Code constructions for multi-node exact repair in distributed storage

We study the problem of centralized exact repair of multiple failures in distributed storage. We present constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction by Tian et al., designed for exact repair of single failure. We firstly improve upon the layered construction for general system parameters. Then, we extend the improved construction to support the repair of multiple failures, with varying number of helpers. In particular, for some parameters, we prove the optimality of one point in terms of the storage size and the repair bandwidth for multiple erasures. Finally, considering minimum bandwidth cooperative repair (MBCR) codes as centralized repair codes, we determine explicitly the best achievable region obtained by space-sharing among all known points, including the MBCR point.