PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

On Minimum Attainable Mean-Square Error in Transmission of a Parameter over a Channel with White Gaussian Noise
M. V. Burnashev
pp. 247–257

Abstract—The article considers the problem of asymptotically optimal ($A\to\infty$) choice of signals for transmission of a parameter over a channel with white Gaussian noise, with a constraint on the signal energy $A$. The quality criterion $e_\alpha(A)$ is the absolute moment of degree $\alpha\geq 2$ of the magnitude of the error. The logarithmically exact asymptotic form of $e_\alpha(A)$ for $\alpha\geq 2$ is obtained.

Convergence Rate of Nonparametric Estimates of Maximum-Likelihood Type
A. S. Nemirovskii, B. T. Polyak, and A. B. Tsybakov
pp. 258–272

Abstract—The authors obtain the rate of convergence of $M$-estimates of nonparametric regression in the $L_2$ metric. It is shown that, for classes of smooth, monotonic, and convex functions, this rate cannot be improved (to within a constant). It is established that in a number of cases, particularly for the class of mono-tonic functions, nonlinear $M$-estimates are better than any linear estimates in terms of the order of the rate of convergence.

Some Problems of Bispectral Analysis of Stationary Stochastic Processes and Uniform Random Fields
V. G. Alekseev
pp. 273–278

Abstract—The author offers generalizations along two lines (namely to the case of a multi-variate stationary stochastic process $\xi(t)=\{\xi_j(t),\: j=\overline{1,m},\: t\in\mathbb Z\}$ and to the case of uniform random field $\{\xi(\mathbf{k}),\: \mathbf{k}\in\mathbb{Z}^2$ or $\mathbb{Z}^3\}$ of some results of [V.G. Alekseev, Probl. Peredachi Inf., 1983, vol. 19, no. 3, pp. 38–51] concerning nonparametric estimation of the bispectral density of a stationary stochastic process $\{\xi(t),\: t\in\mathbb{Z}\}$.

Calculation of Distribution of Convolution of a Wiener Process
A. A. Klyachko and Yu. V. Solodyannikov
pp. 279–384

Abstract—The authors calculate the distribution of the convolution $\int\limits^\tau_0 w(t)w(\tau-t)\,dt$ of a standard Wiener process $w(t)$. Some applications of this functional are considered.

Method of Investigating the Convergence of Adaptive Filtering Algorithms Utilizing Stochastic Lyapunov Functions
O. Yu. Kul'chitskii
pp. 285–297

Abstract—The article describes a method of investigating the convergence of an adaptive filter in the case in which the statistical characteristics of the useful signal and noise are unknown. It is shown how to construct adaptation algorithms so as to ensure satisfaction of the convergence conditions obtained.

Classification of Random Series of Unknown Length
Yu. S. Kharin
pp. 297–307

Abstract—The author considers the problem of classification of multivariate random observations in the situation in which the sequence of true numbers of classes is generated by series (or runs) of unknown length, while the distribution densities of the observations are specified to within parameters. A decision rule is constructed and investigated; this rule is based on the statistics of the homogeneity criterion and surmounts the undesirable “multiplicity effect” inherent in the rule based on the maximum-likelihood criterion.

Linear Regularity Condition for Vector Random Fields
M. G. Avetisian and R. L. Dobrushin
pp. 308–313

Abstract—The authors give necessary and sufficient linear regularity and singularity conditions for vector random fields of both discrete and continuous arguments.

Improved Upper Bound for the Capacity of the Random-Access Channel
Zhen Zhang and T. Berger
pp. 313–317

Abstract—In this paper we improve the bound of Mikhailov and Tsybakov for the capacity of a synchronous random-access channel with a Poisson input and ternary broadcast feedback (from $0.5874$ to $0.5789$). A major role is played by a random functional $m_t$, which we call the “mortgage time.” We show that $m_t\leq t$ with probability $1$, where $t$ is ordinary time, measured in windows. Addition of $r(t-m_t)$ to the objective function of Mikhailov and Tsybakov, where $r$ is an additional optimization parameter, results in the improved upper bound.

Combinatorial Approach to the Biological Assembly Problem: Linear Structure
Ya. A. Smetanich and V. V. Kornilov
pp. 317–326

Abstract—The authors propose a formal scheme that attempts to express some actual features of self-assembly of supramolecular structures. Three linear-assembly problems are considered; their objects are words in some alphabet. In each problem, a class of unique words is identified, and necessary and sufficient conditions characterizing these classes are obtained.

INDEX
pp. 327–332

Method for Determination of Statistic Values of Observations Concerning Variables Subject to Irregular Fluctuations
A. Einstein
pp. 99–100 (Russian issue)

Abstract—Russian translation of “Méthode pour la détermination de valeurs statistiques d’observations concernant des grandeurs soumises à des fluctuations irrégulières,” Arch. Sci. Phys. et Natur., 1914, t. 37, ser. 4, pp. 254–256.

Einstein's 1914 Work on Theory of Randomly Fluctuating Observation Series
A. M. Yaglom
pp. 101–107 (Russian issue)