Decoding Shortened Reed Solomon Codes at Bit Level

This study presents a novel means of shortening a Reed Solomon (RS) code at the bit level, yielding only shortened BCH subcodes. With the use of a certain basis, an RS codes over ) 2 ( m GF is mapped onto a binary image[4], which contains m concatenated BCH sub-codewords and some glue-vector codewords. With the proposed approach, there only exist some shortened BCH subcode generators in the diagonal entries of the corresponding binary image generator matrix of an RS code. Hence, only binary codewords of shortened BCH subcodes exist in concatenation. When such a codeword is transmitted, BCH decoders or an RS decoder can be adopted at the receiver. In simulations of a BPSK coherent system over AWGN channels, the error performance of BCH algebraic decoding is better than that of RS algebraic decoding. The coding gain between both decoding algorithms becomes obvious as the code rate reduces or the error correcting capability of an RS code increases. At the word error rate 10 -5 , the code gain can reach as much as 1.5 dB at the code date 0.747. Additionally, with the proposed method for shortening RS codes over GF(2 8 ), such a shortened RS code can be decoded by two or three BCH decoders in parallel, which greatly reducing the decoding times and computational complexity. Key-Words: RS decoding, shorten RS codes, shorten BCH codes, binary images.