Fast Error and Erasure Decoding Algorithm for Reed-Solomon Codes

Reed-Solomon (RS) codes are widely used to correct errors and erasures. This letter proposes a fast error and erasure decoding algorithm for RS codes. It achieves the best-known complexity
$O(n\log (n-k) + (n-k)\log ^{2}(n-k))$
, where
$n, k$
are the code length and dimension, respectively. Furthermore, the proposed method is efficient for practical codes. For decoding RS(255, 223), compared with the existing method, the new algorithm saves 32% field operations.