Fractional repetition codes for repair in distributed storage systems

We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the concatenation of two components: an outer MDS code followed by an inner repetition code. We refer to the inner code as a Fractional Repetition code since it consists of splitting the data of each node into several packets and storing multiple replicas of each on different nodes in the system. Our model for repair is table-based, and thus, differs from the random access model adopted in the literature. We present constructions of Fractional Repetition codes based on regular graphs and Steiner systems for a large set of system parameters. The resulting codes are guaranteed to achieve the storage capacity for random access repair. The considered model motivates a new definition of capacity for distributed storage systems, that we call Fractional Repetition capacity. We provide upper bounds on this capacity, while a precise expression remains an open problem.