Therefore, many research studies make efforts to optimize the decoding computation of the RS code. However, the typical decoding method of the RS code is the equation solving method over the finite field, and it is equivalent to the matrix inversion method and has very high computational complexity. Moreover, the tolerated failures are not restricted as the fixed number as the array codes. A storage system based on the RS erasure code can achieve the optimal tradeoff between the storage redundancy and the ability of the failure tolerance. The most important property for the RS erasure code is that it is MDS (Maximum Distance Separable) code, which means the RS code can provide the optimal failure recovery ability in a certain data redundancy.

The typical erasure codes are RS (Reed–Solomon) erasure code and the array codes. There are a lot of research studies about the encoding methods, while only a few studies focus on the decoding methods. The original information is first divided into k blocks then, the k blocks are encoded into n blocks using the encoding method when there are less than n− k blocks missed, the lost blocks can be recovered by the decoding method. IntroductionĮrasure coding is a widely used method in the distributed storage system to protect against the failures of the storage nodes it can provide better failure tolerance and much lower storage redundancy. The correctness of the method is proved by the theoretical analysis the experiments about the comparison with the traditional methods show that the proposed method has better decoding efficiency and lower reconstruction bandwidth. The decoding of the failures can be realized based on the transforming process of the decoding transformation matrix, and it is convenient to avoid the overburdened visiting problem by tiny modification of the method. In this paper, a novel erasure decoding method is proposed it is a general decoding method and can be used both over the multivariate finite field and the binary finite field. However, the current research studies about the erasure codes mainly focus on the encoding methods, while there are few studies on the decoding methods.

The erasure codes are widely used in the distributed storage with low redundancy compared to the replication method.

Erasure novel