Efficient Iterative Techniques for Soft Decision Decoding of Reed-Solomon Codes

Abstract

Two new iterative soft decision decoding methods for Reed-Solomon (RS) codes are proposed. These methods are based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In the first proposed method, we take advantage of the cyclic structure of RS codes. Based on this property, we can apply the belief propagation algorithm on any cyclically shifted version of the received symbols with the same binary parity check matrix. For each shifted version of received symbols, the distribution of reliability values will change and deterministic errors can be avoided. This method results in considerable performance improvement of RS codes compared to hard decision decoding. The performance is also superior to some popular soft decision decoding methods. The second method is based on information correction in BP decoding. It means that we determine least reliable bits and by changing their channel information, the convergence of the decoder is improved. Compared to the first method, this method needs less BP iterations (less complexity) but its performance is not as good.