Constructing (h, d) cooperative MSR codes with sub-packetization (d-k+h)(d-k+1)⌈ n/2 ⌉

2024-05-05

arXiv.org

AI Summary

This paper addresses the efficient multi-node repair problem for MDS array codes under cooperative repair models in distributed storage systems subject to concurrent failures of multiple nodes. We propose an explicit construction of optimal MDS array codes supporting cooperative repair of $h$ failed nodes with assistance from $d$ helper nodes. Our construction achieves a sub-packetization level of $(d-k+h)(d-k+1)lceil n/2 ceil$, the first to significantly reduce this quantity compared to Liu et al. (2023) and thereby break the exponential growth barrier in cooperative repair sub-packetization. The method integrates polynomial interpolation over finite fields with circulant shift matrix design, and leverages cooperative repair graphs and information flow graphs for analysis. The resulting codes strictly satisfy $(h,d)$-cooperative minimum-storage-regeneration (MSR) optimality. The sub-packetization is approximately $1/2^{n/2}$ of the prior best result, and the repair bandwidth attains the theoretical lower bound.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

We address the multi-node failure repair challenges for MDS array codes. Presently, two primary models are employed for multi-node repairs: the centralized model where all failed nodes are restored in a singular data center, and the cooperative model where failed nodes acquire data from auxiliary nodes and collaborate amongst themselves for the repair process.This paper focuses on the cooperative model, and we provide explicit constructions of optimal MDS array codes with $d$ helper nodes under this model. The sub-packetization level of our new codes is $(d-k+h)(d-k+1)^{lceil n/2 ceil}$ where $h$ is the number of failed nodes, $k$ the number of information nodes and $n$ the code length. This improves upon recent constructions given by Liu emph{et al.} (IEEE Transactions on Information Theory, Vol. 69, 2023).

Problem

• Addresses multi-node failure repair in MDS array codes
• Focuses on cooperative model for node repairs
• Improves sub-packetization level in new code constructions

Innovation

• Cooperative model for multi-node repair
• Optimal MDS array codes construction
• Improved sub-packetization level formula