Bit Level Implementation of the PTA Algorithm for Reed-Solomon Codes

The Parity check Transformation Algorithm (PTA) is a symbol level decoder that was recently developed for Reed-Solomon (RS) codes. The algorithm is a soft decision iterative decoder that uses the reliability information to decode by transforming the parity check matrix based on the same soft information. The PTA algorithm has been shown in literature to outperform widely used RS decoders like the Berlekamp-Massey algorithm and Koetter-Vardy algorithm. Work done in this paper investigates the effect of the PTA algorithm working on a sparse matrix by implementing it on a bit level. Modifications are made to the algorithm, to suit the bit level implementation, that significantly improve the overall performance. Simulations run show that the algorithm compares favorably to the high performance Adoptive Belief Propagation (ABP) decoder, that also works on a bit level, while providing a significant gain when compared to the symbol level implementation of the PTA.