Fast and Low-Complexity Decoding Algorithm and Architecture for Quadruple-Error-Correcting RS codes

The key-equation solver (KES) and the Chien search & error evaluator (CSEE) are two stages of the decoding algorithms for Reed-Solomon (RS) codes. They determine the error locator polynomial and compute the error magnitudes, respectively. A recursive algorithm called reformulated inversionless Berlekamp Massey (riBM) algorithm is widely used for the KES block. However, for high rate RS codes, such as single-error-correcting (SEC) and double-error-correcting (DEC) RS codes, a method to find errata patterns directly has been proposed in the literature. We extend the method and derive the direct calculation algorithm for quadruple-error-correcting (QEC) RS codes in this work. An optimized architecture of the proposed algorithm is further developed. The computational complexity is reduced significantly by the proposed direct calculation method. Moreover, the data paths of the proposed architecture are all feed-forward and thus pipelining can be easily employed for high-speed applications.