PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii

Volume 28, Number 4, October–December, 1992
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CONTENTS

Entropy of Some Binary Sources
A. G. Dyachkov and V. M. Sidelnikov
pp. 297–307

Abstract—A sequence of independent identically distributed binary random variables in which the probabilities of the binary symbols $0$ and $1$ are not equal to $1/2$ is applied to the homogeneous shift register with $k$, $k\ge 1$, memory locations (a $k$-register). The sequence of binary symbols from the $k$-register output is delivered to the input of a memoryless binary symmetric channel in which noise is independent of the $k$-register input sequence. We show that for $k=1,2,3$, the entropy [R. Gallager, Information Theory and Reliable Communication, Wiley, New York (1968)] of the output sequence from the channel may increase with the increase of $k$.

A Trellis Coding Scheme Based on Signal Alphabet Splitting
K. Sh. Zigangirov and R. Johanneson
pp. 308–316

Abstract—A signal–code construction is proposed that ensures a better relationship between decoding reliability and complexity than the classical scheme. The coder is partitioned into several “elementary” binary convolutional coders and the decoder is partitioned into several Viterbi decoders. The transmission of PSK-modulated signals is considered in more detail.

Capacity of a Communication Channel with Inner Random Coding
V. I. Korzhik and V. A. Yakovlev
pp. 317–326

Abstract—An expression is derived for the capacity of an extended channel consisting of an inner $(n,k)$ random code and a binary symmetric channel in a series. The calculation requires knowledge of the weight distribution of the cosets of the code and a certain subcode. The results are analyzed in application to transmission systems with error-correcting coding and broadcasting systems with unfriendly participants.

Sequential Parameter Estimation with Guaranteed Mean-Square Accuracy for Unstable Linear Stochastic Systems
V. V. Konev and S. M. Pergamenshchikov
pp. 327–340

Abstract—The correlation method is applied to construct estimation procedures for parameters of a random process described by a $p$th-order stochastic differential equation. These procedures estimate the unknown parameters with a prescribed mean-square accuracy when the characteristic polynomial has roots with both positive and negative real parts.

Efficiency of the Generalized Neyman–Pearson Test for Detecting Changes in a Multichannel System
A. G. Tatrtakovskii
pp. 341–350

Abstract—We propose a multialternative, multistage rule for detection of changes. The rule consists of fixed-length stages and it stops when the maximum likelihood statistic crosses the threshold for the first time. Parameter optimization and analysis of the rule are conducted for change detection in the mean of the Wiener process in a multichannel system. In the worst case, the proposed rule is inferior by a factor of two to the asymptotically minimax multialternative sequential rule with the mean time to false alarm tending to infinity. The results remain valid also in the general (non-Gaussian) case if we additionally require convergence of the hypotheses.

Interpolation of Discrete Periodic Data
M. G. Ber and V. N. Malozemov
pp. 351–359

Abstract—We consider the problem of estimating discrete periodic data on a fine grid from known values on a coarse grid. The smoothing functional is the sum of squares of $r$th-order finite differences. An explicit solution scheme is proposed using a discrete Fourier transform and the behavior of the solution is investigated for $r\to\infty$.

Lower Bound on Delay in an RMA System with $N$-Conflicts and Errors
B. S. Tsybakov and A. Yu. Privalov
pp. 360–374

Abstract—We derive a lower bound on delay, which is valid for any random multiple access algorithm in a channel with errors and $N$-conflicts. For $N=2$ and without errors, our lower bound reduces to the bound of [B.S. Tsybakov and N.B. Likhanov, Probl. Peredachi Inf., 27, No. 3, 73–88].

Proof of the Poisson Hypothesis for Circuit-Switching Loss Networks
pp. 375–383

Abstract—We prove the identity for the integral representation of the partial function of the main queueing process in circuit-switching star networks with losses. The integral representation is used to derive sufficient conditions for asymptotic applicability of the Poisson hypothesis for these networks and strict bounds for violations from this hypothesis in the finite case.

A Universal Search Scheme for a Single Significant Factor in a Disjunctive Model
B. Ya. Ryabko
pp. 384–389

Abstract—A sequential search scheme for a single significant factor is constructed for the case where the prior probability of the factor to be significant is unknown. Asymptotically optimal designs minimizing the absolute and the relative redundancy are obtained.

Binary Constant-Weight Codes Correcting Localized Errors
L. A. Bassalygo and M. S. Pinsker
pp. 390–392

Abstract—Asymptotically tight solutions can be obtained from codes correcting localized errors, which is only rarely possible for general error-correcting code. This paper is yet another example of this kind: we find the asymptotically optimal rate $R(\omega,\tau)$ of a binary constant-weight code of weight $\omega n$ correcting $\tau n$ localized errors.

On Varshamov–Tenengolts Codes and a Conjecture of L.A. Bassalygo
D. N. Gevorkian and G. A. Kabatianskii
pp. 393–395

Abstract—We consider a construction problem for binary codes that correct single localized errors. L.A. Bassalygo stated a conjecture that the maximum “cardinality” (the number of messages) of such a code is equal to the integral part of the corresponding value of the Hamming bound. Using Varshamov–Tenengolts codes, we prove that this conjecture holds true for code length $n=p-1$, where $p$ is a prime such that $2$ is its primitive root.

Letter to the Editor (ERRATUM)
G. K. Golubev
p. 395

INDEX
pp. 397–403