# Majority decoding of large repetition codes for the r-ary symmetric channel

## Abstract

A r-ary symmetric channel has as transition probability matrix the r×r matrix qxy=p if x≠y and qxy=1−(r−1)p=q if x=y. Given a set Y of r symbols, the code here consists of r codewords, each one of them is made up of n identical symbols. Whenever q is larger than p, maximum likelihood decoding amounts to find out in the received vector which symbol is repeated most. Thus MLD here reduces to majority decoding.

A generating function for the error probability as well as the probability of decoding failure for the system is obtained. Also recurrence relations are given for computing those probabilities.

*transitive*. A r-ary transitive DMC is a DMC such that there exists a transitive permutation group G on the set Y of symbols such that

The results corresponding to those announced for the r-ary symmetric channel are obtained for the majority decoding repetition codes over r-ary transitive DMC.

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## References

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*An Introduction to Probability Theory and Its Applications*. 1968 John Wiley & Sons.Google Scholar - [2]D. FOATA, M. SCHÜTZENBERGER:
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*The Theory of information and coding*. 1977 Addison-Wesley.Google Scholar - [4]T. ERICSON:
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