General self-repairing codes for distributed storage systems

In distributed storage systems, a data file is encoded and distributed to storage nodes, such that the data file can be recovered from some subsets of the nodes. Upon the failure of a storage node, we want to repair it efficiently by contacting and downloading some encoded bits from a small number of surviving nodes. Using projective-geometric self-repairing codes (PSRC), proposed by Oggier and Datta, one can repair a failed node by contacting only two nodes. However, in their construction, the number of storage nodes in the storage system is a large number, and thus the storage efficiency is low. In this paper, we investigate how to be more flexible in the number of storage nodes. The proposed code in this paper is called general projective geometric self-repairing codes (GPSRC). GPSRC reduces high redundancy of PSRC, while retains the basic property of PSRC. We present some methods for repairing a failed node, in which the number of contacted surviving nodes is flexible. These repairing methods provide tradeoff between repair-degree and repair-bandwidth.