PGZ algorithm for correcting both errors and erasures of RS codes

摘要

It is shown in this paper that a direct solution method developed first by Peterson, Gorenstein and Zierler (PGZ) can be extended to correct any combination of s erasures and ν errors under s + 2ν ≤ 6 of RS code from the Newton's identities when the minimum distance is 7. The extended decoding algorithm and a practical software simulation using the compressed image Lena corrupted by noises are presented.