PMDS Array Codes With Small Sub-packetization Level and Small Repair Bandwidth

Partial maximum distance separable (PMDS) codes are a kind of erasure codes where the storage nodes are divided into multiple groups with each forming an MDS code of a smaller code length. They allow repairing a failed node by contacting only a few helper nodes and can correct all erasure patterns which are information-theoretically correctable. However, the repair of a failed node of PMDS codes still requires a large amount of communication if the group size is large. Recently, PMDS array codes with each local code being an MSR code were introduced to further reduce the repair bandwidth, but codes over small finite fields only exist for two global parities, and require large rebuilding access and unavoidably a large sub-packetization level. In this paper, we propose two constructions of PMDS array codes with two and three global parities, respectively. Both have a small sub-packetization level, small repair bandwidth, and much smaller finite fields than existing ones.