2025/06/23 by Zhao, Hengming, Wu, Dianhua, Cheng, Minquan
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2506.18367
In an (n,k,d) rack-aware storage model, the system consists of n nodes uniformly distributed across n successive racks, such that each rack contains u nodes of equal capacity and the reconstructive degree satisfies k=ku+v where 0≤ v≤ u-1. Suppose there are h≥1 failed nodes in a rack (called the host rack). Then together with its surviving nodes, the host rack downloads recovery data from d helper racks and repairs its failed nodes. In this paper, we focus on studying the rack-aware minimum storage generating (MSR) codes for repairing h failed nodes within the same rack. By using the coupled-layer construction with the alignment technique, we construct the first class of rack-aware MSR codes for all k+1≤d≤n-1 which achieve the small sub-packetization l=s^\lceiln/s\rceil where the field size q increases linearly with n and s=d-k+1. In addition, these codes achieve optimal repair bandwidth for 1≤ h≤ u-v, and asymptotically optimal repair bandwidth for u-v+1≤ h≤ u. In particular, they achieve optimal access when h=u-v. It is worth noting that the existing rack-aware MSR codes which achieve the same sub-packetization l=s^\lceiln/s\rceil are only known for the special case of d=n-1, h=1, and the field size is much larger than ours. Then, based on our first construction we further develop another class of explicit rack-aware MSR codes with even smaller sub-packetization l=s^\lceiln/(s+1)\rceil for all admissible values of d.