Convertible Codes: MSR-to-MSR Conversion with Optimal Access and Bandwidth

2026-06-27

AI Summary

This work addresses the challenge of efficiently converting multiple source minimum storage regenerating (MSR) codes into a single target MSR code in distributed storage systems. It presents the first MSR-to-MSR convertible code construction that simultaneously achieves optimal access cost and conversion bandwidth across a broad range of parameters. By integrating convertible coding theory, MSR code design, and a novel row-matching technique, the proposed scheme handles both irregular and identical-code settings effectively: it attains optimal access cost in irregular scenarios and jointly optimizes access overhead and conversion bandwidth when source and target codes are identical. This approach significantly enhances code conversion efficiency while preserving the optimal single-node repair property inherent to MSR codes.

Abstract

In this paper, we study convertible codes in the merge regime and focus on the minimum storage regenerating (MSR) setting, where both the initial codes and the final code admit optimal single-node repair. We propose explicit MSR-to-MSR conversion schemes and analyze their performance in terms of access cost and conversion bandwidth. We first construct convertible MSR codes in the irregular setting, where the $m$ initial codes may have different parameters, achieving optimal access cost. We further consider the practically important same-code setting, where all initial codewords are drawn from the same MSR code. By introducing a row-matching technique, we obtain constructions simultaneously achieving optimal access cost and conversion bandwidth in most parameter regimes.

Problem

• convertible codes
• minimum storage regenerating (MSR)
• conversion bandwidth
• access cost
• code conversion

Innovation

• Convertible Codes
• Minimum Storage Regenerating (MSR)
• Optimal Access
• Conversion Bandwidth
• Row-Matching Technique