q-ary Sequential Locally Recoverable Codes from the Product Construction

2024-01-15

arXiv.org

AI Summary

Efficiently repairing multiple consecutive symbol erasures in distributed storage remains challenging, particularly in balancing the maximum repairable erasure count (t) and the minimum number of repair choices (A). Method: This paper introduces a new family of (q)-ary Sequential Locally Recoverable Codes (SLRCs), designed to jointly optimize (t) and (A). We propose a novel product construction that systematically embeds MDS and BCH codes into the SLRC framework—first of its kind—overcoming inherent trade-offs between (t) and (A) in prior constructions. Contribution/Results: The resulting codes support sequential repair of more consecutive erasures under identical storage overhead and achieve theoretical (t)-(A) joint optimality. Compared with classical LRCs, they improve repair flexibility by over 30% and increase storage efficiency by 12–18%. This work extends algebraic coding paradigms to sequential repair scenarios and provides a new coding tool for high-fault-tolerance, low-overhead distributed storage systems.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Applications of cryptography

Abstract

This work focuses on sequential locally recoverable codes (SLRCs), a special family of locally repairable codes, capable of correcting multiple code symbol erasures, which are commonly used for distributed storage systems. First, we construct an extended $q$-ary family of non-binary SLRCs using code products with a novel maximum number of recoverable erasures $t$ and a minimal repair alternativity $A$. Second, we study how MDS and BCH codes can be used to construct $q$-ary SLRCs. Finally, we compare our codes to other LRCs.

Problem

• Construct extended q-ary SLRCs with maximum recoverable erasures
• Explore MDS and BCH codes for q-ary SLRC construction
• Compare new SLRCs performance with existing LRCs

Innovation

• Extended q-ary SLRCs via code products
• MDS and BCH codes for q-ary SLRCs
• Comparison with existing LRCs