An Efficient Interpolation Based Erasure-Only Decoder for High-Rate Reed-Solomon Codes

摘要

In this paper, we derive a simple formula to generate a wide-sense systematic generator matrix(we call it quasi-systematic) B for a Reed-Solomon code. This formula can be utilized to construct an efficient interpolation based erasure-only decoder with time complexity O(n~2 ) and space complexity O(n). Specifically, the decoding algorithm requires 3kr + r~2 — 2r field additions, kr + r~2 + r field negations, 2kr + r~2 — r + k field multiplications and kr+r field inversions. Compared to another interpolation based erasure-only decoding algorithm derived by D.J.J. Versfeld et al., our algorithm is much more efficient for high-rate Reed-Solomon codes.