Conjugate-Piggybacking Codes: MDS Array Codes with Lower Repair Bandwidth over Small Field Size

As maximum distance separable (MDS) array codes, piggybacking codes can effectively reduce the repair bandwidth of traditional MDS codes for single-node failure with small sub-packetization. However, the requirement of maintaining MDS property over small field size imposes severe restrictions on the design of piggyback functions in the piggybacking framework, which limits the reduction of repair bandwidth. In this paper, we propose conjugate-piggybacking codes over a small sub-packetization level. We design conjugate transformation for piggyback functions in our codes, which enables some parity nodes to achieve optimal repair bandwidth. We show that our codes are MDS codes over a slightly larger field size than the existing related piggybacking codes. We also show that our codes have lower repair bandwidth than the existing related piggybacking codes under evaluated high-code-rate parameters and $\mathbb{F}_{2^{8}}$.