A Generic Transformation to Enable Optimal Repair in MDS Codes for Distributed Storage Systems

摘要

We propose a generic transformation that can convert any nonbinaryn$(n=k{+}r,k)$nmaximum distance separable (MDS) code into anothern$(n,k)$nMDS code over the same field such that: 1) some arbitrarily chosenn$r$nnodes have the optimal repair bandwidth and the optimal rebuilding access; 2) for the remainingn$k$nnodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved; and 3) the sub-packetization level is increased only by a factor ofn$r$n. Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinaryn$(n,k)$nscalar MDS code can be converted into ann$(n,k)$nMDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal.