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, the authors 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 admit exact and low cost repair of nodes and have arbitrarily high data rates. In this paper, they are interested in the metric of repair locality, which corresponds to the number of disk accesses required during a node repair. Under this metric they characterize an information theoretic trade-off that binds together locality, code distance, and storage cost per node.