Toward a Network Coding Constellation for Two-Way Relay Node Channels

In Physical-Layer Network Coding (PNC), the symbol detected at the relay node in two-way relay channels (TWRC) is the superposition of the symbols transmitted by the sinks. We refer to these symbols as pnc-symbols. In traditional modulation constellations such as Quadrature Amplitude Modulation (QAM) and Phase Shift Keying (PSK), the demodulator may fail to optimally identify pnc- symbols formed from pairs of central symmetrical symbols (CSS) because their superposition may yield to the same output point (i.e., to the same decision region) due to the presence of a central symmetry point. In order to avoid such ambiguity, we propose a non central symmetry constellation (CSC), called 4-TRAQAM, which is used by the sinks such that the decision regions of the output points are pair-wise disjoint.We show that the sinks in the PNC-based TWRC can be considered as a single transmitter using the same modulation as the real sinks with a higher order.We further derive the average energy of pnc- symbols and the error probability of the derived PNC-based TWRC modulation, and we show that the 4- TRAQAM provides the best trade-off between the average energy and the disjointness of the decision regions, compared to other used QAM.