Set Transformation: Trade-Off Between Repair Bandwidth and Sub-Packetization

Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization level being one, however, they require large repair bandwidth defined as the total amount of symbols downloaded from other surviving nodes during single-node failure/repair. In this paper, we present the set transformation, which can transform any MDS code into set transformed code such that (i) the sub-packetization level is flexible and ranges from 2 to
$(n-k)^{\lfloor\frac{n}{n-k}\rfloor}$
in which
$n$
is the number of nodes and
$k$
is the number of data nodes, (ii) the new code is MDS code, (iii) the new code has lower repair bandwidth for any single-node failure. We show that our set transformed codes have both lower repair bandwidth and lower field size than the existing related MDS array codes, such as elastic transformed codes [1]. Specifically, our set transformed codes have 2% - 6.6% repair bandwidth reduction compared with elastic transformed codes [1] for the evaluated typical parameters.