Locally repairable convertible codes with optimal access costs

TL;DR

This paper studies code conversion in locally repairable codes (LRCs) for distributed storage, establishing lower bounds on access costs and proposing constructions that achieve these bounds with optimal efficiency.

Contribution

It introduces a lower bound on access costs for code conversion in LRCs and provides a construction that attains this bound with minimal access overhead.

Findings

Established a lower bound on access cost for LRC code conversion.

Proposed a general construction of LRCs matching the lower bound.

Achieved optimal code conversion with linear field size.

Abstract

Modern large-scale distributed storage systems use erasure codes to protect against node failures with low storage overhead. In practice, the failure rate and other factors of storage devices in the system may vary significantly over time, and leads to changes of the ideal code parameters. To maintain the storage efficiency, this requires the system to adjust parameters of the currently used codes. The changing process of code parameters on encoded data is called code conversion. As an important class of storage codes, locally repairable codes (LRCs) can repair any codeword symbol using a small number of other symbols. This feature makes LRCs highly efficient for addressing single node failures in the storage systems. In this paper, we investigate the code conversions for locally repairable codes in the merge regime. We establish a lower bound on the access cost of code conversion for general LRCs and propose a general construction of LRCs that can perform code conversions with access cost matching this bound. This construction provides a family of LRCs together with optimal conversion process over the field of size linear in the code length.