A Generic Transformation to Generate MDS Array Codes With δ-Optimal Access Property
Yi Liu, Jie Li, Xiaohu Tang · IEEE Transactions on Communications · 2021
Recently, some high-rate maximum distance separable (MDS) array codes were designed to optimally repair a single failed node by connecting all the surviving nodes. However, in practical systems, sometimes not all the surviving nodes are available. To facilitate the practical storage system, a few constructions of$(n,k)$MDS array codes with the property that any single failed node can be optimally repaired by accessing any$d$surviving nodes (i.e., minimum-storage regenerating (MSR) codes) have been proposed, where$d\in [k+1:n-1)$. However, all high-rate MDS array codes with this property either have large sub-packetization levels or are not explicit for all the parameters. To address these issues, we propose a generic transformation that can convert any$(n',k')$MDS array/scalar code to another$(n=n'-\delta,k=k'-\delta)$MDS array code with the optimal repair property and optimal access property for an arbitrary set of two nodes, while the repair efficiency of the remaining$n-2$nodes can be kept, where$2\le \delta \le n'-k'$. By recursively applying the generic transformation to an MDS scalar code multiple times, we get a high-rate MDS array code with the optimal repair property and the optimal access property for all nodes, which outperforms previous known high-rate MDS array codes in terms of either the sub-packetization level or the flexibility of the parameters.