A translation of Problemy Peredachi Informatsii

Volume 44, Number 4, October–December, 2008
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Linear Complexity of Ternary Sequences Formed on the Basis of Power Residue Classes
V. A. Edemskiy
pp. 287–294

Abstract—We propose a computation method for linear complexity of ternary sequences formed on the basis of power residue classes. We find the linear complexity of ternary sequences formed on the basis of two classes of biquadratic residues and the linear complexity of ternary sequences formed on the basis of two classes of sextic residues with close-to-perfect autocorrelation.


On Perfect Codes for an Additive Channel
V. K. Leont'ev, G. L. Movsisyan, and J. G. Margaryan
pp. 295–302

Abstract—We construct a class of perfect codes for an additive channel. The class contains classical Hamming codes.


Stochastic Recovery Problem
B. S. Darkhovsky
pp. 303–314

Abstract—We consider the problem of estimating a functional defined on some functional class from observations (with noise) of values of other functionals at the same functional class. In general, all functionals are nonlinear. We propose a formal mathematical statement of the problem. For the proposed statement, we give a nonasymptotically optimal estimation method under rather weak constraints on the estimated functional and noise. Some examples are considered.


Nonparametric Estimation of Signal Amplitude in White Gaussian Noise
R. Z. Khasminskii
pp. 315–320

Abstract—We assume that a transmitted signal is of the form $S(t)f(t)$, where $f(t)$ is a known function vanishing at some points of the observation interval and $S(t)$ is a function of a known smoothness class. The signal is transmitted over a communication channel with additive white Gaussian noise of small intensity $\varepsilon$. For this model, we construct an estimator for $S(t)$ which is optimal with respect to the rate of convergence of the risk to zero as $\varepsilon\to 0$.


Adaptive Filtering of a Random Signal in Gaussian White Noise
E. N. Belitser and F. N. Enikeeva
pp. 321–332

Abstract—We consider the problem of estimating an infinite-dimensional vector $\theta$ observed in Gaussian white noise. Under the condition that components of the vector have a Gaussian prior distribution that depends on an unknown parameter $\beta$, we construct an adaptive estimator with respect to $\beta$. The proposed method of estimation is based on the empirical Bayes approach.


Gibbs Field Approach for Evolutionary Analysis of Regulatory Signal of Gene Expression
V. A. Lyubetsky, E. A. Zhizhina, and L. I. Rubanov
pp. 333–351

Abstract—We propose a new approach to modeling a nucleotide sequence evolution subject to constraints on the secondary structure. The approach is based on the problem of optimizing a functional that involves both standard evolution of the primary structure and a condition of secondary structure conservation. We discuss simulation results in the example of evolution in the case of classical attenuation regulation.


Limit Theorems for Queueing Systems with Doubly Stochastic Poisson Arrivals (Heavy Traffic Conditions)
L. G. Afanas'eva and E. E. Bashtova
pp. 352–369

Abstract—We consider a single-server queueing system with a doubly stochastic Poisson arrival flow under heavy traffic conditions. We prove the convergence of the limiting stationary or periodic distribution to the exponential distribution. In a scheme of series, we consider the $C$-convergence of the waiting time process to a diffusion process with constant coefficients and reflection at the zero boundary. Examples of computation of the diffusion coefficient in terms of characteristics of the arrival flow and service time are given.


Circle of Interacting Servers: Spontaneous Collective Behavior in the Case of Large Fluctuations
N. D. Vvedenskaya and E. A. Pechersky
pp. 370–384

Abstract—We consider large fluctuations and overload of servers in a network with dynamic routing of messages. The servers form a circle. The number of input flows is equal to the number of servers; the messages of a flow are distributed between two neighboring servers; upon its arrival, a message is directed to the least loaded of these servers. Under the condition that at least two servers are overloaded, the number of overloaded servers in such a network depends on the rate of input flows. In particular, there exists a critical level of the input rate above which all servers are most probably overloaded.


Limiting Distributions in Queueing Networks with Unreliable Elements
G. Sh. Tsitsiashvili and M. A. Osipova
pp. 385–394

Abstract—We consider multichannel systems and open queueing networks with unreliable elements: nodes, paths between nodes, and channels at nodes. Computation of limiting distributions in a product form for these models is based on choosing recovery schemes for unreliable elements (independent recovery, recovery at a single site, recovering network scheme), routing algorithms, and service disciplines. Thus, by introducing a certain control, we constructively relate queueing theory with reliability theory. Results of the paper can be transferred to closed networks almost without changes.


The International Dobrushin Prize
pp. 395–398

pp. 399–402