Joint Design of Piggyback and Conjugate Transformation Functions for Repair Bandwidth Reduction in Piggybacking Codes

2026-05-05

AI Summary

This work addresses the high repair bandwidth in high-rate distributed storage systems, which leads to excessive network overhead and recovery costs. To mitigate this issue, the authors propose a novel MDS array code construction based on conjugate piggybacking. By jointly designing piggyback functions and conjugate transformations, the method overcomes the limitations of conventional piggybacking schemes on function design while preserving low sub-packetization and the MDS property. Under moderate field sizes (e.g., 𝔽₂⁸), the proposed scheme achieves optimal repair bandwidth for a subset of parity nodes and significantly reduces both total repair bandwidth and expected repair traffic, outperforming existing piggybacking approaches and traditional Reed–Solomon code repair strategies.

Abstract

Efficient node repair is a central requirement in distributed storage systems, particularly in high-rate erasure-coded deployments where repair traffic directly affects network overhead and recovery cost. Piggybacking codes reduce the repair bandwidth of MDS array codes while keeping the sub-packetization level small. However, existing piggybacking constructions often rely on restrictive piggyback-function designs to preserve the MDS property over small fields, which limits their repair-bandwidth reduction. We propose {\em conjugate-piggybacking} codes, a new class of MDS array codes that jointly design piggyback functions and conjugate transformations under small sub-packetization. The proposed construction improves repair efficiency while preserving the MDS property over moderate field sizes. In particular, it enables some parity nodes to achieve optimal repair bandwidth and reduces the overall repair bandwidth compared with existing piggybacking-based designs. We analyze the MDS property and repair bandwidth of the proposed codes and evaluate them against existing piggybacking codes under high-code-rate settings over $\mathbb{F}_{2^8}$. We further conduct a repair-traffic simulation under uniform single-node failures to quantify the expected traffic reduction in storage-oriented settings. The results show that our construction consistently achieves lower repair bandwidth than related piggybacking codes and reduces expected repair traffic compared with conventional RS repair. These gains are obtained at the cost of a slightly larger field size, revealing a practical trade-off between repair efficiency and field-size overhead for high-rate distributed storage.

Problem

• repair bandwidth
• piggybacking codes
• MDS array codes
• distributed storage
• sub-packetization

Innovation

• piggybacking codes
• repair bandwidth
• MDS array codes
• conjugate transformation
• sub-packetization