Toward Optimality in Both Repair and Update via Generic MDS Code Transformation

An (n, k) maximum distance separable (MDS) code encodes kα data symbols into nα symbols that are stored in n nodes with α symbols each, such that the kα data symbols can be reconstructed from any k out of n nodes. MDS codes achieve optimal repair access if we can repair the lost symbols of any single node by accessing $\frac{\alpha }{{d - k + 1}}$ symbols from each of d other surviving nodes, where k + 1 ≤ d ≤ n - 1. In this paper, we propose a generic transformation for any MDS code to achieve optimal repair access for a single-node repair among d - k + 1 nodes, while the transformed MDS codes maintain the same update bandwidth (i.e., the total amount of symbols transferred for updating the symbols of affected nodes when some data symbols are updated) as that of the underlying MDS codes. By recursively applying our transformation for existing MDS codes with the minimum update bandwidth, we can obtain multi-layer transformed MDS codes that achieve both optimal repair access for any single-node repair among all n nodes and minimum update bandwidth.