1Storage Capacity of Repairable Networks

In this paper, we introduce a model of a distributed storage system that is locally recoverable from any single server failure. Unlike the usual local recovery model of codes for distributed storage, this model accounts for the fact that each server or storage node in a network is connectible to only some, and not all other, nodes. This may happen for reasons such as physical separation, inhomogeneity in storage platforms etc. We estimate the storage capacity of a network under this model and propose some constructive schemes. From a coding theory point of view, this model is approximately dual of the well-studied index coding problem. The relation between the dimensions of an optimal index code and optimal distributed storage code of our model has been established in this paper. Some extensions and generalizations are also considered. I