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Abundant high-rate (n, k) minimum storage regenerating (MSR) codes have beenreported in the literature. However, most of them require contacting all thesurviving nodes during a node repair process, resulting in a repair degree ofd=n-1. In practical systems, it may not always be feasible to connect anddownload data from all surviving nodes, as some nodes may be unavailable.Therefore, there is a need for MSR code constructions with a repair degree ofd<n-1. Up to now, only a few (n, k) MSR code constructions with repair degreed<n-1 have been reported, some have a large sub-packetization level, a largefinite field, or restrictions on the repair degree d. In this paper, we proposea new (n, k) MSR code construction that works for any repair degree d>k, andhas a smaller sub-packetization level or finite field than some existingconstructions. Additionally, in conjunction with a previous generictransformation to reduce the sub-packetization level, we obtain an MDS arraycode with a small sub-packetization level and $(1+\epsilon)$-optimal repairbandwidth (i.e., $(1+\epsilon)$ times the optimal repair bandwidth) for repairdegree d=n-1. This code outperforms some existing ones in terms of either thesub-packetization level or the field size.

MDS Array Codes With (Near) Optimal Repair Bandwidth for All Admissible Repair Degrees