PROBLEMS OF INFORMATION TRANSMISSION
A translation of Problemy Peredachi Informatsii


Volume 20, Number 2, April–June, 1984
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Centered Codes
K. Sh. Zigangirov and V. D. Kolesnik
pp. 81–91

Abstract—The authors propose a method of constructing and decoding block codes that makes it possible to reduce the complexity of decoding without significantly increasing the error probability. It is shown that in the case of a BSC with strong noise, at transmission rates close to the channel capacity, there exist centered codes for which the exponent of the error probability is equal to the exponent of random coding, while the number of computational operations involved in decoding in proportional to $mn\exp_2(nR/m)$, where $n$ and $R$ are the code length and rate, respectively; $m$ is an arbitrary integer that is bounded from above by a quantity that depends on the difference $C-R$ ($C$ is the channel capacity), that increases as this difference decreases.

 

Viterbi Algorithm for Decoding of Convolutional Codes in a System with Decision Feedback
B. D. Kudryashov
pp. 92–99

Abstract—The author offers a modification of the Viterbi algorithm that can be used for decoding convolutional codes in channels with decision feedback. A new bound is obtained for the attainable decoding-error probability.

 

Minimax Extrapolation of Functions
G. K. Golubev and M. S. Pinsker
pp. 99–111

Abstract—For special classes of functions $\Sigma_T$ the authors calculate the minimax square extrapolation error and construct extrapolation operators on which this error is attained.

 

Multiple-Alternative Adaptive Pattern Recognition with Parameter Estimation, When Ambiguous Decisions Are Allowed
G. P. Tartakovskii
pp. 112–118

Abstract—Under conditions of parametrically specified a priori indeterminacy, the author obtains an adaptive Bayesian solution for the multiple-alternative recognition problem, with estimation of the informative parameters of the patterns. In obtaining a solution, ambiguity of the hypotheses is allowed. The author offers approximations, valid for the case in which the observational data have a high degree of informativeness, such that the recognition-with-estimation algorithm proves to be fairly simple to implement. An example is considered.

 

Signal-Phase Estimation in a Nonparametric Situation
I. A. Ibragimov and R. Z. Khas'minskii
pp. 118–127

Abstract—The authors consider the problem of estimating the phase of a periodic signal when the form of the signal is unknown but can be estimated on the basis of additional observations. A lower bound for the quality of phase estimation, and the estimate on which this bound is asymptotically attained, are determined. The problem of optimum division of the observation time into two parts (signal identification and phase estimation) is examined.

 

Universal Algorithm for Synthesizing Self-Checking Testers for Constant-Weight Codes
V. V. Sapozhnikov and Vl. V. Sapozhnikov
pp. 128–137

Abstract—The authors propose a method that makes it possible to construct self-checking testers for codes with constant weight $m\ge 2$. The method yields testers with minimum complexity as compared to the available ones.

 

Packet Delay in the Case of a Multiple-Access Stack Algorithm
N. D. Vvedenskaya and B. S. Tsybakov
pp. 137–153

Abstract—For an arbitrary memoryless input stream, the authors obtain expressions for the moments and probability distributions of the virtual and actual delays in packet transmission in an RMA system with a stack algorithm. For the case of a Poisson input stream, it is shown that the distributions of the actual and virtual delays coincide, and the average delay and variability coefficient are plotted against the intensity of the input stream.

 


BRIEF COMMUNICATIONS
(available in Russian only)

 

On Quasi-Cyclic Codes Based on Planar Perfect Difference Sets
S. I. Kovalev
pp. 98–105 (Russian issue)

Abstract—For quasi-cyclic codes constructed on the basis of planar difference sets with an odd minimum distance $d$ and rate $1/2$, we compute some of the first elements of their weight spectra. The obtained results yield certain parameters of an optimum decoder. We describe a minimum-distance decoding procedure which corrects any $d-2$ errors and can easily be implemented on the basis of a threshold decoder.

 

Analysis of Efficiency of Universal Coding as a Function of the Block Length
A. P. Klarin and V. A. Shurygin
pp. 105–110 (Russian issue)

Abstract—We estimate the efficiency of universal coding of nonexponential complexity as a function of a block length $n$. We show that accounting of the nonmonotone behavior of the coding redundancy as a function of the length of an $n$-block reduces the coding complexity. We also estimate the airborne usability of this coding.