PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Asymptotic Minimax Estimation of Regression in the Additive Model
G. K. Golubev
pp. 101–112

Abstract—Adaptive estimators of smooth regression functions that are asymptotically minimax in the sense of the quadratic criterion are constructed in the additive model with adaptive choice of the basis.

Estimation of the Minimum Point of an Unknown Function Observed in the Presence of Dependent Noise
O. N. Granichin
pp. 112–116

Abstract—Stochastic approximation algorithms with input disturbances are proposed. From noisy observations of an unknown function dependent on a parameter, these algorithms produce consistent estimators of the minimum point of the function for the mean parameter value. The convergence of the algorithm is proved assuming that the test disturbance injected in the estimation procedure is independent of the observation noise. As an example, we consider estimation of the mean parameter values of the moving-average process observed in the presence of dependent noise.

Comparison of Some Sequential Rules for Detecting Changes in Distributions
A. G. Tartakovskii and I. A. Ivanova
pp. 117–124

Abstract—The characteristics of Page's rule for detecting changes in distributions are established. These characteristics take into account the excesses over threshold and reflecting barriers and are used in the problem of detection of a Gaussian signal with an unknown appearance time from preprocessing results in prelimit situations. The accuracy of the proposed formulas and of the known asymptotic formulas for Shiryaev's rule is estimated. Page's and Shiryaev's change-detection rules are compared.

Informativity in the Category of Linear Measurement Systems
P. V. Golubtsov
pp. 125–140

Abstract—We construct the category of linear stochastic measurement systems (MS) that reflects the known features of the corresponding measurements. Both composition and product in this category allow for possible dependence of measurements. Some basic concepts are considered, such as independence and similarity of measurement systems; decomposition of measurement systems into simpler components is examined. The concept of informativity occupies a central place in the paper and its role emerges in connection with the synthesis of optimal MS. Specifically, a more informative MS produces a better result than a less informative MS.

New Packings on a Finite-Dimensional Euclidean Sphere
V. A. Zinov'ev and Th. Ericson
pp. 141–146

Abstract—A spherical code is a finite set of points in a sphere of radius $1$ in the $n$-dimensional Euclidean space with a given minimum distance $\rho$. The cardinality of the best spherical code with distance $\rho=1$ is called the contact number $\tau_n$. Leech and Sloane (1971) demonstrated how to construct spherical codes using binary block cods (both constant-weight and ordinary). Here we propose new constructions that improve the lower bounds on the cardinality of spherical codes with $\rho\le1$ for $n\le64$.

Partitioning of a Vector Space into Orbits by the Action of Automorphism Groups of Some Codes
Yu. L. Sagalovich
pp. 147–153

Abstract—Exact and asymptotic formulas are obtained for counting the number of orbits into which the space of $q^n$ vectors of length $n$ over the field $\operatorname{\it GF}(q)$ is partitioned by the action of the minimal automorphism group of an arbitrary cyclic code and the automorphism group of the extended BCH code—an affine group. The calculations are carried out for $q=2$, $n=7,15,31$ and $8,16,32$.

Fourier Transform Evaluation in Fields of Characteristic 2
T. G. Zakharova
pp. 154–167

Abstract—We consider the evaluation of the Fourier transform (FT) in the field $\operatorname{\it GF}(2^m)$. The algorithm for an FT calculator proposed in this paper allows the software implementation. The proposed algorithm reduces the number of additions and multiplications during FT evaluation. Short FT algorithms are given.

The Throughput of the Stack Algorithm in a Channel with N-Conflicts
B. S. Tsybakov and A. Yu. Privalov
pp. 168–174

Abstract—A stack algorithm with $Q$-ary conflict resolution is considered in an RMA channel with $N$-conflicts. An equation for the throughput of the stack algorithm for given $N$ and $Q$ is derived. The throughputs for various $N$ and $Q$ are calculated numerically. Throughput optimization by $Q$ for a given $N$ is performed.

Lower Bounds on the Probability of Connectedness in Classes of Random Graphs Generated by 2-Connected Graphs with a Given Base Spectrum
V. P. Poleskii
pp. 175–183

Abstract—We develop a previous result which claims that the base spectrum of the cycle matroid of a graph provides a lower bound on the probability of connectedness of the corresponding random graph. A random graph with a minimum probability of connectedness is constructed in the class of random graphs generated by 2-connected graphs representable as a partition of their two trees.

Integral Method for Calculating Closed Queueing Networks
A. I. Gerasimov
pp. 184–195

Abstract—A method is proposed for the analysis of closed queueing networks with one or several classes of customers. The method produces analytical expressions for the main network characteristics. Formulas that have practical value are developed. The optimization problem for closed queueing networks with one class of customers is posed and solved.

Two Extremal Problems for Oriented Lattices
S. L. Bezrukov
pp. 196–197

Abstract—We consider two problems of existence of directed cycles in a graph, which are relevant for decoding of convolutional codes.