Explicit Constructions of Rack-Aware Regenerating Codes for Multi-Node Failures

In data centers, storage nodes are typically organized in racks and rack-aware regenerating codes (RRCs) can achieve the optimal trade-off between storage capacity and cross-rack repair bandwidth. In this paper, we present explicit constructions for multiple erasure tolerance of rack-aware regenerating codes (MET-RRCs), i.e., RRCs with optimal cross-rack repair bandwidth for multi-node failures. We refine the MET-RRC framework in [2] under more extensive parameters and extend the existing construction methods of RRCs. Specifically, we leverage the parity-check matrix structure to present a general framework for multiple erasure tolerance of minimum storage rack-aware regenerating (MET-MSRR) codes. The existing parity-check matrix construction of MSRR codes can be elucidated with this framework. Moreover, we present the construction for multiple erasure tolerance of minimum bandwidth rack-aware regenerating (MET-MBRR) codes using the product-matrix framework.