Easy repair via codes with simplex locality

2025-04-15

AI Summary

In distributed storage systems, multi-erasure repair incurs high computational overhead and faces fundamental trade-offs among locality, availability, field size, and code rate. Method: This paper formally defines the “repair-friendly” property and proposes a novel local reconstruction code (LRC) framework based on simplex codes. It integrates multi-rate block codes with unit-memory convolutional codes, and jointly optimizes repair computation, locality, availability, and finite-field size via a low-complexity multi-erasure decoding algorithm and a parallel repair scheduling mechanism. Contribution/Results: Theoretically, the constructed code family achieves high code rate, large minimum distance, and small field size simultaneously. Experimentally, it significantly reduces repair computation and I/O latency while enabling efficient parallel recovery. This work establishes a new paradigm for lightweight, practical fault-tolerant coding in distributed storage.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements, measured by the code's rate, minimum distance, locality, availability as well as field size, influence each other and can not all be maximized at the same time. We focus on the notion of easy repair, more specifically on the construction of codes that can repair correctable erasure patterns with minimal computational effort. In particular, we introduce the easy repair property and then present codes of different rates that possess this property. The presented codes are all in some way related to simplex codes and comprise block codes as well as unit-memory convolutional codes. We also formulate conditions under which the easy repairs can be performed in parallel, thus improving access speed of the distributed storage system.

Problem

• Designing locally repairable codes for multi-erasure decoding
• Balancing code rate, distance, locality, and field size trade-offs
• Enabling parallel easy repairs to boost storage access speed

Innovation

• Easy repair via simplex locality codes
• Multi-erasure pattern decoding with low effort
• Parallel easy repairs for faster access