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.

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. 
@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},
     journal = {Diskretnaya Matematika},
     pages = {41--50},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_2_a2/}
}
TY  - JOUR
AU  - A. N. Chuprunov
AU  - B. I. Khamdeev
TI  - On probability of correction of a~random number of errors in an error-correcting coding
JO  - Diskretnaya Matematika
PY  - 2010
SP  - 41
EP  - 50
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2010_22_2_a2/
LA  - ru
ID  - DM_2010_22_2_a2
ER  - 
%0 Journal Article
%A A. N. Chuprunov
%A B. I. Khamdeev
%T On probability of correction of a~random number of errors in an error-correcting coding
%J Diskretnaya Matematika
%D 2010
%P 41-50
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2010_22_2_a2/
%G ru
%F DM_2010_22_2_a2
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/

[1] Novikov F. A., Diskretnaya matematika dlya programmistov, Piter, Sankt-Peterburg, 2004

[2] Kolchin V. F., “Odin klass predelnykh teorem dlya uslovnykh raspredelenii”, Litovskii matem. sb., 8:1 (1968), 53–63 | MR | Zbl

[3] Kolchin V. F., Sluchainye grafy, Fizmatlit, Moskva, 2000 | MR | Zbl

[4] Kolchin A. V., “Predelnye teoremy dlya obobschennoi skhemy razmescheniya”, Diskretnaya matematika, 15:4 (2003), 148–157 | MR | Zbl

[5] Kolchin A. V., Kolchin V. F., “O perekhode raspredelenii summ nezavisimykh odinakovo raspredelennykh sluchainykh velichin s odnoi reshetki na druguyu v obobschennoi skheme razmescheniya”, Diskretnaya matematika, 18:4 (2006), 113–127 | MR | Zbl

[6] Kolchin A. V., Kolchin V. F., “Perekhod s odnoi reshetki na druguyu raspredelenii summ sluchainykh velichin, vstrechayuschikhsya v obobschennoi skheme razmescheniya”, Diskretnaya matematika, 19:3 (2007), 15–21 | MR | Zbl

[7] Avkhadiev F. G., Chuprunov A. N., “The probability of a successful allocation of ball groups by boxes”, Lobachevskii J. Math., 25 (2007), 3–7 | MR | Zbl