## 1 Introduction
In reference [10], [PERSON] and [PERSON] combined layered modulation with network code to achieve the spectral efficiency of the bidirectional relay channel through network coding and solve the asymmetry of the bidirectional relay channel through layered modulation technology. Finally, the end-to-end error probability and spectral efficiency of the asymmetric relay channel are significantly improved. In reference [11], [PERSON] and [PERSON] studied the proposed joint hierarchical modulation and physical-layer network coding (HM-PNC) scheme under the asymmetric additive Gaussian white noise (AWGN) bidirectional relay channel; it not only ensures the efficient transmission of the better-quality channel but also ensures the reliable transmission of the poor-quality channel. In reference [12], [PERSON] and [PERSON] designed a bit interleaved coded modulation (HMNC-BICM) scheme based on hierarchical modulation and network coding assistance. For coded modulation TWRC systems, this scheme has better performance in terms of average bit error rate. In reference [13], [PERSON] designed a physical-layer network coding (2/4 PSK-PNC) scheme using 2/4 PSK layered modulation under asymmetric channels, derived the BER performance of the relay and end-to-end under AWGN channels and Rayleigh fading channels, and used it to solve the performance degradation of the communication system. The above document applies the hierarchical modulation network coding scheme to the two-way relay channel; although the performance of the communication system is improved, there is still some room for improvement in its performance. Moreover, the hierarchical modulation, combined with the network coding scheme, is not applied to the free space optical communication system, and the performance improvement needs to be further studied. This paper, aiming at the asymmetric reception problem at the destination node, proposes a hierarchical modulation joint physical-layer network coding scheme to improve system performance. The scheme allocates different transmission power according to the relative importance of the information to be sent to ensure the high reliability of the data. This paper applies the scheme to the collaborative FSO communication system. The hierarchical modulation mode is used at the source node and the relay node, and the physical-layer network encoding method is used for the received information at the relay node. Finally, the original information is recovered at the destination node. According to the 4/16-QAM modulation method used in this scheme, the bit error rate and average channel capacity performance of the collaborative FSO communication system using the hierarchical modulation-combined physical-layer network coding scheme are analyzed. However, under the conditions of different signal transmission power, different turbulence intensity, and different channel average signal-to-noise ratios, the priority parameters of different constellations and the asymmetric parameters of channels are systematically simulated, and the simulation results show that this scheme is suitable for strong atmospheric turbulence channels and can solve the problem of bit error rate performance degradation caused by the asymmetry of the channel in collaborative FSO communication systems. It can also improve the average channel capacity of the system.