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- W1842188052 abstract "We study the performance of Reed-Solomon (RS) codes for the em exact repair problem em in distributed storage. Our main result is that, in some parameter regimes, Reed-Solomon codes are optimal regenerating codes, among MDS codes with linear repair schemes. Moreover, we give a characterization of MDS codes with linear repair schemes which holds in any parameter regime, and which can be used to give non-trivial repair schemes for RS codes in other settings. More precisely, we show that for $k$-dimensional RS codes whose evaluation points are a finite field of size $n$, there are exact repair schemes with bandwidth $(n-1)log((n-1)/(n-k))$ bits, and that this is optimal for any MDS code with a linear repair scheme. In contrast, the naive (commonly implemented) repair algorithm for this RS code has bandwidth $klog(n)$ bits. When the entire field is used as evaluation points, the number of nodes $n$ is much larger than the number of bits per node (which is $O(log(n))$), and so this result holds only when the degree of sub-packetization is small. However, our method applies in any parameter regime, and to illustrate this for high levels of sub-packetization we give an improved repair scheme for a specific (14,10)-RS code used in the Facebook Hadoop Analytics cluster." @default.
- W1842188052 created "2016-06-24" @default.
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- W1842188052 date "2015-09-15" @default.
- W1842188052 modified "2023-09-27" @default.
- W1842188052 title "Repairing Reed-Solomon Codes" @default.
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