关键词: RS柯西码, 极大距离可分码, 二进制矩阵, 阵列化, 编码效率

Abstract:

Aiming at the problems of Reed-Solomon algorithm（RS）, such as the encoding process involving finite field operations, high complexity, low efficiency, high computational cost that is difficult to accept by large-scale distributed storage systems, a new improved algorithm of RS Cauchy code is proposed. Firstly, the algorithm uses the greedy algorithm to select the local optimal Cauchy matrix, which reduces the computational complexity of the Cauchy code. At the same time, the binary matrix is replaced by the finite field elements in the Cauchy matrix to be arrayed. The finite field operation is converted into the XOR operation. And the array is optimized, which further reduces the calculation amount and increases the encoding efficiency of the Cauchy code. The results of simulation experiments indicate that the improved RS Cauchy code algorithm has less computation than the Cauchy code of the optimal Cauchy matrix. The array code is known for its high encoding efficiency. The improved algorithm has higher encoding efficiency than the EVENODD code and the STAR code in the array code. And it can choose a simpler and more efficient decoding method, which has the similar array code property. To a certain extent, the decoding efficiency can be improved.

Key words: RS Cauchy code, Maximum Distance Separable（MDS） code, binary matrix, array, encoding efficiency