Balanced Locally Repairable Codes

TL;DR

This paper introduces balanced locally repairable codes (BLRCs) with flexible repair locality, enabling construction for arbitrary parameters and improved robustness against double failures, addressing open problems in LRC design.

Contribution

The paper proposes a new family of BLRCs with relaxed locality constraints, allowing for arbitrary code parameters and enhanced fault tolerance, which advances the design of locally repairable codes.

Findings

BLRCs can be constructed for arbitrary n and k.

Relaxed locality improves robustness against double failures.

BLRCs show favorable metrics compared to existing LRCs.

Abstract

We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low repair locality. The novelty that we introduce in our construction is that we relax the strict requirement the repair locality to be a fixed small number $l$, and we allow the repair locality to be either $l$ or $l+1$. This gives us the flexibility to construct BLRCs for arbitrary values of $n$ and $k$ which partially solves the open problem of finding a general construction of LRCs. Additionally, the relaxed locality criteria gives us an opportunity to search for BLRCs that have a low repair locality even when double failures occur. We use metrics such as a storage overhead, an average repair bandwidth, a Mean Time To Data Loss (MTTDL) and an update complexity to compare the performance of BLRCs with existing LRCs.