On Rack-Aware Cooperative Regenerating Codes and Epsilon-MSCR Codes

In distributed storage systems, cooperative regenerating codes tradeoff storage for repair bandwidth in the case of multiple node failures. In rack-aware distributed storage systems, there is no cost associated with transferring symbols within a rack. Hence, the repair bandwidth will only take into account cross-rack transfer. Rack-aware regenerating codes for the case of single node failures have been studied and their repair bandwidth tradeoff characterized. In this paper, we consider the framework of rack-aware cooperative regenerating codes for the case of multiple node failures where the node failures are uniformly distributed among a certain number of racks. We characterize the storage repair-bandwidth tradeoff as well as derive the minimum storage and minimum repair bandwidth points of the tradeoff. We also provide explicit constructions of minimum bandwidth rack-aware cooperative regenerating codes and minimum storage rack-aware cooperative regenerating codes for a large range of parameters. We also consider another extension of minimum storage cooperative regenerating codes, in which we design slightly sub-optimal cooperative regenerating codes with much lower sub-packetization. $\epsilon $ -MSR codes are a class of codes introduced to tradeoff sub-packetization level for a slight increase in the repair bandwidth for the case of single node failures. We introduce the framework of $\epsilon $ -MSCR codes which allow for a similar tradeoff for the case of multiple node failures. We present a construction of $\epsilon $ -MSCR codes, which can recover from two node failures, by concatenating a class of MSCR codes and scalar linear codes. We give a repair procedure to repair the $\epsilon $ -MSCR codes in the event of two node failures and calculate the repair bandwidth for the same. We characterize the increase in repair bandwidth incurred by the method in comparison with the optimal repair bandwidth. Finally, we show the subpacketization level of $\epsilon $ -MSCR codes scales logarithmically in the number of nodes.