PROBLEMS OF INFORMATION TRANSMISSION

A translation of *Problemy Peredachi Informatsii*

Volume 32, Number 4, October–December, 1996

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**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