A Low-Complexity Error-and-Erasure Decoding Algorithm for t=2 RS Codes

Reed-Solomon (RS) codes are widely adopted in numerous digital communication systems to handle the possibly occurred errors and/or erasures during the data transmission. This paper focuses on the $t=2$ RS codes and proposes a low-complexity error-and-erasure decoding algorithm for them. The proposed algorithm directly computes the errata location polynomial instead of performing the iterative Berlekmap-Massey (BM) algorithm which is usually adopted in the conventional RS decoding algorithm. Moreover, a method to directly compute the errata locations and errata magnitudes is also presented. For a (255,251) RS code, the proposed error-and-erasure decoding algorithm can save over 90% multiplications and additions of the conventional decoding algorithm. In addition, the complexity reduction becomes more significant as code length increases.