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

Qian GUO  Haibin KAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.5   pp.978-981
Publication Date: 2012/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.978
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Coding Theory
erasures-only decoding,  Reed-Solomon codes,  quasi-systematic generator matrix,  interpolation based decoding,  fault-tolerance,  

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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(n2) and space complexity O(n). Specifically, the decoding algorithm requires 3kr + r2 - 2r field additions, kr + r2 + r field negations, 2kr + r2 - 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.