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High-rate minimum storage regenerating (MSR) codes are known to require alarge sub-packetization level, which can make meta-data management difficultand hinder implementation in practical systems. A few maximum distanceseparable (MDS) array code constructions have been proposed to attain a muchsmaller sub-packetization level by sacrificing a bit of repair bandwidth.However, to the best of our knowledge, only one construction by Guruswami etal. can support the repair of a failed node without contacting all thesurviving nodes. This construction is certainly of theoretical interest but notyet practical due to its requirement for very large code parameters. In thispaper, we propose a generic transformation that can convert any $(\overline{n},\overline{k})$ MSR code with a repair degree of $\overline{d}<\overline{n}-1$into another $(n=s\overline{n},k)$ MDS array code that supports $d<n-1$ with asmall sub-packetization level and $(1+\epsilon)$-optimal repair bandwidth(i.e., $1+\epsilon$ times the optimal value) under a specific condition. Weobtain three MDS array codes with small sub-packetization levels and$(1+\epsilon)$-optimal repair bandwidth by applying this transformation tothree known MSR codes. All the new MDS array codes have a small repair degreeof $d<n-1$ and work for both small and large code parameters.

MDS Array Codes With Small Sub-packetization Levels and Small Repair Degrees