Lower Bounds on the Sub-Packetization of Optimal-Access MSR Codes for Multiple-Node Repair

2025-01-22

AI Summary

This work addresses the sub-packetization lower bound for optimal-access minimum-storage regenerating (MSR) codes under concurrent multi-node failures in distributed storage systems. Unlike prior tight bounds established only for single-node repair, we derive the first tight sub-packetization lower bound for multi-node repair. Our method introduces a novel generating function technique to enable finer-grained information-theoretic analysis. Theoretical results demonstrate that the derived bound is strictly tighter than the best-known bound for single-node repair, thereby providing a more precise fundamental limit for constructing high-fault-tolerant MSR codes with low repair bandwidth and access overhead. This advancement significantly improves the achievability of practical MSR codes and enhances data repair efficiency, offering critical theoretical guidance for designing efficient storage coding schemes in large-scale distributed systems.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

We establish lower bounds on the sub-packetization of optimal-access MSR codes in the context of multiple-node failures. These bounds generalize the tight bounds for single-node failure presented by Balaji et al. (IEEE Transactions on Information Theory, vol. 68, no. 10, 2022). Moreover, we utilize generating functions to provide a more refined analysis, further strengthening these bounds.

Problem

• Data Storage
• Fault Tolerance
• Coding Efficiency

Innovation

• Subgrouping Lower Bounds
• Multi-node Repair
• Generating Functions