PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Fiftieth Anniversary of the Formation of the USSR
pp. 269–270

Asymptotic Bounds of the Error Probability for a Gaussian Channel with Feedback and a Peak-Power Constraint on the Input Signal
A. G. D'yachkov
pp. 271–284

Abstract—The block transmission of discrete messages in a stationary memoryless Gaussian channel with full feedback and a peak-power constraint on the input signal is described. Two types of channels are investigated: a binary-input semicontinuous channel (with constant peak power) and a continuous-time channel with white Gaussian noise and a peak-power constraint on the input signal. Upper and lower asymptotic bounds are obtained for the optimum error probability for the investigated block transmission.

Asymptotic Behavior of the Capacity of a Continuous Channel with Large Nonadditive Noise
V. V. Prelov
pp. 285–289

Abstract—Upper and lower bounds are derived for the capacity of continuous nonadditive-noise channels specified by a conditional probability density function. It is shown that when the signal power tends to zero the derived upper and lower bounds coincide asymptotically.

Weak Signal Transmission in a Memoryless Channel
I. A. Ibragimov and R. Z. Khas'minskii
pp. 290–299

Abstract—An asymptotic expression is derived for the Shannon information between the input and output signals for a relatively broad class of continuous memoryless channels in the case of weak input signals. This expression, which relates the Fisher information and the Shannon information, is also used to derive an asymptotic representation for the capacity and to suggest a symbol transmission mode whereby this capacity is asymptotically attained.

An Adaptive Algorithm for Determining Variations of the Characteristics of an Observed Random Process
V. M. Linkin and B. P. Naumov
pp. 300–304

Abstract—An adaptive algorithm is proposed for the determination of the variations of the characteristics of an observed random process. It is postulated that the indicated variations behave according to the law of an unobservable homogeneous Markov chain with unknown transition probabilities. The number of states of the Markov chain and the conditional distribution functions for the observed variables are presumed to be known. At each instant (discrete time) the a posteriori distribution with respect to the unobservable states of that chain is computed. An algorithm converging to the true values is described for estimating the unknown transition probabilities of the chain. An example is given of the operation of the formulated adaptive algorithm in the probabilistic model of a Markov chain with observables having a binomial distribution function.

Asymptotic Behavior of the Bayes Estimates of a Signal Parameter in the Presence of Nonstationary Normal Noise
A. P. Trifonov
pp. 305–312

Abstract—It is shown that for large classes of a priori distributions and loss functions the Bayes estimate reduces to the conditional maximum-likelihood estimate for an unbounded increase of the signal-to-noise ratio. An approximate calculation is carried out for the error of approximation of the Bayes estimate by its limiting value for large but finite signal-to-noise ratios.

Probability of Large Deviations of the Power of a Stationary Gaussian Process
I. Yu. Linnik
pp. 313–323

Abstract—The asymptotic behavior of the probability function $P_T=P\Bigl(\int\limits^T_0\xi^2(t)\,dt>TR(0)x_T\Bigr)$ is investigated, where $\xi(t)$ is a stationary Gaussian process with expectation $E\xi(t)=0$ and correlation function $R(t)$.

Maximum of the Connectivity Probability
M. V. Lomonosov and V. P. Polesskii
pp. 324–328

Abstract—A particular case of maximization of the connectivity probability of a random graph is investigated.

Control in Networks with a Designated Branch Indeterminacy
A. S. Vinogradskii
pp. 329–335

Abstract—The article is devoted to optimization problems for stochastic networks. Existence and uniqueness theorems for minimum path and maximum flow are deduced under stringent constraints on the network, and the problem of constructing a flow minimizing a special type of penalty function is investigated.

Superposition in the Large as a Pattern Recognition Technique
I. Sh. Pinsker and V. V. Shakin
pp. 336–340

Abstract—The authors have developed an approach to pattern recognition on the basis of the concept of superposition in the large of the comparison images. The method is described for the case in which the images (absolute descriptions) of the objects to be analyzed represent lines (or vector functions of a scalar argument) in a finite-dimensional space.

Density of a Derivation Tree and the Active Capacity of a Grammar
A. Ya. Dikovskii
pp. 341–350

Abstract—The relationship between the concepts of density and active capacity (index) is established. The existence of infinite hierarchies of languages of different densities and capacities is proved.

A Class of Polynomial Codes
L. E. Mazur
pp. 351–353

Abstract—Codes dual to the primitive Bose–Chaudhuri–Hocquenghem codes are investigated.

Minimax Signal Detection Under Normal Noise Conditions
V. F. Nesteruk
pp. 354–356

Abstract—The problem of signal detection against a normal noise background is investigated by reduction for a selected loss function to the solution of a simple minimax problem.

Single-Server Queueing System with a Simple Input Process and a Service Time Dependent on the Waiting Time
M. Libura
pp. 357–360

Abstract—A single-server queueing system with a Poisson input process and a service time that depends on the waiting time is analyzed. An integrodifferential equation is derived for the virtual waiting-time distribution function, and a method is proposed for its solution. The solution of the well-known Barrer problem is discussed as a special case of the investigated model.

Approximative Capabilities of Passive $RC$ ($RL$) Networks
P. Ya. Nudel'man and V. G. Fel'dmus
pp. 361–362

Abstract—The limiting capabilities of $RC$ ($RL$) networks for the approximation of arbitrary functions in a frequency domain are described.

LETTERS TO THE EDITOR
Cross-Correlation of Sequences (L. E. Mazur)
p. 363

INDEX
pp. 365–371