Low-repair array codes based on nested structures

To address the problem of low repair efficiency of single- and double-disk of localized horizontal array code, this paper retains the original advantages of horizontal array code, transforms it on the basis of RDP 2D array code, and proposes a 2D array code model based on nested structure - NRDP (Nested Rows Diagonal Parity Code). The overall layout of the NRDP code is the same as that of the RDP code. However, when deploying data columns, the NRDP code deploys the RDP code of one prime number level smaller as a whole in the data columns of the NRDP code, forming a nested relationship. The increased redundant data reduce the repair overhead and error recovery time. Through theoretical analysis, NRDP has good compiled code complexity, improves the problem of uneven reading and writing during disk repair, and reduces the total amount of data that needs to be read during single- and double-disk failures, improving the success rate of single- and double-disk repair. The experimental results show that compared with RDP, LRRDP, and DRDP, NRDP can save $7.03 \%-\mathbf{3 0. 0 1 \%}$ of the single-disk failure repair time and $14.79 \%-26.51 \%$ of the dual-disk repair time.