On network coding and modulation mapping for three-phase bidirectional relaying

In this paper, we consider the network coding (NC) enabled three-phase protocol for information exchange between two users in a wireless two-way (bidirectional) relay network. Modulo-based (nonbinary) and XOR-based (binary) NC schemes are considered as information mixture schemes at the relay while all transmissions adopt pulse amplitude modulation (PAM). We first obtain the optimal constellation mapping at the relay that maximizes the decoding performance at the users for each NC scheme. Then, we compare the two NC schemes, each in conjunction with the optimal constellation mapping at the relay, in different conditions. Our results demonstrate that, in the low SNR regime, binary NC outperforms nonbinary NC with 4-PAM, while they have mixed performance with 8-PAM. This observation applies to quadrature amplitude modulation (QAM) composed of two parallel PAMs.