal Processing of Space-Time Fields in Selective-Fading Channels
D. D. Klovskii and V. A. Soifer
pp. 58–63

Abstract—Discrete-variable models are discussed for space-time communication channels with selective fading. An algorithm is synthesized for the optimal processing of fields with the discrimination of discrete messages for signals of arbitrary waveform.

Recursive Estimation in the Presence of a Control Parameter
I. M. Slivnyak
pp. 64–72

Abstract—A system containing an estimated parameter and a control parameter is analyzed. The measurement errors arc additive and the probability density function of the measurement error is concentrated on a finite interval with jumps at both ends. Recursive asymptotic optimal control strategies an estimate of the unknown parameter, and an asymptotic expression for the risk in the case of a large number of measurements are found for a quadratic loss function.

Bernoulli Scheme with Closure
M. V. Lomonosov
pp. 73–81

Abstract—A problem of the following type is investigated: Given a finite set $E$ in which a class of subsets has been identified, what is the probability that a set of elements sampled from $E$ by the Bernoulli scheme will belong to that class? Inequalities analogous to those obtained earlier [M.V. Lomonosov and V.P. Polesskii, Probl. Peredachi Inf., 1971, vol. 7, no. 4, pp. 78–81; 1972, vol. 8, no. 2, pp. 47–53] for the special case of the connectivity probability of a random graph are proved with certain assumptions on the identified class of subsets. Concurrently, all the proofs are simplified, and some of the results are strengthened.

Limit Distributions of Additive-Type Functionals in a Particular Queuing Problem
N. M. Akulinichev and V. A. Ivannikov
pp. 82–88

Abstract—The limit distribution functions as $t\to\infty$ for the total number $w_t$ of lost calls in an interval $(0,t)$ by the $GI|M|n|n+m$ queuing system are investigated for the cases $m=0$ and $m\ne0$. The asymptotic normality of the additive functional $w_t$ as $t\to\infty$ is proved, and the parameters of the corresponding limit distributions are calculated. Examples are given.

Binary Symmetric Channel Capacity Is Attained with Irreducible Codes
V. D. Goppa
pp. 89–90

Abstract—The asymptotic optimality of irreducible codes for a binary symmetric channel is proved.