Locally Repairable Codes

One main challenge in the design of distributed storage codes is the {\it Exact Repair Problem}: if a node storing encoded information fails, to maintain the same level of reliability, we need to exactly regenerate what was lost in a new node. A major open problem in this area has been the design of codes that {\it i)} admit exact and low cost repair of nodes and {\it ii)} have arbitrarily high data rates. In this paper, we are interested in the metric of {\it repair locality}, which corresponds to the the number of disk accesses required during a node repair. Under this metric we characterize an information theoretic trade-off that binds together locality, code distance, and storage cost per node. We introduce {\it Locally repairable codes} (LRCs) which are shown to achieve this tradeoff. The achievability proof uses a "locality aware" flow graph gadget which leads to a randomized code construction. We then present the {\it first} explicit construction of LRCs that can achieve arbitrarily high data-rates.