Asymptotically Optimal Repair of Reed-Solomon Codes with Small Sub-Packetization under Rack-Aware Model

TL;DR

This paper introduces a novel repair scheme for Reed-Solomon codes in rack-aware storage systems that achieves asymptotically optimal bandwidth with reduced sub-packetization, improving efficiency over existing methods.

Contribution

It proposes a new approach using multi-base expansion and monomials for linear repair schemes, achieving optimal repair bandwidth with smaller sub-packetization in rack-aware models.

Findings

Achieves asymptotically optimal repair bandwidth.

Reduces sub-packetization compared to existing schemes.

Applicable to homogeneous storage models with improved efficiency.

Abstract

This paper presents a comprehensive study on the asymptotically optimal repair of Reed-Solomon (RS) codes with small sub-packetization, specifically tailored for rack-aware distributed storage systems. Through the utilization of multi-base expansion, we introduce a novel approach that leverages monomials to construct linear repair schemes for RS codes. Our repair schemes which adapt to all admissible parameters achieve asymptotically optimal repair bandwidth while significantly reducing the sub-packetization compared with existing schemes. Furthermore, our approach is capable of repairing RS codes with asymptotically optimal repair bandwidth under the homogeneous storage model, achieving smaller sub-packetization than existing methods.