F-code: An optimized MDS array code

Abstract

Based on the research of MDS array code of size nxn in distributed storage system, in this paper, we present a novel encoding scheme called the F-code and prove that the column distance of the F-code is 3, i.e. F-code is a MDS array code given that odd number n is greater than 3 and does not include factor 3. And we also implement a novel decoding algorithm of the F-code. The algorithm only needs two decoding chains in each linear equation group and is able to recover all unknown symbols on two erasure columns. The analysis of F-code shows that our method extends the range of number n in nxn MDS array code and gets lower/reduction algorithmic complexity. Therefore, the reliability of a distributed storage system that features the F-code can be effectively reinforced. © Springer-Verlag Berlin Heidelberg 2007.