Bandwidth Cost of Locally Repairable Convertible Codes in the Global Merge Regime
2026-04-16 • Information Theory
Information Theory
AI summaryⓘ
The authors study how to efficiently change stored data in distributed systems when switching between different error-correcting codes, focusing on the data transfer needed during this change. They look at special codes called Locally Repairable Codes (LRCs) that make fixing broken storage parts easier. By analyzing how multiple old codewords merge into one new codeword without losing repair benefits, they find fundamental limits on the minimum data transfer needed for this conversion. Their results improve understanding of the efficiency of these code changes without assuming simple code structures and confirm that some known code designs are already optimal in this sense.
Distributed storage systemsRedundancy adaptationCode conversionLocally Repairable Codes (LRCs)Bandwidth costInformation localitySystematic codesError correctionCodeword mergingRepair degree
Authors
Saransh Chopra, Shubhransh Singhvi, K. V. Rashmi
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.