Comparison on Vandermond and Cauchy MDS Array Codes in Distributed Storage Systems

Binary maximum distance separable (MDS) array codes are an important class of MDS codes with low computational complexity, as only XOR operations are involved in the encoding/decoding procedures. Most existing binary MDS array codes are constructed based on Vandermonde matrix or Cauchy matrix, as we have efficient decoding methods for Vandermonde and Cauchy linear systems. We call the array codes with encoding matrix being Vandermonde matrix and Cauchy matrix as Vandermonde MDS array codes and Cauchy MDS array codes, respectively. In this paper, we implement Vandermonde MDS array codes and Cauchy MDS array codes, and evaluate their encoding and decoding performance. Our implemented results show that Vandermonde MDS array codes have better encoding/decoding performance than that of Cauchy MDS array codes. Specifically, the encoding rate of Vandermonde MDS array codes is about 58% higher than that of Cauchy MDS array codes, and the decoding rate of Vandermonde MDS array codes is about 70% higher than that of Cauchy MDS array codes. In our implementation, the efficient decoding method is based on the LU factorization of Vandermonde matrix and Cauchy matrix. Thus, only some pattern of the decoding procedure of Vandermonde MDS array codes is considered in this paper.