Optimal-cost repair in multi-hop distributed storage systems with network coding

We study the transmission cost of repair in a distributed storage system, where storage nodes are connected together through an arbitrary network topology, and there is a cost in the use of the network link. Contrary to the classical model, where there exists a link between a pair of storage node, in our repair model there might not exist a link between some pairs of storage nodes or it might be expensive to use. For that, we propose surviving nodes cooperation in repair, meaning that the surviving nodes as the intermediate nodes combine their received packets with their own stored packets and then transmit coded packets towards the new node. We show that surviving node cooperation can reduce the repair-cost, the sum of the costs for transmitting repairing data between the surviving nodes and the new node. For the system that allows surviving node cooperation, we find the minimum-cost codes in repair by firstly deriving a lower bound of the repair-cost through an optimization problem and then proposing achievable codes. We show the gain of the proposed codes in reducing the repair-cost in some scenarios. Copyright (c) 2016 John Wiley & Sons, Ltd.