An Efficient Piggybacking Design Framework with Sub-packetization $l\le r$ for All-Node Repair

Piggybacking design has been widely applied in distributed storage systems since it can greatly reduce the repair bandwidth with small sub-packetization. Compared with other existing erasure codes, piggybacking is more convenient to operate and the I/O cost is lower. In this paper, we propose a new efficient design which can further reduce the repair bandwidth with the sub-packetization $l\le r$ where $r = n-k$. Generally, we let $l\le 8$. Compared with other analogous designs, our design has lower $l$ and the value of $l$ is more flexible. Moreover, our design can repair all nodes with small repair bandwidth. Therefore our piggybacking design is more feasible.