PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Generalized Shannon Codes
Yu. M. Shtar'kov
pp. 155–167

Abstract—The article proposes a block coding method for discrete sources using words of variable length.

New Binary Linear Codes
Zh. G. Margarian and G. L. Movsisian
pp. 167–173

Abstract—New classes of binary linear codes are obtained; for some $n$ and $k$ values these classes improve the available lower bounds [H.J. Helgart and R.D. Stinaff, IEEE Trans. Inf. Theory, 1973, vol. 19, no. 3, pp. 344–356] for the function $d_{\max}(n,k)$. The weight spectra of these codes are described. Uniformly packed binary linear codes with minimum distance $4$ are constructed.

Twice-Universal Coding
B. Ya. Ryabko
pp. 173–177

Abstract—Assume that $A$ is a finite alphabet; $\Omega_i$ is a set of Markov sources of connectedness $i$ that generate letters from $A$ ($i=1,2,\dots$); and $\Omega_0$ is a set of Bernoulli sources. A code is proposed whose redundancy as a function of the block length on each $\Omega_i$ is asymptotically as small as that of the universal code that is optimal on $\Omega_i$ ($i=0,1,2,\dots$). A generalization of this problem to the case of an arbitrary countable family of sets of stationary ergodic sources is considered.

Signal Processing by the Nonparametric Maximum-Likelihood Method
A. S. Nemirovskii, B. T. Polyak, and A. B. Tsybakov
pp. 177–192

Abstract—The authors propose a class of estimates that are a generalization of maximum-likelihood and $M$-estimates in the nonparamagnetic regression problem. Existence conditions and calculation methods for such estimates are considered, and it is shown that they are consistent.

On the Choice of Parametric Representation in Numerical Approximation and Encoding of Curves
V. G. Polyakov, E. A.-I. Aidu, V. S. Nagornov, and V. G. Trunov
pp. 192–201

Abstract—The article discusses the possibilities of abridged description of curves, associated with the issue of the least deviation of a specified approximation operator on the set of parametric representations of the curve. As one such abridgement method, the article considers choosing representations whose approximation for complex-valued functions of a parameter leaves either the modulus or the argument unaltered.

On a Property of Distribution of a Class of Recursively Defined Stochastic Processes
M. B. Nevel'son
pp. 201–210

Abstract—The author examines the limiting properties of distributions of a general class of stochastic processes that are encountered in solving various statistical problems involving determination of unknown parameters by recursive methods of stochastic-approximation type.

Minimax Testing of Hypotheses Defined by Moments
N. G. Cherkashin
pp. 211–218

Abstract—The author considers the problem of testing (or discriminating) two complex hypotheses specified by a finite number of moments with respect to a system of moment functions of general form. It is shown that a minimax rule for discriminating a pair of least favorable distributions exists; its structure is investigated. The validity of the minimax theorem is established.

On Almost-Certain Convergence of Multiple Kotel'nikov–Shannon Series
O. I. Klesov
pp. 218–231

Abstract—The author considers multiple Kotel'nikov–Shannon series that correspond to homogeneous random fields with a bounded spectrum. Conditions for almost certain convergence of such series are given.

On Representation of a Class of Continuous Functions by a Discrete Set of Their Values
D. O. Avetisian
pp. 94–96 (Russian issue)

Abstract—We prove a theorem which allows us to represent each continuous function from a certain class by a discrete set of its values that correspond to equidistant values of the argument. For a particular case where the continuous functions are fundamental oscillations of dynamical systems with lumped parameters, we suggest a simple method for graphically determining the argument quantization step sufficient for representation of these functions by a discrete set of their values.

Error Estimation for Reconstruction of a Signal from a Finite Sample
S. A. Kas'yanyuk
pp. 96–101 (Russian issue)

Abstract—We present an exact error estimate for the reconstruction of signals of the form $f(z)=\int\limits_{G}g(z,t)u(t)\,dt$ from samples $\omega_k=f(z_k)$, $k=1,\dots,n$, for reconstruction according to the generalized sampling theorem. Ways for reducing the error are shown.

Interval Distribution for the Output Message Flow in a Section of a Communication Network
A. Ya. Tolchan
pp. 101–105 (Russian issue)

Abstract—We consider a flow of served messages at the output of a section of a switching communication network. For the case where the section is a lossless single-line FIFO system, we give a scheme for determining the Lebesgue–Stieltjes transform of the interval distribution function of the output flow, which is efficient in a wide class of recurrence input processes.

On a Generalization of the Johnson Bound for Constant-Weight Codes
V. A. Zinoviev
pp. 105–108 (Russian issue)

Abstract—New upper and lower bounds on the cardinality of a constant-weight code of a finite length are obtained. These bounds are a natural generalization of the well-known Johnson upper bound for binary codes.