On the undetected error probability of linear codes
Chong Tean Ong · cIRcle (University of British Columbia) · 2010
The probability of undetected error P[formula omitted](є) for the primitive triple-error-correcting BCH codes of blocklength 2[formula omitted] 1, used solely for error detection on a binary symmetric channel with crossover probability є ≤ 1/2, is examined. It is shown that for odd values of m, P[formula omitted(є) increases monotonically with є. For even values of m, this is not necessarily true. However, for a fixed є, as m increases, P[formula omitted](є) approaches 2‾[formula omitted] where p is the number of parity bits. The extended double and triple-error-correcting primitive BCH codes are also examined. The undetected error probability of these codes is shown to have similar characteristics as the non-extended cases. An improved upper bound on the probability of undetected error which is valid for any linear code is derived. Comparison of this improved upper bound with the Kasami upper bound for some classes of codes is shown.