## 1 Introduction
### Related Work  
Currently, precoding technology in communication systems has been widely studied [16; 17; 18]. [PERSON] et al. [16] proposed a symbol-level precoding method that can be applied to a dual-functional radar-communication (DFRC). This scheme not only provided additional degrees of freedom (DoFs) but also ensured that the radar sensing obtains a better instantaneous transmission beam pattern. [PERSON] et al. [17] studied the issue of maximizing the energy efficiency (EE) of a multi-beam satellite system under total power constraints and service quality constraints, and proposed pre-programmed design schemes based on zero-forcing (ZF) and successive convex approximation (SCA), respectively. [PERSON] et al. [18] proposed a novel precoder based on exponential singular value decomposition for massive MIMO visible light communication (VLC), which reduces the condition number of the overall channel matrix and enhances the bit error rate (BER) performance of the system. Photon counting has been the subject of extensive research in recent years. In [11], the FSO MIMO communication problem under the Poisson photon-counting detection model was studied. Aiming at the goal of a high bit rate, [PERSON] et al. proposed a spatial multiplexing (SMux) scheme using multi-level pulse position modulation and conducted asymptotic performance analysis. [PERSON] et al. [12] developed a reliable symbol synchronization method based on pulse position modulation for underwater photon-counting communications, which can achieve time slot synchronization and frame synchronization, effectively reducing the BER of the system. [PERSON] et al. [19] proposed a precoder design for photon-counting ultraviolet (UV) MIMO systems that addresses the challenges of Poisson shot noise in signal processing. Simulation results show that the design can effectively combat atmospheric fading and mitigate multi-user (MU) interference. [PERSON] et al. [20] constructed a polarization multiplexing modulation underwater wireless optical communication (UWOC) model based on photon counting and theoretically analyzed the improvements in BER and communication capacity. As a promising emerging technology, IRSs not only provide higher link reliability and wider coverage at a lower cost but can also be potentially applied in MIMO FSO to modify channels in order to improve multiplexing gain [21; 22]. [PERSON] et al. [23] considered the downlink MU scenario and studied the problem of maximizing the dirty-paper-coding(DPC) sum rate of the IRS-assisted broadcast channel. In [24], the unique \"inter-element interference (IEI) free\" characteristic of the optical IRS reflection channel was revealed. Based on this analysis, [PERSON] et al. continued to study the capacity of optical IRS-assisted MIMO VLC under different transmitter antenna power constraints and jointly optimized the optical IRS element alignment and transmitter transmit power to maximize the capacity. Additionally, [PERSON] et al. [25] addressed the optimization problem of the IRS-assisted MIMO VLC communication system under the point source assumption, primarily focusing on the joint design of the IRS and transceiver signal processing to minimize the mean square error (MSE) of the system. In addition, [PERSON] et al. [26] also studied the adaptive channel estimator using a general arbitrarily shaped IRS to explore time-varying millimeter wave channels. They also proposed a deep learning network framework using fixed-point iteration and cascading to reduce the complexity of the solution. To the best of our knowledge, there is no research on applying optical IRS technology to photon-counting communication systems and even less work on the configuration optimization of optical IRS. Therefore, it is very meaningful to combine the research on signal processing technology for MU photon-counting communication systems with IRS configuration optimization to solve the non-line-of-sight (NLOS) transmission problem.