PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 18, Number 4, October–December, 1982
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CONTENTS

Lower Bound for Error Probability in a Discrete Memoryless Channel with Feedback
A.Yu. Sheverdyaev
pp. 227–234

Abstract—It is shown that in the case of block transmission of length $N$ with feedback over a discrete memoryless channel, the error probability satisfies the lower spherical-packing bound at rates less than the channel capacity, while the probability of correct reception satisfies the Arimoto upper bound at rates greater than the capacity. Thus, the logarithmic asymptotic behavior (as $N\to\infty$) of the error probability and probability of correct reception is known at least for all rates greater than the critical one.

Capacity in the Case of Transmission by Smooth Surfaces in Multiparametric Gaussian White Noise
M. Nusbaum
pp. 235–244

Abstract—The author computes the asymptotic behavior of the capacity of a channel with multiparametric Gaussian white noise when the signal is a smooth periodic function of many variables. Constraints are imposed on the average power of the signal and its partial derivatives. The derivatives may be of different order $\beta_T$ in different directions. It is shown that when the noise intensity $\varepsilon^2$ tends to zero, the capacity increases as $\varepsilon^{-2/(\gamma+1)}$, where $\gamma=(\sum\beta_i^{-1})^{-1}$.

On Methods of Code Lengthening
V. A. Zinov'ev and S. N. Litsyn
pp. 244–254

Abstract—The available methods of increasing code lengths are presented in a more general form, leading to a variety of optimal codes. The initial codes are provided by embedded systems of generalized concatenated codes, as well as BCH, Hamming, Preparata, Kerdock, Goethals, and Delsarte–Goethals codes.

Multivariate Asymptotically Optimal Stochastic Approximation Procedure
A. M. Benderskii and M. B. Nevel'son
pp. 255–262

Abstract—The authors consider the problem of estimating the root of the regression equation in the multivariate case. It is shown that if there exists an estimate that converges to the unknown value of the root at some rate, then it can be used, practically without any additional conditions, to construct a recursive procedure of stochastic-approximation type which is optimal in the sense of the minimum covariance matrix of the limiting normal law.

Sequential Parameter Estimation and Filtering of Stochastic Processes
A. G. Tartakovskii
pp. 263–272

Abstract—The article considers problems of truncated sequential estimation of constant and variable random parameters in a Bayesian formulation. Conditions are given under which the (nonasymptotically) optimal estimation procedure is a nonsequential procedure. An optimal sequential-estimation procedure is obtained for the parameter of an exponential distribution.

On Minimax Filtering of Functions in $L_2$
G. K. Golubev
pp. 272–278

Abstract—The article considers the problem of filtering of nonrandom functions $s(t)\in\Sigma_T$ in white noise. It is assumed that class $\Sigma_T$ is made up of all possible responses of a linear time-optimal filter. The minimax quadratic risk and minimax estimate for $s(t)$ are obtained in this case.

Upper Bound for the Delay in a Multiple-Random-Access System with a Splitting Algorithm
B. S. Tsybakov and N. B. Likhanov
pp. 279–285

Abstract—Papers [R.G. Gallager, Proc. AFOSR Workshop in Commun. Theory Appl., 1978, pp. 74–76; B.S. Tsybakov and V.A. Mikhailov, Probl. Peredachi Inf., 1980, vol. 16, no. 4, pp. 65–79] propose a multiple-random-access algorithm which, in a sense, has been a record-setter in terms of transmission rate up to now. In this paper we obtain an upper bound for the mean-session packet-transmission delay for this algorithm.

Unidirectional Loop Communication Networks with Packet Switching
L. V. Andreev
pp. 285–298

Abstract—The article describes a model of a unidirectional loop communications network with packet switching, in which all stations can exchange messages; the model is a generalization of a number of models investigated earlier. Formulas are obtained for the basic characteristics of the network for an extensive class of priority distributions between flows entering the network.

Some Inequalities for a Multiphase System
A. A. Pukhal'skii
pp. 299–307

Abstract—The author considers a multiphase queuing system with intermediate storage of finite capacity and blocking. Properties of external monotonicity for the capacity of the system are established. A bound is obtained for the capacity of the three-phase system.

INDEX
pp. 309–314

BRIEF COMMUNICATIONS
(available in Russian only)

Decay of the Dependence on an Initial State for Some Multicomponent Markov Systems
L. G. Mityushin
pp. 117–123 (Russian issue)

Abstract—The notion of dependence between two Markov-related random variables is introduced. For two classes of multicomponent Markov systems, we estimate the dependence of the state at time $t$ from an initial state.

On the Asymptotic Expansion of the Mean Square Risk for a Bayesian Estimate
E. K. Trishchenko
pp. 123–125 (Russian issue)

Abstract—We consider the problem of estimation of an unknown parameter affected by unit Gaussian noise. We show that continuity of the a priori density $p(x)$ of this parameter and mean-square differentiability of $\sqrt{p(x)}$ are necessary and sufficient conditions for the second term of the asymptotic expansion of the mean square risk of a Bayesian estimate to be of order $n^{-2}$.