On the Decoder Error Probability for BCH Codes
Mingoo Kim, Jaehong Lee · International Symposium on Information Theory and its Applications · 1994
A general formula is derived to obtain the decoder error probability for linear block codes. A bounded-distance decoder is assumed. It is shown that the decoder error probability for binary linear codes becomes a constant value if the weight distribution of the code is binomial-like. An exact decoder error probability for Reed-Solomon codes is obtained from this formula. Bounds on the decoder error probability for binary BCH codes are derived because the weight distributions of binary BCH codes are unknown except for some special codes. It is also shown that the decoder error probability approaches to (formula) rapidly in t-errors correcting (n, k) binary primitive BCH codes as code length n increases and the weight of word h approaches to n2.