PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Unit Sphere Packings and Coverings of the Hamming Space
G. A. Kabatyanskii and V. I. Panchenko
pp. 261–272

Abstract—A new method of construction of sphere packings and coverings is used to prove that the density of the best unit sphere coverings and packings of the $n$-dimensional Hamming space goes to $1$ as $n\to\infty$. The proposition proved about packings is equivalent to asymptotic exactness of the Hamming bound on the cardinality of single-error-correcting codes.

Construction and Characteristics of New Modulation/Convolutional Coding Systems
V. V. Zyablov, S. L. Portnoy, and S. A. Shavgulidze
pp. 272–280

Abstract—We give some methods of construction and bounds of minimum Euclidean distance for various modulation/convolutional coding systems. These systems are constructed using generalized concatenated codes with phase and amplitude/phase modulation in the inner stage and unit-memory convolutional codes in the outer stage.

Classification with Parameter Estimation for Objects in a System
A. I. Golubev and G. P. Tartakovskii
pp. 281–288

Abstract—We obtain an adaptive Bayes solution of the problem combining classification with parameter estimation for objects that are part of a system. The solution allows for the dependence of the loss function on the presence and the parameters of other objects in the system and on the decisions made regarding these other objects. The problem is solved under parametric prior uncertainty. An example is given.

On Estimating the Period of a Signal of Unknown Shape Corrupted by White Noise
G. K. Golubev
pp. 288–299

Abstract—We consider the estimation of the period of a signal of unknown shape corrupted by white noise. Asymptotically efficient estimates of the period have been constructed under certain prior restrictions on the class of allowed signals.

Sequential Testing of Many Simple Hypotheses with Independent Observations
A. G. Tartakovskii
pp. 299–309

Abstract—We consider the Bayesian problem of truncated sequential testing of many simple hypotheses with a loss function arbitrarily dependent on the observation step index. We show that, with independent observations, the optimal decision rule is representable as a comparison of the posterior probability for the hypothesis characterized by minimum current posterior risk with a variable threshold that depends on the posterior probabilities for the other hypotheses. We define the class of cases where this rule remain optimal with dependent observations. We derive an explicit expression for the least posterior risk function, which makes it possible to determine the optimal stopping regions in the case of “far” hypotheses. An example of detection of deterministic signals corrupted by autoregressive noise is considered.

Investigation of the Properties of an Optimal Reception Algorithm for Binary Signals
S. T. Grinchenko and N. D. Tarankova
pp. 310–317

Abstract—We consider the optimal processing of binary symbols generated by a Markov source and transmitted by a channel with memory modeled by a two-state probabilistic automaton. We derive the upper and lower bounds on error probability of symbol-by-symbol reception optimal the sense of the ideal observer criterion. A bound on the potentially attainable reception accuracy is given and the conditions of singleton decoding are derived.

Analysis of a Buffered Floating-Threshold Hybrid Switching System
G.I. Falin
pp. 318–323

Abstract—We describe a model of a floating-threshold hybrid switching data transmission system. Unlike previously studied models, our model assumes that priority (channel-switched) calls are not lost, and remain waiting until a channel is freed. An algorithm of exact numerical computation of stationary characteristics is given, the high-traffic behavior of the system is determined, and simple bounds on the average characteristics of the queueing process are obtained.

Design of Fast Checkers for Constant-Weight Codes
V. V. Sapozhnikov and Vl. V. Sapozhnikov
pp. 323–330

Abstract—A method is proposed for the construction of self-checking checkers for codes of constant weight $m\ge 2$, which produces checkers having specified speed. The proposed checkers are implemented by programmable logic arrays.

Packings and Coverings over an Arbitrary Alphabet
V. I. Panchenko
pp. 331–333

Abstract—The method of homogeneous unit-sphere packings and coverings of $q$-ary Hamming spaces is extended to the case where $q$ is not a prime power but there exists a perfect single-error-correcting $q$-ary code of length $q+1$.

Experimental Proof of the Use of Numerals in the Language of Ants
Zh. I. Reznikova and B. Ya. Ryabko
pp. 334–338

Abstract—We describe experiments in which ants were presented with a construction in the form of a trunk with $60$ branches carrying a food source on one of the branches. In order to reach the food source, the ants had to communicate to one another the information about the number of the branch with the food. The results suggest that ants can count up to a few tens, and their language contains numerals in the relevant range. The time to transmit the number $i$ in the language of ants was found to be approximately proportional to $i$, and not to $\log i$ as in modern human languages.

Frequency Distribution of Letters in the Russian Language
S. M. Gusein-Zade
pp. 338–342

Abstract—A model is proposed describing the ranked frequency series of the letters in a language. According to this model, the $r$th frequency in the ordered series, $p(r)$, is approximately given by $$ (1/n)(1/r+1/(r+1)+\dots+1/n)\approx(1/n)(\ln(n+1)-\ln r), $$ where $n$ is the total number of letters in the language. The frequency distribution of the letters in the Russian language fits this model.

INDEX
pp. 343–349