Piggybacking+ Codes: MDS Array Codes over Small Fields 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 erasure by adding some piggyback functions to a subset of parity symbols. However, the repair bandwidth reduction is limited since the number of parity symbols the piggyback function can be added should be strictly less than a value to maintain the MDS property. In this paper, we first propose a new transformation on parity nodes that can effectively reduce the repair bandwidth of parity nodes, and the MDS property can still be maintained without changing the field size of the base code. Combined with the new transformation, we jointly design piggyback functions to reduce the repair bandwidth of data nodes. Since the new transformation no longer obeys the constraints under the piggybacking framework, we call the newly obtained codes as piggybacking+ codes. We theoretically show that the repair bandwidth of the piggybacking+ code is strictly lower than that of the existing piggybacking codes at high-code-rate parameters. We also show that our piggybacking+ codes have 3% to 29% repair bandwidth reduction than the existing piggybacking codes for the evaluated high-code-rate parameters.