On the minimum storage overhead of distributed storage codes with a given repair locality

The repair locality of a storage code is the maximum number of nodes that may be contacted during the repair of a failed node. Having small repair locality is desirable since it is proportional to the number of disk accesses required during a node repair, which for certain applications seems to be the main bottleneck. However, recent publications show that small repair locality comes with a penalty in terms of code distance or storage overhead, at least if exact repair is required. Here, we first review some of the recent work on possible (information-theoretical) trade-offs between repair locality and other code parameters like storage overhead (or, equivalently, coding rate) and code distance, which all assume the exact repair regime. Then, we present some new information theoretical lower bounds on the storage overhead as a function of the repair locality, valid for most common coding and repair models.