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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., QC 20161118

There have been emerging lots of applications for distributed storage systems e.g., those in wireless sensor networks or cloud storage. Since storage nodes in wireless sensor networks have limited battery, it is valuable to find a repair scheme with optimal transmission costs (e.g., energy). The optimal-cost repair has been recently investigated in a centralized way. However a centralized control mechanism may not be available or is very expensive. For the scenarios, it is interesting to study optimal-cost repair in a decentralized setup. We formulate the optimal-cost repair as convex optimization problems for the network with convex transmission costs. Then we use primal and dual decomposition approaches to decouple the problem into subproblems to be solved locally. Thus, each surviving node, collaborating with other nodes, can minimize its transmission cost such that the global cost is minimized. We further study the optimality and convergence of the algorithms. Finally, we discuss the code construction and determine the field size for finding feasible network codes in our approaches., QC 20140205