An Efficient Piggybacking Design with Lower Repair Bandwidth and Lower Sub-packetization

Piggybacking is a class of coding framework for MDS array codes that can achieve small repair bandwidth with small sub-packetization. An ( $n, k, \alpha$ ) piggybacking code can be represented by an $n\times \alpha$ array such that each node (row) stores $\alpha$ symbols and any $k$ rows can retrieve all $k\alpha$ data symbols. In this paper, we first propose a new piggybacking framework for MDS array codes with lower sub-packetization and then propose two specific piggybacking codes based on the proposed framework. We show that the average repair bandwidth of any single-node failure of our piggybacking codes is lower than all the existing piggybacking codes with the same parameters when the sub-packetization is small (usually $\alpha\leq 8$ ) and $n-k\geq 10$ .