This article is cited in 3 papers

The probability of correcting errors by an antinoise coding method when the number of errors belongs to a random set

A. N. Chuprunov, B. I. Khamdeyev

Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, Kazan, Russia

Abstract: We consider $n$ messages of $N$ blocks each, where each block is encoded by some antinoise coding method. The method can correct no more than one error. We assume that the number of errors in the $i$th message belongs to some finite random subset of nonnegative integer numbers. Let $A$ stand for the event that all errors are corrected; we study the probability $\mathbf P(A)$ and calculate it in terms of conditional probabilities. We prove that under certain moment conditions probabilities $\mathbf P(A)$ converge almost sure as $n$ and $N$ tend to infinity so that the value $n/N$ has a finite limit. We calculate this limit explicitly.

Keywords: generalized allocation scheme, convergence almost sure, Hamming code.

UDC: 519.281

Received: 28.10.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:8, 67–73

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