Minimum Storage Rack-Aware Regenerating Codes with Exact Repair and Small Sub-Packetization

Modern data centers often organize storage nodes in racks, in which the cross-rack communication cost is typically much higher than the intra-rack communication cost. Rack-aware regenerating codes have recently been proposed to achieve the optimal trade-off between storage redundancy and cross-rack repair bandwidth, subject to the condition that the original data can be reconstructed from a sufficient number of any non-failed nodes. In this paper, we present a coding framework that transforms any minimum-storage regenerating (MSR) code to a minimum-storage rack-aware regenerating (MSRR) code, such that the cross-rack repair bandwidth is minimized subject to the minimum storage redundancy. To this end, we can construct a family of exact-repair constructions for the MSRR codes for all admissible parameters. Furthermore, our constructions achieve low sub-packetization, which is critical for mitigating the I/O overhead during repair.