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
$n-k\geq 10$
.