PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

CONTENTS                  

Estimation of the Density Support and Its Functionals
A. P. Korostelev and A. B. Tsybakov
pp. 1–15

Abstract—We consider the recovering problem for the density support, i.e., the domain, where observable points are located. We study a nonparametric version of the problem; the asymptotics of the minimax risk as the number of observations tends to infinity is investigated. Together with the support restoring problem, we resolve an estimation problem for smooth functionals, for instance, the volume (area in the two-dimensional case) of the studied domain, the barycenter, etc. The asymptotic orders of the estimation precision are found and optimal estimates are obtained.

Characteristics of Robust Rules for Testing Two Hypotheses
A. A. Slepokurov
pp. 16–20

Abstract—The characteristics of a robust rule for testing two hypotheses are examined. We deal with the case where the alternative sets are neighborhoods of unknown multivariate probability distributions and a decision statistics is a censored version of the likelihood ratio. The decision rule is randomized. The results obtained are applied for a wide class of the alternative sets and can be useful for various problems of hypothesis testing and signal detection in noise. Some examples are considered.

A Method of Constructing the Restoring Operators for Equations of Convolution Type
E. G. Zhilyakov
pp. 21–26

Abstract—The problem of finding an approximate solution for the integral equations of convolution type is considered.

Multidimensional Lattices and Limit Efficiency of Modulation and Coding
A. N. Trofimov
pp. 27–37

Abstract—For the Gaussian channel we investigate how the exponent of the additive estimate for the mean coding error probability over the ensemble of codes (the computational rate) $R_0$ depends on the signal-to-noise ratio per sample provided that the input symbols for the channel are chosen from a subset of a multidimensional lattice. The asymptotic behavior of $R_0$ is considered with respect to the S/N per sample, the alphabet's cardinality, and the number of samples. Some numerical results are presented and some examples are discussed.

Uniqueness of Some Linear Subcodes of the Extended Binary Golay Code
S. M. Dodunekov and S. B. Encheva
pp. 38–43

Abstract—We prove that up to equivalence, there exist only two $[18,6,8]$ codes and only one $[n,n-12,8]$ code, $19\le n\le 23$. All the considered codes can be obtained after a suitable shortening of the binary $[24,12,8]$ Golay code.

Decoding of the Trellis Codes in a Linear Asynchronous Multiple Access Channel
F. A. Taubin
pp. 44–49

Abstract—The transmission of asynchronized stations using individual trellis codes over the linear sum multiple access channel is considered, provided that there are interferences both within each of the subchannels and among the various subchannels. The structure of the general maximum likelihood decoder and the corresponding upper bound of error probability per symbol for each of the sources is presented.

Development of Discrete Models for Fading Channels
I. E. Bocharova and B. D. Kudryashov
pp. 50–57

Abstract—A method is proposed that enables an approximate discrete mapping model to be developed for exponentially correlated Raleigh or Rician fading. Generally, the approximate model is a function of a pseudo-Markov chain. The accuracy of the approximation for varying model ranks is investigated.

Fast Evaluation of $\zeta(3)$
E. A. Karatsuba
pp. 58–62

Abstract—We prove that the complexity of evaluating $\zeta(3)$ with precision $2^{-n}$ is $O(n\log^3n\log\log n)$ elementary operations, $\zeta(s)$ being a Riemann zeta function.

Asymptotics of the Shannon Function for Switching Circuits in the Sheffer Stroke Basis with Partial Unreliability
V. V. Tarasov
pp. 63–69

Abstract—We give the asymptotics of the Shannon function $L(n,\varepsilon(n))$ for a class of circuits of functional elements in the basis of the partially unreliable element “Sheffer stroke.”

Random Access Algorithms with Multiple Reception Capability and $n$-ary Feedback Channel
N. Likhanov, E. Plotnik, Y. Shavitt, M. Sidi, and B. Tsybakov
pp. 70–79

Abstract—Random access algorithms to a common channel with multiple reception capability by receivers and an $n$-ary feedback channel are presented. The algorithms belong to the class of splitting algorithms. It is shown that the throughput of these algorithms is 1.5–3% higher than the throughput of the best known algorithm with ternary feedback channel

Poisson Limit Theorem for Message Switching Networks with Low Transit Traffics
M. Ya. Kelbert
pp. 80–84

Abstract—A sequence of communication networks with increasing branching and low traffic intensities on the transit routes is considered. The limiting message throughput delay distribution is shown to be the same that for the series of stochastically independent queues. This is an example of the so-called Poisson conjecture being valid for a sufficiently complex queueing network.

Defect-Correcting Codes
V. A. Davydov
pp. 85–89

Abstract—We suggest a new construction of additive codes and universal tests. For the given parameters we construct best known codes and tests.

On the Transmission of a Gaussian Random Variable in a White Noise Channel with Feedback
P. K. Katyshev
pp. 90–94

Abstract—The transmission of a Gaussian random variable through a white Gaussian channel with fixed feedback signal delay is considered. In the class of linear codings we determine the minimum mean square decoding error and construct the optimal transmission scheme. Furthermore we examine the effect of a small noise on the optimal transmission scheme, designed for the channel with noise-free feedback.