Optimal Busy-Node Repair of (k+4,k,4) MDS Codes With Small Sub-Packetization Level

IEEE Communications Letters(2023)

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Abstract
Maximum distance separable array codes with small sub-packetization level (MDS-SSL) are of practical importance in distributed storage systems. This letter addresses their repair of a single failed node in the case that there exists a busy node during the repair. Additional check relations among codeword symbols excluding those in the busy node are formed to compensate for the absence of information. Then, it allows us to repair the failed node without symbols in the busy node. A lower bound of the busy-node repair bandwidth is derived for $(k+4,k,4)$ MDS-SSL codes, consisting of four groups of nodes. It indicates that its achievability requires a cubic constraint among elements in the parity-check matrix. Then, an explicit busy-node repair scheme is proposed to achieve a lower bound in the case of the failed node and the busy node being in different groups.
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Key words
Distributed storage system,busy-node repair,optimal access,small sub-packetization,bandwidth
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