New Cauchy MDS Array Codes with Flexible Sub-Packetization and Efficient Decoding

Cauchy maximum distance separable (MDS) array codes are widely used in storage systems that can support high fault tolerance with systematic form. However, Cauchy MDS array codes suffer from high encoding/decoding complexities and limited parameters. In this paper, we first construct new Cauchy MDS array codes with circulant structure over quotient rings that have flexible sub-packetization. We show that our codes can support more parameters than the existing Cauchy MDS array codes. The sub-packetization of our codes is a multiple of prime minus one, while the sub-packetization of the existing Rabin-Like codes and circulant Cauchy codes is prime minus one. Second, we propose a fast decoding method by designing new division algorithm and employing the LU decomposition of Cauchy matrix for the proposed Cauchy MDS array codes. We show that the decoding complexity of our codes is nearly the same as new Rabin-Like codes [16], and lower than all the other Cauchy MDS array codes.