Optimal Locally Repairable Codes with Improved Update Complexity

TL;DR

This paper investigates the update complexity of optimal locally repairable codes (LRCs) in distributed storage, establishing bounds and proposing new codes that improve update efficiency without losing optimality.

Contribution

It provides bounds on update complexity for optimal LRCs and introduces a new class of codes with reduced update complexity while maintaining optimal parameters.

Findings

Established bounds on update complexity for optimal LRCs.

Proposed a new class of optimal LRCs with lower update complexity.

Demonstrated that the new codes do not sacrifice optimality.

Abstract

For a systematic erasure code, update complexity (UC) is defined as the maximum number of parity blocks needed to be changed when some information blocks are updated. Locally repairable codes (LRCs) have been recently proposed and used in real-world distributed storage systems. In this paper, update complexity for optimal LRC is studied and both lower and upper bounds on UC are established in terms of length (n), dimension (k), minimum distance (d), and locality (r) of the code, when (r+1)|n. Furthermore, a class of optimal LRCs with small UC is proposed. Our proposed LRCs could be of interest as they improve UC without sacrificing optimality of the code.