Bidirectional Piggybacking Design for Systematic Nodes with Sub-Packetization $l=2$

TL;DR

This work addresses repair bandwidth in MDS array codes used for distributed storage by introducing a Bidirectional Piggybacking Design (BPD) with sub-packetization $l=2$. The authors provide a explicit construction over $\mathbb{F}_q$ with $q=O\big(n^{\lfloor r/2\rfloor+1}\big)$, prove the MDS property via a polynomial-based argument leveraging a minimal polynomial degree bound, and demonstrate concrete gains in average repair bandwidth for systematic nodes, including a Reed-Solomon example $(14,10)$ over $\mathbb{F}_{2^8}$ with about $41\%$ savings. They also show practical RS repair feasibility for small redundancy ($r\le 4$) using a subfield $\mathbb{E}=\mathbb{F}_{2^4}$ and discuss field-size trade-offs against prior approaches such as HashTag Erasure Codes. Overall, BPD offers substantial bandwidth reductions for $l=2$ at the expense of larger field sizes, with explicit constructions and performance benchmarks guiding deployment considerations.

Abstract

In 2013, Rashmi et al. proposed the piggybacking design framework to reduce the repair bandwidth of $(n,k;l)$ MDS array codes with small sub-packetization $l$ and it has been studied extensively in recent years. In this work, we propose an explicit bidirectional piggybacking design (BPD) with sub-packetization $l=2$ and the field size $q=O(n^{\lfloor r/2 \rfloor \!+\!1})$ for systematic nodes, where $r=n-k$ equals the redundancy of an $(n,k)$ linear code. And BPD has lower average repair bandwidth than previous piggybacking designs for $l=2$ when $r\geq 3$. Surprisingly, we can prove that the field size $q\leq 256$ is sufficient when $n\leq 15$ and $n-k\leq 4$. For example, we provide the BPD for the $(14,10)$ Reed-Solomon (RS) code over $\mathbb{F}_{2^8}$ and obtain approximately $41\%$ savings in the average repair bandwidth for systematic nodes compared with the trivial repair approach. This is the lowest repair bandwidth achieved so far for $(14,10)_{256}$ RS codes with sub-packetization $l=2$.

Figures (2)

• Figure 1: The bidirectional piggybacking design
• Figure 2: A $(9,6;2)$ BPD code

Theorems & Definitions (16)

• Example 1
• Theorem 1
• proof
• Example 2
• Theorem 2
• Lemma 3
• proof
• Lemma 4
• proof
• Claim 5