PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Sequential Decoding Algorithm in a Multiple-Access Channel
V. B. Balakirskii
pp. 163–172

Abstract—The article describes a sequential decoding algorithm in a multiple-access channel. An upper bound is obtained for the distribution of the number of decoder calculations; this bound has the form of a Pareto distribution. It is shown that, at transmission rates greater than the computing rates, sequential decoding in a multiple-access channel can provide better exchange relations between the complexity and decoding error probability than the Viterbi algorithm.

Characteristics of Coding and Modulation Systems from the Standpoint of Concatenated Codes
S. L. Portnoi
pp. 173–184

Abstract—The article considers several modulation and coding systems (MCS) for a memoryless Gaussian channel. The asymptotic dependences (with respect to dimension) of the code transmission rate on the Euclidean distance normalized with respect to the average energy and on the signal-to-noise ratio are investigated. For many systems, an explicit expression is obtained for the exponent of incorrect decoding, and “rate/energy” exchange relations for specific lengths and error probabilities. Some considerations regarding the complexity of realization of decoders in the systems under consideration are given.

Synchronization of Isolated Words of MDS Codes in Noise
S. A. Popov
pp. 185–192

Abstract—The article considers synchronization of code words of $(n,k)$ maximum-distance separable codes (MDS codes) in the case where each code arrives from the channel in noise. The author introduces the concept of the index of nonintersection at $n-s$ positions ($m_{n-s}$) as the minimum of the paired distances between $n-s$ symbol prefixes and $n-s$ symbol suffixes of code words under shift $s$. A method of constructing MDS codes with maximum $m_{n-s}$ values is given, as well as relations that make it possible to determine $P_{\rm{syn}}(s)$ (the probability of false synchronization) for them and to estimate $P_e(s)$ (the probability of error associated with false synchronization). Results of numerical computer calculations are presented.

Extremal Problems in Minimax Estimation of Sequences
G. K. Golubev and M. S. Pinsker
pp. 192–206

Abstract—The authors consider extremal problems of estimation of sequences, in particular minimax problems of filtration, interpolation, and extrapolation. For quadratic losses and classes of sequences formed from all possible responses of a linear system, they determine the minimax risk and set up estimates on which it is attained.

On Uniform Asymptotically Efficient Estimation of a Constant Signal in Additive Noise of Unknown Structure
M. B. Nevel'son
pp. 206–217

Abstract—The article considers the problem of extracting an unknown constant signal that is observed in additive symmetrical noise with unknown probability distribution density. Asymptotically efficient estimates (in both the weak and the strong sense) of this signal are constructed, that are uniform with respect to certain natural sets of densities. The basic condition that is imposed on these sets is that they be compact in the corresponding normed spaces.

Sequential Method of Detecting Signals of Random Shape with Simultaneous Estimation of Parameters
E. S. Koneva
pp. 218–228

Abstract—The article considers the problem of detecting signals of random shape with simultaneous estimation of their informative parameters. A sequential decision procedure is set up which guarantees specified probabilities of correct classification, for some class of signals under conditions of nonparametric a priori indeterminacy, and makes it possible to set up a confidence interval of fixed width for the informative parameters with specified confidence coefficient.

Convergence and Optimality of Realizable Adaptation Algorithms (Information-Theory Approach)
M. L. Vil'k and S. V. Shil'man
pp. 229–236

Abstract—Realizable variants of optimal and robust Tsypkin–Polyak stochastic optimization procedures are investigated. A Liapunov function of information type is used to prove convergence of realizable algorithms. It is shown that realizable procedures possess asymptotically optimal properties.

Weak Dependence of Random Field Describing State of a Switching Network with Small Transit Flows
M. Ya. Kel'bert and Yu. M. Suhov
pp. 237–245

Abstract—The authors give the decay conditions for the space and time correlations of the total random field describing the state of a switching network, as well as the conditions of its continuous dependence on the random field of external flows.

On Efficiency of Small-Sample Estimates
A. N. Efimov and E. V. Krivorukov
pp. 99–106 (Russian issue)

Abstract—In order to estimate the expectation of a function of random argument, we introduce a biased inconsistent pseudo-estimator, which is the same functional transformation of a sample mean. Its efficiency is compared with minimum variance unbiased estimates and then with the Cramér–Rao bound. We give conditions for a “small-sample effect” to occur, which means the advantage of pseudo-estimates according to mean-square criterion in the case of a small sample.

Explicit Expression for Linear Extrapolation Mean Square Error for a Stationary Process with $R$-Quazipolynomial Spectral Density
E. P. Fadeeva
pp. 106–111 (Russian issue)

Abstract—Based on the well-know formula which expresses mean-square error $\sigma_\tau^2$ in terms of spectral function $\Phi_\tau(\lambda)$ of the optimal linear extrapolation and also on the explicit form of $\Phi_\tau(\lambda)$ obtained earlier by the author for a class of stationary processes with $R$-quasipolynomial spectral density, for this class of processes we derive an explicit formula for the mean square extrapolation error $\sigma_\tau^2$. In the derivation of the formula for $\sigma_\tau^2$, we employ residue theory and Cauchy's integral theorem.