Generalized Rack-aware Regenerating Codes for Jointly Optimal Node and Rack Repairs

In data centers, storage nodes are organized in racks and the cross-rack communication bandwidth is often much lower than the intra-rack communication bandwidth. Two common failures in data centers are single-node failures and single-rack failures. In this paper, we study the problem of minimizing the cross-rack repair bandwidth in both repairing single-node failures and repairing single-rack failures. We characterize, given that the minimum cross-rack repair bandwidth for single-node failures is achieved, the optimal trade-off between storage and cross-rack repair bandwidth for single-rack failures. We further propose a general family of storage codes, Generalized Rack-aware Regenerating Codes (GRRC), that achieve the optimal trade-off. We obtain two extreme points of GRRC, namely the minimum storage generalized rack-aware regeneration (MSGRR) point and the minimum bandwidth generalized rack-aware regeneration (MB-GRR) point. We show that MSGRR codes have strictly less cross-rack repair bandwidth for single-rack failures than the related minimum storage multi-node repair codes for most parameters. We also show that MBGRR codes have less cross-rack repair bandwidth for single-rack failures than the minimum bandwidth multi-node repair codes for all our evaluated parameters.