Tight Bandwidth Lower Bounds and Optimal Constructions of Locally Repairable Convertible Codes in the Global Split Regime

Haoming Shi; Weijun Fang

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arXiv · 2606.26742

Tight Bandwidth Lower Bounds and Optimal Constructions of Locally Repairable Convertible Codes in the Global Split Regime

Haoming Shi·Weijun Fang

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Abstract

Erasure coding is a key technique for providing fault tolerance in modern distributed storage systems. In practice, as storage systems evolve, the parameters of the deployed erasure code may need to be adjusted to accommodate changes in storage scale, reliability requirements, and disk failure rates. Such adaptation is achieved through code conversion, which transforms data encoded by an initial code into data encoded by a final code. Convertible codes are designed to carry out this transformation efficiently while preserving desirable code properties. In this work, we study code conversion between systematic optimal-distance locally repairable codes (LRCs) in the global split regime, using read bandwidth as the conversion-efficiency metric. Specifically, we focus on the parameter range $g^I,g^F \leq r$, where the numbers of initial and final global parity nodes are at most the local information dimension $r$. Over this entire parameter range, we derive lower bounds on the read bandwidth of stable optimal-distance locally repairable convertible codes (LRCCs) via an information-theoretic approach, without imposing any linearity assumption on the initial codes, the final codes, or the conversion procedure. We then develop constructions based on MDS array codes with prescribed repair or alignment properties. Depending on the relative sizes of $g^I$ and $g^F$, we handle the construction separately in the three cases $g^F=g^I$, $g^F>g^I$, and $g^F<g^I$, and show that each attains the corresponding lower bound. This yields a complete characterization of the optimal read bandwidth for stable optimal-distance LRCCs over the entire parameter range $g^I,g^F\le r$.

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BibTeX RIS

Haoming Shi, Weijun Fang. 2026-08-01. Tight Bandwidth Lower Bounds and Optimal Constructions of Locally Repairable Convertible Codes in the Global Split Regime. https://arxiv.org/abs/2606.26742

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