A New Progressive Algebraic Soft Decoding Algorithm for Reed-Solomon Codes

The progressive algebraic soft decoding (PASD) algorithm can leverage the average complexity for algebraic soft decoding (ASD) of Reed-Solomon (RS) codes. With a progressively enlarged decoding parameter that is the designed factorization output list size (OLS), it adapts the expensive interpolation computation to the quality of the received information and makes the average complexity of multiple decoding events channel dependent. However, the complexity reduction is realized at the expense of system memory since the intermediate interpolation information needs to be stored. Addressing this issue, this paper proposes a new PASD algorithm that can significantly reduce the memory requirement through the establishment of a condition on expanding the interpolated polynomial group without using the intermediate information. It has also embraced the interpolation coordinate transform (ICT) that alleviates the iterative polynomial construction task, resulting in the new proposal less computationally expensive than its predecessor, the PASD algorithm. Our numerical analysis shows that its memory requirement will be at most half of that of the PASD algorithm and it is less complex than various ASD algorithms, while the error-correction capability of ASD is preserved.