Geodesic
The probability of correcting errors by an antinoise coding method when the number of errors belongs to a~random set
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 81-88

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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. 
@article{IVM_2010_8_a8,
     author = {A. N. Chuprunov and B. I. Khamdeyev},
     title = {The probability of correcting errors by an antinoise coding method when the number of errors belongs to a~random set},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {81--88},
     publisher = {mathdoc},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_8_a8/}
}
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A. N. Chuprunov; B. I. Khamdeyev. The probability of correcting errors by an antinoise coding method when the number of errors belongs to a~random set. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 81-88. http://geodesic.mathdoc.fr/item/IVM_2010_8_a8/