Asymmetric regenerating codes for heterogeneous distributed storage systems

Distributed storage systems provide reliability by distributing data over multiple storage nodes. Once a node fails, a new node is introduced to the system to maintain the availability of the stored data. The new node downloads information from other surviving nodes called helper nodes to recover the lost data in the failed node. The number of helper nodes is called repair degree. Compared to traditional approaches, e.g., replication and erasure codes, the regenerating codes proposed recently can significantly reduce the repair bandwidth in homogeneous distributed storage systems. Most existing works focus on uniform settings (e.g., in terms of repair degree and repair bandwidth). However, due to network structures or connectivity limitations, for each failed node, the number of required helper nodes may be different for distinct failed nodes. Furthermore, considering the limits of network traffic of bandwidth, the amount of information allowed to be downloaded from each helper node could also vary. Thus we are motivated to investigate heterogeneous distributed storage systems where the repair degree and the amount of information downloaded from each helper node can be different. In order to obtain the minimal bandwidth to recover a failed node, we construct an information flow graph for such heterogeneous systems. By analyzing the cut-set bound of the information flow graph, the optimal tradeoff between storage capacity and repair bandwidth is derived. We then propose asymmetric regenerating codes that can achieve the curve of the optimal tradeoff. A linear construction of asymmetric regenerating codes is presented. Compared with previous regenerating codes, asymmetric regenerating codes are shown to have a lower repair bandwidth under a certain constraint condition, whose reduction can be up to 36.2%.