On probability of correction of a random number of errors in an error-correcting coding

摘要

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_1εΩ_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→1 in such a manner that a D n=N → a_0 < ∞ the probabilities P.A/ converge to one and the same limit for almost all ω_1εΩ_1, and the value of this limit is found.