An Explicit Construction of Systematic MDS Codes with Small Sub-packetization for All-Node Repair

TL;DR

This paper introduces HashTag+ codes, a new explicit systematic MDS code construction with small sub-packetization levels that optimize repair bandwidth for all-node repair, reducing data access and transfer costs.

Contribution

It presents a novel explicit construction of HashTag+ codes with arbitrary sub-packetization, achieving optimal MSR points for all-node repair with improved efficiency.

Findings

HashTag+ codes achieve 20-40% savings in data accessed during repair.

They attain the optimal MSR point for parity node repair at small sub-packetization levels.

The repair bandwidth for systematic nodes depends on sub-packetization level.

Abstract

An explicit construction of systematic MDS codes, called HashTag+ codes, with arbitrary sub-packetization level for all-node repair is proposed. It is shown that even for small sub-packetization levels, HashTag+ codes achieve the optimal MSR point for repair of any parity node, while the repair bandwidth for a single systematic node depends on the sub-packetization level. Compared to other codes in the literature, HashTag+ codes provide from 20% to 40% savings in the average amount of data accessed and transferred during repair.