Towards Efficient Repair and Coding of Binary MDS Array Codes with Small Sub-packetization

Large-scale high code-rate maximum distance separable (MDS) codes are critical and important in distributed storage systems that can provide high fault tolerance with extremely small storage redundancy. Repair access (defined as the total amount of symbols accessed in repairing one single-node failure) is a key metric of designing MDS codes. In large-scale MDS codes, one single-node failure can be recovered by connecting a large number of helper nodes. However, one or more helper nodes may be busy and can not send symbols during the repair process. In this paper, we define the total amount of symbols accessed in repairing one single-node failure with one or more busy nodes as the repair access with busy-node. We then propose a class of MDS array codes over a well-designed binary cyclic ring that is with small sub-packetization, small repair access, small repair access with busy-node, and small encoding complexity.