PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Goppa Codes That Are Better Than the Varshamov–Gilbert Bound
M. A. Tsfasman
pp. 163–166

Abstract—It is shown that there exist an infinite series of $q$-ary linear Goppa codes that arise from objects of algebraic geometry, whose parameters are asymptotically higher (as $n\to\infty$) than the Varshamov–Gilbert bound.

Bounds on the Length of Disjunctive Codes
A. G. D'yachkov and V. V. Rykov
pp. 166–171

Abstract—A new lower bound for the length of disjunctive codes [W.H. Kautz and R.C. Singleton, IEEE Trans. Inf. Theory, 1964, vol. 10, no. 4, pp. 363–377] is proved. An upper bound obtained by the method of random coding is given.

On Cyclicity of Extended Goppa Codes
A. L. Vishnevetskii
pp. 171–175

Abstract—The author obtains a cyclicity criterion for extended Goppa code $T(L,g)$, for some constraint on set $L$. A similar criterion is obtained for the nonextended code.

Estimation of Square-Integrable Probability Density of a Random Variable
S. Yu. Efroimovich and M. S. Pinsker
pp. 175–189

Abstract—The article investigates the mean-square risk of the estimate of the unknown probability density of a sequence of random observations. It is assumed that the distribution density is a point of an ellipsoid in Hilbert space. It is shown that a linear estimation plan is asymptotically optimal.

Robust Estimates of a Function
A. B. Tsybakov
pp. 190–201

Abstract—The class of estimates of function values that was introduced in [A.B. Tsybakov, Probl. Peredachi Inf., 1982, vol. 18, no. 2, pp. 44–60] is considered. The asymptotic distribution and convergence of the moments of the estimates is established. A solution is offered for the problem of choosing a robust estimation strategy, i.e., of choosing estimates from the class under consideration that are optimal in the sense of the minimax of the asymptotic standard error.

On One Algorithm in the Problem of Interpolation of Multidimensional Time Series
A. P. Mirabel and L. I. Piterbarg
pp. 202–208

Abstract—To reconstruct one of the missing values $t+\tau$ of time series $x(t)$ that is a realization of a multidimensional stationary process with discrete time, the authors propose the following linear interpolation form: $$ \widehat x(t+\tau)=\sum^p_{j+1}[\alpha_j x(t-1)+\beta_j x(t+T+j)], $$ where $\alpha_j$ and $\beta_j$ are numerical matrices to be determined; $T$ is the length of the omission ($0\leq\tau\leq T$). A system of normal equations in $\alpha_j$ and $\beta_j$ is constructed in accordance with the least-squares principle. Provided that the real time series is modeled by an autoregression process of order $p$, the authors develop an iterative solution procedure for the system, written in terms of the forward and backward prediction coefficients, and demonstrate that the procedure converges for an extensive class of random processes.

Universal Synthesis Algorithm for $1/n$ Testers
V. V. Sapozhnikov and V. Rabara
pp. 209–218

Abstract—The authors develop a method of synthesizing $1/n$ testers, these being control circuits that establish the fact that a binary vector belongs to a one-out-of-$n$ code. Some practical results of the use of the method are given.

Description of Cascade Networks of Finite Automata in Terms of Codings and Coverings
G. P. Agibalov and N. V. Evtushenko
pp. 218–226

Abstract—The authors introduce the concepts of consistent codings and consistent systems of coverings of the set of states of a finite automaton. In terms of this concept, they characterize cascade networks of automata representing a given automaton, and particular cases of them, namely parallel-sequential, parallel, and sequential networks. They establish necessary and sufficient existence conditions for exact representations of an automaton by sequential and parallel-sequential networks, formulated in terms of embedded sequences of partitions of the set of states of the automaton.

Performance Evaluation for a Class of Algorithms of Random Multiple Access to a Radio-Communication Channel
G. I. Falin
pp. 85–90 (Russian issue)

Abstract—We consider algorithms of random multiple access to a broadcast channel for which the probability to be transmitted in the nearest window is one and the same for all packets in the system. For such algorithms, we find a lower estimate for the packet queue length and upper estimate for the system capacity.

On the Level-Quantization Error in Estimation of the Autocorrelation of a Gaussian Process
E. G. Zhilyakov
pp. 90–94 (Russian issue)

Abstract—We derive an equation which allows us to correct quantization error and choose a quantization step that precisely corresponds to a given error level of estimation of the autocorrelation of a Gaussian process.