Physical-layer shaped network coding with M-PAM modulation

In this paper, we investigate the shaping loss in a two-user Gaussian multiple-access channel (MAC) with network coding. We conjecture that the shaping loss in this system model is much larger than 1.53 dB, verified by simulation results. To recover such large shaping loss, we consider the combination of physical-layer network coding with constellation shaping, and propose a physical-layer shaped network coding (PLSNC) scheme. Exploiting the constellation shaping, the proposed PLSNC scheme enables the network codeword to be shaped and the relay recovers the network codeword from the shaped network codeword instead of decoding individual node´s shaping bits. We thus investigate the design criteria for constructing a non-linear shaping code to avoid the ambiguous detection. The corresponding decoding algorithm of shaped network codeword is then presented to calculate the likelihood of the information about the transmitted shaped network codeword based on the bit-interleaved coded modulation (BICM) scheme. Furthermore, we derive the achievable rate of the proposed scheme. The simulation results show that the proposed scheme with 16-PAM can achieve a maximum shaping gain of 2.61 dB.