PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii


Volume 23, Number 1, January–March, 1987
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$\varepsilon$-Entropy of the Gibbs Field
L. A. Bassalygo and R. L. Dobrushin
pp. 1–11

Abstract—For high-temperature Gibbs fields, the difference between $\varepsilon$-covering and entropy is fairly easily calculated for sufficiently small $\varepsilon$.

 

On Equations for Shannon Information in Transmission of Markov Diffusion Signals Through Channels with Memory
N. S. Demin and V. I. Korotkevich
pp. 11–21

Abstract—We derive equations for Shannon information in transmission of a multidimensional Markov diffusion signal through a multidimensional channel, when the output signal carries information not only about the current value of the transmitted signal but also about its past value with some fixed delay. We consider both continuous and continuous-discrete transmission, when the receiver input is a collection of realizations of continuous and discrete stochastic processes.

 

An Exhaustion Bound for Algebraic-Geometric “Modular” Codes
S. G. Vlǎduţ
pp. 22–34

Abstract—We construct a new lower bound for asymptotic parameters of codes arising from modular curves. For $q=4,9,16,25$, it is identical to the Varshamov–Gilbert bound, whereas for $q=p^{2a}\ge 49$ it improves the best known lower bound in two ranges of $\delta$.

 

Algebraic-Geometric Codes from Curves of Small Genus
A. M. Barg, G. L. Katsman, and M. A. Tsfasman
pp. 34–38

Abstract—We construct $q$-ary codes from algebraic curves of genus $1$, $2$, and $3$. From these codes we obtain binary codes with parameters better than those of known codes.

 

An Improvement of Greismer Bound for Some Classes of Distances
S. M. Dodunekov and N. L. Manev
pp. 38–46

Abstract—Linear binary codes are considered. We prove that for $d=2^{k-2}-2^a-2^b$, $0\le b\lt a\le k-3$, $2\le a$, $9\le k$, the block length of a $k$-dimensional code with code distance $d$ is not less than $$ 2+\sum_{j=0}^{k-1}\left\lceil\frac{d}{2^j}\right\rceil. $$

 

Adaptive Asymptotically Minimax Estimators of Smooth Signals
G. K. Golubev
pp. 47–55

Abstract—We solve the problem of asymptotically minimax filtering of a smooth signal from white Gaussian noise with incomplete prior information about the class of signals being estimated.

 

Transmission Accuracy of a Continuous Signal with Binary Quantization
A. B. Tsybakov
pp. 56–65

Abstract—We obtain lower bounds on estimation accuracy of a smooth signal transmitted using memoryless binary quantization. A method is proposed which attains the lower bound in order of magnitude. It is shown that in transmission with pseudorandom noise quantization, the estimation accuracy is an order of magnitude lower than in the proposed method.

 

Reconstruction of Signals Corrupted by Pulse Noise
L. I. Piterbarg
pp. 65–73

Abstract—We discuss a nonparametric approach to detection of signals corrupted by a stream of short pulses. An analog of the $L$-estimator of the location parameter of a distribution is proposed for this purpose. Robustness of the proposed procedure in deterministic and stochastic cases is established. A medium filter is characterized in the class of relevant estimators.

 

Binary Programs and Their Realization by Asynchronous Automata
Yu. L. Sagalovich and A. A. Shalyto
pp. 74–80

Abstract—We consider coding of states of asynchronous automata designed to evaluate systems of Boolean functions by means of binary programs. We show that for a fairly wide class of systems of Boolean functions race-proof state coding is irredundant.

 

A Multiaccess Stack Algorithm for an Asynchronous System
B. S. Tsybakov, V. L. Bakirov, A. V. Zhukov, I. D. Kalashnikov, A. I. Martynov, and S. E. Sokolov
pp. 81–89

Abstract—We construct a mathematical model of a multiple access asynchronous packet transmission system. Two versions of the asynchronous RMA stack algorithm are proposed. The algorithm is investigated by simulation.

 


BRIEF COMMUNICATIONS
(available in Russian only)

Description of Maximal Subsets of a Given Diameter in a Hamming space
S. L. Bezrukov
pp. 106–109 (Russian issue)

Abstract—We describe all maximal (with respect to cardinality) subsets of a unit $n$-cube $B^n$ that have a given diameter. As a corollary, for an arbitrary number $m$, $1\leq m\leq 2^n$, we find one of the subsets of cardinality $m$ with the minimum possible diameter.

 

On Concatenated Constant-Weight Codes Beyond the Varshamov–Gilbert Bound
V. A. Zinoviev and T. Ericson
pp. 110–111 (Russian issue)

Abstract—We show that concatenated constant-weight codes based on Goppa codes exceed the Varshamov–Gilbert bound for constant-weight codes.