  The denoise-and-forward (DNF) method of physical-layer network coding (PNC)
is a promising approach for wireless relaying networks. In this paper, we
consider DNF-based PNC with M-ary quadrature amplitude modulation (M-QAM) and
propose a mapping scheme that maps the superposed M-QAM signal to coded
symbols. The mapping scheme supports both square and non-square M-QAM
modulations, with various original constellation mappings (e.g. binary-coded or
Gray-coded). Subsequently, we evaluate the symbol error rate and bit error rate
(BER) of M-QAM modulated PNC that uses the proposed mapping scheme. Afterwards,
as an application, a rate adaptation scheme for the DNF method of PNC is
proposed. Simulation results show that the rate-adaptive PNC is advantageous in
various scenarios.
