On probability of correction of a random number of errors in an error-correcting coding
Алексей Николаевич Чупрунов, B. I. Khamdeev · Discrete Mathematics and Applications · 2010
We consider the probability P ( A ) of the event A that while n messages each consisting of N blocks are encoded by a Hamming-type code all errors are corrected. It is assumed that the i th message has m i ( ω 1 ) errors, ω 1 ∈ Ω 1 , where m i are independent identically distributed random variables defined on the probability space (Ω 1 , 𝔄 1 , P 1 ). The probability P ( A ) is determined in the framework of the generalised allocation scheme introduced by V. F. Kolchin. It is shown that in the case where n , N → ∞ in such a manner that α = n / N → α 0 < ∞ the probabilities P ( A ) converge to one and the same limit for almost all ω 1 ∈ Ω 1 , and the value of this limit is found.