Piggybacking+ Codes: MDS Array Codes with Linear Sub- Packetization to Achieve Lower Repair Bandwidth.

Piggybacking codes are a class of maximum distance separable (MDS) array codes that can achieve repair bandwidth reduction of single-node failure by adding some piggyback functions in a subset of parity symbols. However, the repair bandwidth reduction is limited since the number of parity symbols of which the piggyback function can be added should be strictly less than a value in order to maintain the MDS property. In this paper, we present a new class of MDS array codes, call piggybacking+ codes with linear sub-packetization level and small finite field that can achieve lower repair bandwidth compared with the existing piggybacking codes. We show that our piggybacking+ codes have 3% to 29% repair bandwidth reduction of the existing piggybacking codes for the evaluated high -code- rate parameters. Our main idea is that we design piggyback functions for data node repair and transformation functions for parity node repair such that the number of parity symbols which can add piggyback function or transformation function is larger than that of the existing piggybacking codes.