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| Blaum-Roth codes, i.e., Reed-Solomon(RS) codes over the polynomial rings modulo sum_{i=0}^{p-1}x^{i} over GF(q), where p is a prime, is a family of maximum distance separable(MDS) array codes, which has important applications in storage systems, such as magnetic tapes, RAID architectures and distributed file systems. Compared to EVENODD codes or other existing coding schemes used in storage systems, low-rate Blaum-Roth codes seems more applicable when the size of the storage nodes becomes large and the erasures appear frequently.In this paper, we propose a new systematic encoding procedure for Blaum-Roth codes. Our method generalizes the interpolation-based erasure-only decoder for RS codes proposed by D.J.J. Versfeld et al., which is efficient for low-rate RS codes. Later, we derive a systematic encoder from this decoder, since encoding can be implemented as a special case of decoding. Compared to the systematic encoding procedure introduced by M. Blaum and R. Roth, our encoding procedure is much more efficient for low-rate Blaum-Roth codes. |
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| Keywords:Array codes;Blaum-Roth codes;erasures-only decoding;encoding;Reed-Solomon codes over rings;storage systems |
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