Local erasure correction codes with unequal locality profile

When a node of a distributed storage system fails, it needs to be repaired quickly enough to maintain system integrity. While typical erasure codes can provide significant storage advantage over replication, they suffer from poor repair efficiency. Locally repairable codes (LRCs) tackle this issue by reducing the number of nodes participating in the repair process (locality), at the cost of reduced minimum distance. In this paper, we study the tradeoff characteristics between locality and minimum distance for LRCs, where the local codes have an arbitrary distance requirement. In our study, different from previous approaches, the localities specified are not necessarily the same for every symbol. Such property can be advantageous for distributed storage systems with non-homogeneous characteristics. We present a new Singleton-type minimum distance upper bound and also provide an optimal code construction with respect to this bound.