Novel burst error correcting algorithms for Reed-Solomon codes
Yingquan Wu · 2009
In this paper, we present three novel burst error correcting algorithms for an (n,k,r = n - k) Reed-Solomon code. The algorithmic complexities are of the same order for erasure-and-error decoding, O(rn), moreover, their hardware implementation shares the elements of the Blahut erasure-and-error decoding. In contrast, all existing single-burst error correcting algorithms, which are equivalent to the proposed first algorithm, have cubic complexity, O(r2n). The first algorithm corrects the shortest single-burst with length ff-r, where q denotes the field size. The second algorithm extends the first one to correct the shortest burst with length f2qf+1-r. The third algorithm aims to correct the shortest burst with length f¿+1q-(r-f-¿)while its defect rate is bounded by nq-(r-2¿-f)¿(whereas no defect occurs to the proposed first and second algorithms).