PROBLEMS OF INFORMATION TRANSMISSION

A translation of *Problemy Peredachi Informatsii*

Volume 25, Number 2, April–June, 1989

Back to contents page

** Direct Estimation of the Spectrum of Stationary Stochastic Processes
**

Yu. M. Perlov

pp. 87–94

**Abstract**—The spectrum of real-valued stationary stochastic processes
is estimated directly from observations. The estimators are shown to be unbiased and
consistent. A method is proposed for estimating the spectra of the additive
components of the observed process $X(t)$ of the form $X(t)=X_r(t)+X_s(t)+V(t)$,
where $X_r(t)$ is a regular stochastic process, $X_s(t)$ is a singular stochastic
process, and $V(t)$ is white noise.

** Stochastic Filters and Generation of Stochastic Processes
**

N. N. Evtikhiev and E. A. Sandler

pp. 94–100

**Abstract**—Constructive procedures are proposed for generation
of discrete-time stochastic processes having jointly specified univariate
distributions and spectral densities. These procedures are realized using
special recurrences and ensure generation of stationary ergodic random
sequences with arbitrary univariate distributions and various
fractional-rational spectral densities.

** Minimax Signal Detection in the Presence of Noise with an Incompletely
Specified Spectral Density
**

O. M. Kurkin, G. V. Berdavtsev, and Yu. B. Korobochkin

pp. 100–106

**Abstract**—We consider signal detection in the presence of
Gaussian noise, which is an additive mixture of two components; the spectral
density of one of the components is known and the spectral density of the
other component is unknown but satisfies a given system of moment
inequalities. It is shown that a decision rule having a maximum guaranteed
probability of correct detection for a given guaranteed probability of false
alarms is the Neyman–Pearson rule in which the
noise spectral density and the compatible linear filter are a saddle point of
the signal/noise functional. An example is considered.

** On the Existence of $q$-ary Generalized Concatenated Codes with Optimal
Error-Correcting Properties
**

V. V. Zyablov and S. A. Shavgulidze

pp. 107–119

**Abstract**—We investigate the class of $q$-ary generalized concatenated
codes with inner random block codes and outer nonrandom Reed–Solomon codes. We
show that in memoryless $q$-ary symmetric discrete channels these codes
asymptotically attain, for all transmission rates, the optimal error exponent of
block codes.

** On Distribution of Values of Recurrence Sequences
**

I. E. Shparlinsky

pp. 120–125

**Abstract**—We analyze the joint distribution of the values of
several different solutions of difference equations.

** A Nonhomogeneous Frame RMA Algorithm
**

B. S. Tsybakov and V. B. Fayngold

pp. 126–136

**Abstract**—We consider nonhomogeneous frame random multiple
access algorithms. The algorithms are optimized by frame size, the number of
tree branches, and the probability that a packet visits a given branch.
Packet delays and the algorithm rates are calculated. The frame stack
algorithm with a binary tree is shown to be optimal.

** Optimized Algorithms for Numerical Calculation of the Characteristics of
Multistream Models with Repeated Calls
**

S. N. Stepanov

pp. 136–144

**Abstract**—We present an optimal numerical algorithm for
estimating the stationary characteristics of multistream models with repeated
calls. The estimates are obtained by solving a system of statistical
equilibrium equations. Optimality of the algorithms is achieved by
elimination of states having negligibly small probability.

** Equivalent Definitions of the Probabilistic Characteristics of Models
with Repeated Calls and Their Application
**

S. N. Stepanov and I. I. Tsitovich

pp. 145–153

**Abstract**—Alternative definitions of the probabilistic
characteristics of models with repeated calls are introduced and their
equivalence is proved. It is demonstrated that a successful choice of
definition may largely simplify the estimation procedure of the corresponding
parameters.

** The Number of Mappings of Graphs, Ordering of Graphs, and Muirhead's
Theorem
**

A. M. Leontovich

pp. 154–165

**Abstract**—The following ordering of graphs is introduced: we say that a
graph $D_1$ is greater than a graph $D_2$ if for any graph $\Gamma$ the number of
mappings of the graph $D_1$ to the graph $\Gamma$ is not less than the number of
mappings of the graph $D_2$ to the graph $\Gamma$. We prove a number of theorems that
allow comparison of some graphs. An interesting relationship of this problem with the
theory of homogeneous polynomials is established, in particular with Muirhead's
well-known theorem.

** Design of High-Speed Checkers for Berger Codes
**

M. K. Bimukanov, V. V. Sapozhnikov, and Vl. V. Sapozhnikov

pp. 165–171

**Abstract**—Methods are proposed for the construction of high-speed
self-checking $k$-out-of-$n$ checkers, designed as check circuits that decide the
membership of a binary vector in a Berger code. It is shown that maximum-speed
$k$-out-of-$n$ checkers have circuits with four levels of elements. The methods are
adapted for application of programmable logic arrays. The minimum number of arrays
that can be used to implement $k$-out-of-$n$ checkers is $2$.