Generalized Simple Regenerating Codes: Trading Sub-packetization and Fault Tolerance

TL;DR

This paper introduces generalized simple regenerating codes (GSRCs) that expand parameter options, balancing sub-packetization and fault tolerance, with improved repair bandwidth and local repair capabilities over existing codes.

Contribution

The paper proposes GSRCs supporting more parameters than SRCs, establishing a trade-off between sub-packetization and fault tolerance, and demonstrating enhanced repair efficiency and local repair features.

Findings

Fault tolerance increases linearly with sub-packetization.

GSRCs can locally repair any single-symbol or single-node erasure.

Repair bandwidth is smaller than existing related codes.

Abstract

Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve both smaller repair bandwidth and smaller repair locality than traditional MDS codes in repairing single-node erasure. In this paper, we propose {\em generalized simple regenerating codes} (GSRCs) that can support much more parameters than that of SRCs. We show that there is a trade-off between sub-packetization and fault tolerance in our GSRCs, and SRCs achieve a special point of the trade-off of GSRCs. We show that the fault tolerance of our GSRCs increases when the sub-packetization increases linearly. We also show that our GSRCs can locally repair any singe-symbol erasure and any single-node erasure, and the repair bandwidth of our GSRCs is smaller than that of the existing related codes.