Geodesic
On probability of correction of a random number of errors in an error-correcting coding
Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 41-50 
A. N. Chuprunov; B. I. Khamdeev. On probability of correction of a random number of errors in an error-correcting coding. Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 41-50. http://geodesic.mathdoc.fr/item/DM_2010_22_2_a2/
@article{DM_2010_22_2_a2,
     author = {A. N. Chuprunov and B. I. Khamdeev},
     title = {On probability of correction of a~random number of errors in an error-correcting coding},
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     pages = {41--50},
     year = {2010},
     volume = {22},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_2_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the probability $\mathbf P(A)$ 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 ith message has $m_i=m_i(\omega_1)$ errors, $\omega_1\in\Omega_1$, where $m_i$ are independent identically distributed random variables defined on the probability space $(\Omega_1,\mathfrak A_1,\mathbf P _1)$. The probability $\mathbf P(A)$ is determined in the framework of the generalised allocation scheme introduced by V. F. Kolchin. It is shown that in the case where $n,N\to\infty$ in such a manner that $\alpha=n/N\to\alpha_0\infty$ the probabilities $\mathbf P(A)$ converge to one and the same limit for almost all $\omega_1\in\Omega_1$, and the value of this limit is found.

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