On storage codes allowing partially collaborative repairs

We consider the design of codes for distributed storage systems that are amenable to repair. We introduce the notion of partial collaboration to capture the property that nodes participating in a repair process may collaborate to different extents, bringing more nuances to the known cases: no collaboration or full collaboration during repair. We compute for this scenario the storage (per node) when the repair bandwidth (per node) is minimal, and conversely the repair bandwidth when the storage is minimal. We provide a generic code construction that enables repair of several failures through partial collaboration.