PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 34, Number 4, October–December, 1998
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CONTENTS

Nonequivalent Cascaded Convolutional Codes Obtained from Equivalent Constituent Convolutional Encoders
S. Höst, R. Johannesson, and V. V. Zyablov
pp. 291–299

Abstract—Cascaded convolutional codes with conventional convolutional codes as constituent codes are powerful and attractive to use in communication systems where very low error probabilities are needed. This paper clearly demonstrates the dramatic effect the replacement of the inner convolutional encoder by an equivalent one could have upon the distance properties of the cascaded convolutional encoder.

On Linear Hash Codes
V. Yu. Solomennikov and Yu. L. Sagalovich
pp. 300–308

Abstract—We find bounds on parameters of linear hash codes and estimates for the hash distance of certain known codes.

Upper and Lower Bounds and Asymptotics of Optimal Filtering Error of a Stationary Process with a Small Information Rate
M. S. Pinsker and V. V. Prelov
pp. 309–321

Abstract—Upper and lower bounds are obtained for the mean-square error of the optimal (nonlinear) filtering of a discrete-time stationary process $X=\{X_j\}$ from the observations $Y=\{Y_j\}$, where $Y=X+Z$ and $Z=\{Z_j\}$ is a sequence of i.i.d. random variables. These bounds are linear functions of the information rate $\overline I(X; Y)$. It is shown that the lower bound is asymptotically tight in the case where both $\overline I(X; Y)$ and the peak power of the signal $X$ tend to zero. The situations where $X_n$ is estimated from either the observations $\{Y_j,\:j\leq n-1\}$ or the observations $\{Y_j,\:j\leq n\}$ are both considered.

Comparison Analysis of the Hexagonal Multilevel QAM and Rectangular Multilevel QAM
K. Engdahl and K. Sh. Zigangirov
pp. 322–331

Abstract—The performances of two multilevel modulation systems are compared in terms of capacity and cutoff rate, under the condition that the average energy per channel use is the same for the two systems. The systems are versions of the scheme of Imai and Hirakawa, and we consider the multistage suboptimal receiver for the Gaussian channel. The first system is an eight-level modulation system using rectangular QAM-signaling and a binary alphabet, and the second is a five-level modulation system using hexagonal QAM-signaling and a ternary alphabet. It is shown that, under these conditions, the capacity for the hexagonal system is close to 1 dB better than the capacity for the rectangular system for a range of signal-to-noise ratios. The Chernoff bounding parameter is also calculated for hexagonal QAM with an infinite number of signal points.

Existence and Uniqueness Theorems for fBm Stochastic Differential Equations
M. L. Kleptsyna, P. E. Kloeden, and V. V. Anh
pp. 332–341

Abstract—Existence and uniqueness theorems are proved for stochastic differential equations driven by fractional Brownian motion (fBm).

Fast Evaluation of the Hurwitz Zeta Function and Dirichlet $L$-Series
E. A. Karatsuba
pp. 342–353

Abstract—Based on the FEE method, an algorithm of fast evaluation of the Hurwitz zeta function $\zeta(s,a)$ for integer $s$ and algebraic $a$ is proposed. Fast evaluation of Dirichlet $L$-series is considered. The evaluation complexity is close to the best possible.

Large Deviations for Random Processes with Independent Increments on Infinite Intervals
R. L. Dobrushin and E. A. Pechersky
pp. 354–384

Abstract—Methods developed in the theory of large deviations are an appropriate tool for investigation of probabilities of large fluctuations in queueing systems. In the paper, the large-deviation principle for generalized Poisson processes defined on the positive half-line $[0,+\infty)$ is proved. Our approach is to find a representation of a parameter of the queueing system under investigation in terms of input flows of the system. Then the probabilities of large fluctuations of this parameter can be examined if the large-deviation principle for input processes is proved. With the help of the large-deviation principle proved here, we give a new proof for the known result on the asymptotics of the logarithm of the probability of large delay in a queueing system with a single server and Poisson input flow.

Author Index
pp. 385–386

Tables of Contents
pp. 387–389