Bidirectional Piggybacking Design for All Nodes with Sub-Packetization l = r

Abstract

Piggybacking design has been applied extensively in distributed storage systems in recent years, since it can reduce repair bandwidth significantly with small sub-packetization. In this work, we propose a bidirectional piggybacking design (BPD) with sub-packetization l = r, where r = n − k equals the redundancy of an [n,k] linear code. Unlike most existing piggybacking designs, there is no distinction between systematic nodes and parity nodes in BPD and the piggybacks are added bidirectionally. Consequently, BPD leads to lower average repair bandwidth than previous piggybacking designs at equal subpacketization level when r ≥ 3. However, BPD needs larger fields to maintain the MDS property. We prove two upper bounds on the field size for explicit BPD and existential constructions respectively. By computer search, our BPD can be given over a field much smaller than the proved upper bounds. As an example, we provide the BPD for the [14], [10] Reed-Solomon (RS) code over F28 and obtain approximately 50% savings in the average repair bandwidth compared with the trivial repair approach. This is the lowest repair bandwidth achieved so far for [14], [10]256 RS codes with sub-packetization l ≤ 4.