On the energy efficiency of HARQ-IR protocols for wireless network-coded butterfly networks

In this paper, we investigate the energy-delay tradeoff (EDT) of data transmissions in wireless butterfly networks consisting of two source nodes, a relay node and two destination nodes. Two network coding (NC) techniques, namely physical-layer NC (PLNC) and analog NC (ANC), are exploited to reduce the number of transmissions at the relay by half. Additionally, hybrid automatic repeat request with incremental redundancy (HARQ-IR) is applied to assure the reliability of data transmissions in wireless network-coded butterfly networks (WNCBNs). By deriving the EDT of both PLNC and ANC schemes in WNCBNs, we evaluate not only their energy efficiency, but also the effectiveness of the relay positions in WNCBNs. It is found that the PLNC scheme is more energy efficient than both the ANC and direct transmission (DT) schemes when the relay is located either at the centre or close to the destinations. In addition, it is shown that both the PLNC and ANC schemes are shown to be less energy efficient than the DT scheme when the relay is located near the sources.