A translation of Problemy Peredachi Informatsii

Volume 25, Number 2, April–June, 1989
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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 $2$.