PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii


Volume 33, Number 4, October–December, 1997
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On Binary Cyclic Codes with Minimum Distance $d=3$
P. Charpin, A. Tietäväinen, and V. Zinoviev
pp. 287–296

Abstract—We consider binary cyclic codes of length $2^m-1$ generated by a product of two or several minimal polynomials. Sufficient conditions for the minimum distance of such a code to be equal to three are found.

 

Codes Correcting a Set of Clusters of Errors or Erasures
M. Bossert, M. Breitbach, V. Zyablov, and V. Sidorenko
pp. 297–306

Abstract—We propose a class of codes correcting multiple bursts of errors or erasures in columns of a two-dimensional array. Erasure-correcting codes possess minimum possible redundancy. The redundancy of error-correcting codes is close to minimum.

 

Guaranteed Estimation of a Periodic Signal Distorted by an Autoregressive Noise with Unknown Parameters
V. V. Konev and S. M. Pergamenshchikov
pp. 307–323

Abstract—The problem of estimating coefficients of a trigonometric signal from observations with an additive noise is considered, where the noise is a stationary autoregressive process with unknown parameters and unknown distribution. Based on the least-squares method, a sequential procedure for estimation of signal coefficients is constructed, which guarantees a specified mean-square estimation accuracy for any values of the nuisance parameters. Asymptotic formulas for the duration of the procedure are obtained. The asymptotical normality of the estimators proposed and the duration of estimation is established.

 

Estimation of Functions of a Distribution Density from Dependent Observations
V. A. Vasil'ev and G. M. Koshkin
pp. 324–338

Abstract—We propose estimates for functions of a multivariate distribution density to which a sequence of conditional distribution densities of dependent random variables converges, whereas the random variables are observed with an additive dependent noise. The rate of convergence of the deviation moments of the estimates proposed and the principal part of their mean-square deviation are found. It is shown that the estimates of functions of a density have the same rate of convergence as the improved estimates of the density.

 

Empirical Spectral Analysis of Periodically Correlated Stochastic Processes. An Alternative Approach
V. G. Alekseev
pp. 339–345

Abstract—The work is devoted to construction and statistical analysis of a “shifted” periodogram intended to serve as a “half-finished product” when constructing an estimate of the spectral density $f_k(\lambda)$, $k\in {\Bbb Z}$, of a periodically correlated stochastic process $\{\xi(t),\, t\in {\Bbb R}\}$. Each modification of the shifted periodogram proposed in the study possesses the following property: its expectation depends on the spectral density $f_k(\lambda)$ only and does not depend on the spectral densities $f_j(\lambda),\: j\neq k$. The correlation properties of one of the simplest modifications of the shifted periodogram are studied. Two techniques for using the shifted periodogram to construct an estimate of the spectral density $f_k(\lambda)$ are presented.

 

On a Problem of Route Optimization and Its Applications
B. B. Zobnin, L. N. Korotaeva, and A. G. Chentsov
pp. 346–361

Abstract—We consider an abstract problem of routing a finite system of subproblems with multivariant passages from the solution of one subproblem to that of another. A modified procedure of dynamic programming is constructed. Hypothetical applications to the problems of experimental designs are viewed.

 

Sequential Search for Significant Variables of an Unknown Function
M. B. Malyutov and I. I. Tsitovich
pp. 362–377

Abstract—Assume that an unknown function of $t$ variables can be measured sequentially with random errors at arbitrarily assigned $t$-tuples of its arguments. Let this function depend actually only on a variables' subset $S$. We propose an algorithm of search for a subset $S$, $|S|=s$, including sequential choice of the variables' values as inputs, a stopping time, and a decision based on outputs. Under the uniform a priori distribution we estimate the mean error probability and mean duration of our strategy and study their asymptotic behavior as $t\to\infty$, $s={\rm const}$. The case of an unknown (but bounded from above) amount of significant variables is also studied.

 

Letter to the Editor
J. L. Massey
pp. 378–380

Author Index
pp. 381–382

Tables of Contents
pp. 383–385