Locally repairable codes

One main challenge in the design of distributed storage codes is the 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 i) admit exact and low cost repair of nodes and ii) have arbitrarily high data rates. In this paper, we are interested in the metric of 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 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 first explicit construction of LRCs that can achieve arbitrarily high data-rates.