PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Coding Theorems for Classes of Arbitrarily Varying Discrete Memoryless Channels
R. L. Dobrushin and S. Z. Stambler
pp. 97–112

Abstract—Subject to certain constraints, an expression is derived for the capacity of classes of arbitrarily varying channels for codes whose error probability is given as the average over code words.

Lower Bound for the Error Probability of Multiple-Access Channels
E. A. Haroutunian
pp. 113–123

Abstract—A lower bound is formulated for the optimum error probability of channels with several correlated sending stations and a single receiving system.

Approximation of $L_2(\omega_1,\omega_2)$ Functions by Minimum-Energy Transfer Functions of Linear Systems
M. G. Krein and P. Ya. Nudel'man
pp. 124–142

Abstract—The approximation with specified error in $L_2(\omega_1,\omega_2)$ metric of an arbitrary function $F\in L_2(\omega_1,\omega_2)$ by a physically realizable transfer function of a linear system (network) with minimum energy is investigated. The problem is solved on the basis of a spectral decomposition constructed for an integral operator in $L_2(0,\infty)$ with kernel $$ \frac{\sin\omega_2(t-s)}{\pi(t-s)}-\frac{\sin\omega_1(t-s)}{\pi(t-s)}. $$ Secondarily, a criterion is found for a predetermined function $F\in L_2(\omega_1,\omega_2)$ to coincide almost everywhere on $(\omega_1,\omega_2)$ with a certain physically realizable transfer function $G_0$, and a rule is given for reconstructing the function $G_0$ from $F$ in the appropriate complex half-plane.

Asymptotic Behavior of the Power of a Homogeneous Gaussian Field
I. Yu. Linnik
pp. 143–148

Abstract—The asymptotic behavior of the power of a homogeneous Gaussian random field is investigated in a domain expanding homothetically to infinity.

Convergence of Recursive Estimates of the Zero of an Unknown Function
M. B. Nevel'son
pp. 149–162

Abstract—Simple recursive estimates are constructed for the zero of an unknown function observed with random errors when the expectation of a certain monotonic function of those errors is known. The results are applied to a problem in the nonparametric estimation of an unknown parameter (and, in particular, a location parameter).

Optimal Nonlinear Extrapolation, Filtering, and Interpolation of Functions of Gaussian Processes
N. P. Zabotina
pp. 163–171

Abstract—An optimal (in the sense of mean-square deviation) prognosis of the values of a function of a stationary Gaussian process $f(x_{t+\tau})$, $\tau>0$, is constructed from known values of the process $x_s$, $s\le t$. The more general problem of optimal prognosis of $f(x_{t+\tau})$ from known values of a process $z_s$, $s\le t$, stationarily related to $x_t$ is solved. The conditions are analyzed for the error-free interpolation of an unknown value $f(x_t)$, $t\in U$, from values of the process $x_s$ known on the entire number line excluding the interval $U$.

On Certain Forney Bounds
L. F. Gorshkov
pp. 172–173

Abstract—Intermediate results of Forney are used to derive strict upper bounds for the probability of incorrect decision for error-correcting-only, erasure-plus-error-correcting, and generalized-minimum-distance decoding schemes.

General Solution of the Signal Sampling Problem
E. I. Krupitskii
pp. 174–179

Abstract—A general criterion is given of solvability of the sampling problem, along with a procedure for the reconstruction of signals from their sampled values.

Note on the Article “Estimation of the Mean in a Normal Set”
I. A. Ibragimov and R. Z. Khas'minskii
pp. 179–180