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IEEE International Symposium on Information Theory (ISIT)

The worst-case probability of undetected error for linear codes on the local binomial channel

Torleiv Kløve

Published Nov 19, 2002• 0 citations
Publisher

Abstract

The worst-case probability of undetected error for a linear [n,k;q] code used on a local binomial channel is studied. For the two most important cases it is determined in terms of the weight hierarchy of the code. The worst-case probability of undetected error for simplex codes is determined explicitly. A conjecture about Hamming codes is given.

DOI
10.1109/isit.1995.550329

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International Journal of Statistics and Applied Mathematics•Jan 1, 2017•1 citation
The worst-case probability of undetected error for a linear [n,k;q] code used on a local binomial channel is studied. For the two most important cases it is determined in terms of the weight hierarchy of the code. The worst-case probability of undetected error for simplex codes is determined explicitly. A conjecture about Hamming codes is given.
The problem of computing the probability of undetected error is considered for linear block codes used for error detection. The recent literature is first reviewed and several results are extended. It is pointed out that an exact calculation can be based on either the weight distribution of a code or its dual. Using the dual code formulation, the probability of undetected error for the ensemble of all nonbinary linear block codes is derived as well as a theorem that shows why the probability of undetected error may not be a monotonic function of channel error rate for some poor codes. Several bounds on the undetected error probability are then presented. We conclude with detailed examples of binary and nonbinary codes for which exact results can be obtained. An efficient technique for measuring an unknown weight distribution is suggested and exact results are compared with experimental results.