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The probability of correcting errors by an antinoise coding method when the number of errors belongs to a random set

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Abstract

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 ith 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 P(A) and calculate it in terms of conditional probabilities. We prove that under certain moment conditions probabilities 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.

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Authors and Affiliations

  1. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, ul. Professora Nuzhina 1/37, 420008, Kazan, Russia

    A. N. Chuprunov & B. I. Khamdeev

Authors
  1. A. N. Chuprunov
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  2. B. I. Khamdeev
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Corresponding author

Correspondence to A. N. Chuprunov.

Additional information

Original Russian Text © A.N. Chuprunov and B.I. Khamdeev, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 8, pp. 81–88.

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Chuprunov, A.N., Khamdeev, B.I. The probability of correcting errors by an antinoise coding method when the number of errors belongs to a random set. Russ Math. 54, 67–73 (2010). https://doi.org/10.3103/S1066369X10080098

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  • DOI: https://doi.org/10.3103/S1066369X10080098

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