Enabling All-Node-Repair in Minimum Storage Regenerating Codes

We consider the problem of constructing exact-repair minimum storage regenerating (MSR) codes, for which both the systematic nodes and parity nodes can be repaired optimally. Although there exist several recent explicit high-rate MSR code constructions (usually with certain restrictions on the coding parameters), quite a few constructions in the literature only allow the optimal repair of systematic nodes. This phenomenon suggests that there might be a barrier between explicitly constructing codes that can only optimally repair systematic nodes and those that can optimally repair both systematic nodes and parity nodes. In the work, we show that this barrier can be completely circumvented by providing a generic transformation that is able to convert any non-binary linear maximum distance separable (MDS) storage codes that can optimally repair only systematic nodes into new MSR codes that can optimally repair all nodes. This transformation does not increase the alphabet size of the original codes, and only increases the sub-packetization by a factor that is equal to the number of parity nodes. Furthermore, the resultant MSR codes also have the optimal access property for all nodes if the original MDS storage codes have the optimal access property for systematic nodes.