Optimal-Repair-Cost MDS Array Codes for a Class of Heterogeneous Distributed Storage Systems

In this paper, the problem of designing the maximum-distance-separable (MDS) array codes for repairing a single node failure in a distributed storage system (DSS) is addressed. We consider the class of heterogeneous DSSs which can be represented as a fully connected storage network consisting of links having possibly different per-symbol transmission costs and assume that the repair process only allows a single-hop transmission from any helper node to a failed node. First, we consider the repair cost of a failed node to be the total transmission cost from all helper nodes incurred by the repair process. For a storage network represented by a complete weighted graph with the weights being the per-symbol transmission costs, we derive a repair cost lower bound of every node. Somewhat surprisingly, even for a storage network represented by a complete weighted graph with time-varying weights, we can also construct a single optimal-repair-cost MDS array code that can achieve the repair cost lower bounds of all nodes. Next, we consider the repair cost of a failed node to be the worst-case transmission cost over all helper nodes incurred by the repair process. For a storage network represented by a static complete weighted graph, we derive a lower bound on the repair cost of every node and construct a single optimal-repair-cost MDS array code that can achieve the repair cost lower bounds of all nodes.