Optimal Encoding and Decoding Algorithms for the RAID-6 Liberation Codes

Abstract

RAID-6 is gradually replacing RAID-5 as the dominant form of disk arrays due to its capability of tolerating concurrent failures of any two disks, as well as the case of encountering an uncorrectable read error during recovery. Implementing a RAID-6 system relies on some erasure coding schemes, and so far the most representative solutions are EVENODD codes [1], RDP codes [2] and Liberation codes [3], none of which has emerged as a clear "all-around" winner. In this paper, we are interested in revealing the undiscovered potential of the Liberation codes, since these codes have the following attractive features: (a) they have the best update performance, (b) they have better scalability, and (c) they are open-sourced and publicly available, as well as the following drawbacks: fair encoding performance and, more importantly, relatively poor decoding performance. Specificly, we present novel optimal encoding and decoding algorithms for the Liberation codes by introducing an alternative, geometric presentation of these codes. The proposed algorithms completely eliminate redundant computations during the encoding and decoding procedures by extracting and reusing common expressions between the two types of parity constraints, and do not involve any matrix operations on which the original algorithms are based. Our experiment results show that compared with the original solution, the proposed encoding and decoding algorithms reduce the number of XOR’s by up to 16 percent and 15 ~20 percent respectively, and the encoding and decoding throughputs are increased by 22.3 percent and at most 155 percent respectively. Moreover, the encoding complexity reaches the theoretical lower bound, while the decoding complexity is also very close to the theoretical lower bound.