PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Prediction of Random Sequences and Universal Coding
B. Ya. Ryabko
pp. 87–96

Abstract—The prediction is represented as a set of probability estimates of possible continuations of the stochastic process. The prediction problem is solved in two settings: (1) given that the sequence is computable or (2) given that the sequence is stationary. In mathematical terms, the problem is related to coding theory and its solution accordingly relies on known information-theoretical results.

Decoding of Berman Modular MDS Codes
I. I. Grushko
pp. 96–101

Abstract—A new algorithm is described for decoding of cyclic MDS codes with the parameters $(p,k,p-k+1)$, where $p$ is an arbitrary odd prime. The decoding is based on Berman's definition [Kibernetika, 1967, no. 1, pp. 31–39] of modular $p$-codes, as the MDS codes considered in this paper are a particular subclass of Berman's modular codes.

Formally Self-Dual Polynomials
N. G. Lomadze
pp. 101–108

Abstract—We describe formally self-dual polynomials of $p$ variables ($p$ an arbitrary prime). Such polynomials have been described previously only for $p=2,3,5,7$.

On Estimating the Spectral Densities of a Gaussian Periodically Correlated Stochastic Process
V. G. Alekseev
pp. 109–115

Abstract—We propose and analyze nonparametric estimators of the spectral densities $f_j(\lambda)$, $j\in\mathbb Z$, of a Gaussian periodically correlated stochastic process $\xi(t)$, $t\in\mathbb R$, with mean $\mathbf{M}\xi(t)\equiv 0$. Some suggestions are made regarding the choice of parameters for estimation of the spectral density $f_j(\lambda)$.

Detection of Signals with Random Moments of Appearance and Disappearance
A. G. Tartakovskii
pp. 115–124

Abstract—We consider optimal detection of a signal with random moment of appearance and random length. Given the prior probability distributions of the moments of appearance and disappearance, the optimal nonsequential detection algorithm is based on a comparison of the likelihood ratio averaged over the joint distribution of these moments to some threshold. Fast algorithms generating the average likelihood ratio for discrete- and continuous-time observations are proposed. The structure of the optimal Bayesian sequential detection rule is established.

Signal Filtering on the Output of an Analog-Digital Converter
V. P. Yakovlev
pp. 124–130

Abstract—We calculate the error spectrum of an analog-digital converter for a signal with normal and exponential correlation function allowing for filtering after reconstruction from discrete data. We find the quantization step, the discretization frequency, the number of quantization levels, and the output filter band minimizing the error for a given number of bits per unit time in the discrete representation.

On Minimax Filtering of Signals from Nonstationary Filters
S. N. Podkorytov
pp. 130–138

Abstract—We consider the filtering of nonstochastic complex-valued functions $s(t)\in\Sigma_T$ corrupted by white noise. We assume that the class $\Sigma_T$ consists of all possible responses of a linear filter, which is possibly not time-invariant. The known results for invariant filters are extended to this case.

Stability Analysis of a Packet Switching Network and Its Application to the Construction of a Unified Approach to Synchronous and Asynchronous ALOHA Radio Networks
B. S. Tsybakov and V. L. Bakirov
pp. 139–151

Abstract—A sufficient condition of stability is obtained for a packet switching network. A generalized ALOHA algorithm, incorporating synchronous and asynchronous ALOHA, is described. Several examples of various networks are examined and the corresponding stability conditions are given.

Cycles in Collectives of Threshold Automata
I. N. Karbovskii
pp. 152–158

Abstract—We prove that cycles of length $m\ge 3$ are impossible for symmetrical connection matrices in the class of regular collectives of threshold automata, which includes finite collectives and homogeneous networks as subclasses.

δ-Decodable Code Constructions for a $T$-User Adder Channel
G. G. Khachatryan
pp. 159–163

Abstract—Some general constructions of $\delta$-decodable codes for a $T$-user adder channel are given for the first time.

Capacity Parametrization of a Multiple-Access Binary Adder Channel with Shared Information
A. Ya. Belokopytov
pp. 163–167

Abstract—The results of [D. Slepian and J.K. Wolf, Bell Syst. Tech. J., 1973, vol. 52, no. 7, pp. 1037–1076; T.M. Cover and C.S.K. Leung, IEEE Trans. Inf. Theory, 1981, vol. 27, no. 3, pp. 292–298; F.M.J. Willems, IEEE Trans. Inf. Theory, 1982, vol. 28, no. 1, pp. 93–95] are applied to derive analytical expressions for the characteristic cross sections of the set of admissible rate triples for a binary adder channel with shared information. The numerical values of the coordinates of the extreme points in these regions are determined.

An Optimal Ensemble of Binary Sequences Based on the Union of the Ensembles of Kasami and Bent-Function Sequences
B. Zh. Kamaletdinov
pp. 167–169

Abstract—We show that the union of ensembles of Kasami and bent-function sequences forms a new optimal ensemble (in the sense of sphere packing bounds), which is virtually twice as large as each of the component ensembles.

OBITUARY. Andrei Nikolaevich Kolmogorov
pp. 170–171