A Generic Transformation to Enable Optimal Repair/Access MDS Array Codes With Multiple Repair Degrees

In the literature, most of the known high-rate $(n,k)$ MDS array codes with the optimal repair property only support a single repair degree (i.e., the number of helper nodes contacted during a repair process) $d$ , where $k\le d\le n-1$ . However, in practical storage systems, the number of available nodes changes frequently. Thus, it is preferred to construct $(n,k)$ MDS array codes with multiple repair degrees and the optimal repair property for all nodes. To the best of our knowledge, only two high-rate MDS array codes have such properties in the literature, which were proposed by Ye and Barg (IEEE Trans. Inform. Theory, 63(10), 2001–2014, 2017). However, their sub-packetization levels are relatively large. In this paper, we present a generic construction method that can convert some MDS array codes with a single repair degree into ones with multiple repair degrees and optimal repair property for a set of nodes, while the repair efficiency/degrees of the remaining nodes can be kept. As an application of the generic construction method, an explicit construction of high-rate MDS array code with multiple repair degrees and the optimal access property for all nodes is obtained over a small finite field by choosing the code proposed by Vajha et al. as the base code. Especially, the sub-packetization level is much smaller than that of the two codes proposed by Ye and Barg concerning the same parameters $n$ and $k$ .