Belief propagation decoding of Reed-Solomon codes; a bit-level soft decision decoding algorithm

In this article we propose the application of Belief Propagation (BP) algorithm as a novel bit-level soft decision decoding (SDD) technique for Reed-Solomon (RS) codes. A brief tutorial on Belief Propagation algorithm is presented. A central issue in the application of BP algorithm to decoding RS codes is the construction of a sparse parity check matrix for the binary image of the code. It is demonstrated that Vardy´s technique may be applied to find a sparse parity check matrix for RS codes. However, this technique is not applicable to all cases. The BP algorithm is applied to two test codes. In one case, simulation models show that the BP algorithm outperforms the hard decision Euclidean decoding by more than 2 dB of additional coding gain. The results with the second test code are not as promising.