PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 32, Number 4, October–December, 1996
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CONTENTS

Minimax Bahadur Efficiency for Small Confidence Levels
A. P. Korostelev and S. L. Leonov
pp. 303–313

Abstract—We investigate the problem of estimating an unknown regression function at a fixed point. As the efficiency criterion, we use the risk function initially suggested by R. Bahadur. We construct efficient estimates for the classes of Lipschitz and Hölder regression functions. The principle of constructing efficient estimates is illustrated by the estimation of the shift parameter, which is a classic example of the parametric problem.

Polynomial Trigonometric Kernels and Their Application to Designing Low-Pass Filters
V. G. Alekseev
pp. 314–319

Abstract—This study continues the effort made in [1] to develop out digital low-pass filters with an improved amplitude-frequency characteristic. As in [1], the main attention is given to using the expansion in a Fourier series of polynomial Jackson-type kernels for designing the filters. Pulse responses of a new four-filter set are proposed. These newly designed filters significantly surpass those suggested in [1], concerning the level of the side lobes of the amplitude-frequency characteristic side lobes. In addition, we also indicate the possibility of an alternative approach to designing low-pass filters with the use of expansion in a Fourier series of the polynomial kernels of Jackson–Vallée-Poussin type.

Large Deviations for Past-Dependent Recursions
F. K. Klebaner and R. Sh. Liptser
pp. 320–330

Abstract—The large-deviation principle is established for stochastic models defined by past-dependent nonlinear recursions with small noise. In the Markov (locally Gaussian) case, we use the result to obtain an explicit expression for the asymptotics of the exit time.

Estimation of the Approximation Accuracy by Means of Superposition of Potential Functions
A. A. Pervozvanskii
pp. 331–341

Abstract—Estimates of the number of elements of an artificial neural network based on using elements of the potential-function type are given. It is shown that, under a reasonable choice of characteristics of the elements and not too large a dimension of space, the attainable approximation accuracy of smooth functions is not worse than that for sigmoidal-type perceptrons, while the adjustment is accomplished by a single parameter.

Dominance Theorems and Ergodic Properties of Polling Systems
S. G. Foss and N. I. Chernova
pp. 342–364

Abstract—We consider a class of polling systems with stationary ergodic input flow such that the control in a system obeys a certain regeneration property. For this class, necessary and sufficient conditions for the queue-length process to be bounded in probability are found. Under these conditions, we prove that a stationary regime exists and the queue-length process for a system that starts from the zero initial state converges to this regime. In the proof, we use some monotonicity properties of the models considered and some dominance theorems based on these properties.

The Best and Worst Packet Transmission Policies
B. S. Tsybakov and P. Papantoni-Kazakos
pp. 365–384

Abstract—We consider the problem of optimizing the order of transmitting and discarding packets for queueing packet networks. The problem gives rise to a queueing system consisting of a finite-capacity buffer, a constant service-time server, and a service policy. We show that for any given sampling function of an input traffic, the LIFO discipline is the best in terms of delays, while FIFO is the worst. We give a comparison of basic performances for LIFO, FIFO, RANDOM, and the PUSH-OUT discipline $d^*$. The proof of optimality is given for general input traffic, the delay distribution functions for LIFO, FIFO, RANDOM, and $d^*$ are found for stationary memoryless traffic, and a numerical comparison of disciplines is given for the Poisson traffic. We consider discrete-time systems only.

Author Index
pp. 385–386

Tables of Contents
pp. 387–389