Set Transformation: Trade-off Between Repair Bandwidth and Sub-packetization

TL;DR

This paper introduces set transformation, a method to convert MDS codes into variants with adjustable sub-packetization levels, reducing repair bandwidth and field size for storage systems.

Contribution

The set transformation technique allows flexible sub-packetization levels in MDS codes while decreasing repair bandwidth and field size compared to existing methods.

Findings

Achieves 2%-6.6% reduction in repair bandwidth.

Supports sub-packetization levels from 2 to (n-k)^{floor(n/(n-k))}.

Maintains MDS property after transformation.

Abstract

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 {\em 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 \cite{10228984}. Specifically, our set transformed codes have $2\%-6.6\%$ repair bandwidth reduction compared with elastic transformed codes \cite{10228984} for the evaluated typical parameters.