A Weight Method of Decoding the Binary BCH Code

Abstract

In this paper, a weight method with using a reduced lookup table is developed to decode the three possible errors in (15, 5, 7) and (31, 16, 7) BCH code. The data in the reduced lookup table consists of syndrome patterns and corresponding error patterns which only have one and two errors occurred in the message block of the received codeword. The proposed algorithm makes use of the properties of cyclic codes, weight of syndrome, and the reduced lookup table. It often results in a significant reduction in the memory requirements comparing to the traditional lookup table or other algebraic decoding methods. This weight decoding algorithm together with a reduced lookup table makes a fast and low complexity of the table lookup decoding algorithm. Moreover, a computer simulation shows that such a novel method is a much faster algorithm in software than the traditional full lookup table searching algorithm.