Rack-Aware MSR Codes With Error Correction Capability for Multiple Erasure Tolerance

The minimum storage rack-aware regenerating (MSRR) code is a variation of regenerating codes that achieves the optimal repair bandwidth for a single node failure in the rack-aware model. Some explicit constructions of MSRR codes for all parameters to repair a single failed node have been reported. This paper studies MSRR codes with error-correcting capability for multiple erasure tolerance. First, we propose a general repair model of maximum distance separable (MDS) codes with error-correcting capability for multiple erasure tolerance and derive lower bounds on the number of symbols downloaded and accessed, respectively from helper racks for the purpose of correction and repair. Then, we construct a class of MDS array codes and scalar Reed-Solomon (RS) codes with the optimal repair bandwidth and error resilient capability for multiple node failures. Further, our codes are shown to have the low-access property. In particular, they have the optimal access property for repairing u failed nodes when the dimension of the code is divisible by the rack size u.