An Alternative Generic Transformation for Optimal Repair Bandwidth and Rebuilding Access in MDS Codes

Abstract

In last ISIT, we reported a generic transformation on maximum distance separable (MDS) codes, which can convert any non-binary (k+r, k) MDS code into another (k+r, k) MDS code such that an arbitrarily chosen $r$ nodes will have the optimal repair bandwidth and the optimal rebuilding access by modifying their data. However, the resultant code thus obtained is no longer in a systematic form if we wish to optimal repair $r$ systematic nodes, and another linear transformation is needed to convert it into one, which may break the inherent simplicity in the decoding and repair procedure. In this work, we propose an alternative generic transformation to solve this issue. In the alternative generic transformation, any $r$ systematic nodes can be optimally repaired with their data keeping unchanged through instead modifying the data on the $r$ parity nodes. As a result, by applying multiple times the two transformations in combination, we can directly obtain systematic MDS codes with optimal rebuilding access for all nodes or for a subset of nodes from any non-binary scalar MDS codes, which have the optimal sub-packatization level as well.