Bandwidth Cost of Locally Repairable Convertible Codes in the Global Merge Regime

2026-04-16

AI Summary

This work addresses the high bandwidth overhead associated with code rate conversion in locally repairable codes (LRCs) under global merge operations in distributed storage systems. It establishes, for the first time, a non-trivial information-theoretic lower bound on conversion bandwidth that does not rely on linearity assumptions. The paper proposes a stable convertible code design methodology that minimizes data migration costs by maximizing the number of unchanged nodes during conversion. By integrating LRC and convertible code theories, the authors derive a tight lower bound on LRC conversion bandwidth and demonstrate that the construction by Maturana and Rashmi achieves this bound across a broad range of parameters, thereby attaining bandwidth optimality.

Technology Category

• Machine Learning: Online Learning & Bandits
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Recent studies have shown that distributed storage systems can achieve significant space savings by adapting redundancy levels to varying disk failure rates. This adaptation is performed via code conversion, wherein data encoded under an initial code are transformed to data encoded under a final code. While this process is typically resource-intensive, convertible codes are designed to enable these transformations efficiently while preserving desirable decodability constraints such as repair degree, or the number of nodes accessed during node repair. In this work, we focus on the bandwidth cost of conversion, or the total amount of data transferred during the conversion process. We study fundamental limits on the bandwidth cost of conversion between systematic optimal-distance Locally Repairable Codes (LRCs). We restrict our focus to the global merge regime, in which multiple initial codewords are combined to form a single final codeword while preserving information locality. We focus on stable convertible codes, wherein the number of unchanged nodes is maximized during conversion. We generalize an information-theoretic approach for modeling code conversion to the LRC setting, and derive the first non-trivial lower bounds on the bandwidth cost of conversion in this regime. Notably, our bounds do not rely on any linearity assumptions. Consequently, we show that the constructions of Maturana and Rashmi are bandwidth-optimal across a broad range of parameters in the global merge regime.

Problem

• bandwidth cost
• locally repairable codes
• code conversion
• global merge regime
• distributed storage systems

Innovation

• Locally Repairable Codes
• Convertible Codes
• Bandwidth Cost
• Global Merge Regime
• Information Locality