Bidirectional Piggybacking Design for All Nodes With Sub-Packetization 2 ≤ l ≤ r

Piggybacking design has been applied extensively in distributed storage systems in recent years, since it can reduce repair bandwidth significantly with small sub-packetization. In this work, a bidirectional piggybacking design (BPD) is proposed with sub-packetization
$2\leq l\leq r$
, where
$r=n-k$
equals the redundancy of an
$[n,k]$
linear code. Unlike most existing piggybacking designs, there is no distinction between systematic nodes and parity nodes in BPD and the piggybacks are added bidirectionally. Consequently, BPD leads to lower average repair bandwidth than previous piggybacking designs at the equal sub-packetization level. However, BPD needs larger fields to maintain the MDS property. We prove two upper bounds on the field size for explicit BPD and existential constructions, respectively. By computer search, specific BPD can be given over a field much smaller than the proved upper bounds. As examples, BPD codes with sub-packetization
$l=4$
based on the
$[{12,8}]$
and
$[{14,10}]$
Reed-Solomon codes are given over
$\mathbb {F}_{2^{8}}$
, which obtain about 16% savings in the average repair bandwidth over previous designs with
$l\leq 4$
.