## 5 Conclusions  
In this paper, we analyzed the performance of the 32-PPM photon-counting communication system under specific water conditions and designed an experimental setup combining the blue CW laser modulated by 32-PPM and a photon-counting module with an average dead time of 18.26 ns. The attenuation coefficient in this experiment was \(c=0.51\) m\({}^{-1}\), which was close to that of the Jerlov II water (\(c=0.528\) m\({}^{-1}\)). The total link loss can reach 80.72 dB. The communication link for a 35.64 m distance was achieved based on the Monte Carlo simulation results shown in Figure 6b. The attenuation length (AL = \(c\times z\)) was 18.82 and the equivalent link distances are 855.36 m (Jerlov I water) and 672.14 m (Jerlov IB water). To reduce the influence of the multipath effect and background light, we limited the initial light divergence angle and field-of-view (FOV) to 286 \(\upmu\)rad and 100 mrad, respectively. The experimental results revealed that the photon-counting communication system can achieve a communication rate of 1.9 Mbps at a signal-to-noise ratio of 0.1 dB. The mean number of experimentally received photon counts in a signal slot was 1.72, with one signal pulse representing 5 bits of information for a 32-PPM system. Therefore, the photon-counting receiver described in this paper can achieve a receiving sensitivity of 0.34 photons/bit. To the best of our knowledge, this is the lowest receiving sensitivity ever reported at a communication rate of 1.9 Mbps and 0.1 dB of SNR. It should be noted that the optical quantum efficiency of the photon-counting module used in this paper was 10%, and if the quantum efficiency of the detector could be increased, this photon-counting communication system would achieve greater link loss.  
In future work, signal processing technology to reject background noise will be investigated. In addition, the highly accurate system of underwater narrow laser pointing and tracking will also be the focus of research.  
[PERSON] contributed to the conception and organized the manuscript of the study; [PERSON] and [PERSON]. ([PERSON]) performed the experiment; [PERSON] and [PERSON] contributed significantly to analysis and manuscript preparation; [PERSON] and [PERSON] helped perform the analysis with constructive discussions. [PERSON]. ([PERSON]) and [PERSON] revised the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Key R&D Program, grant number 2021 YFC2800504 and National Key R&D Program, grant number 2022 YFC2806000.  
The study did not require ethical approval.  
The study did not involve humans.  
Not applicable.  
We are grateful to the four anonymous reviewers for their constructive and helpful comments on the manuscript.  
No conflict of interest exists in the submission of this manuscript, and the manuscript is approved by all authors for publication. I would like to declare on behalf of my  
Figure 15: BER as functions of (**a**) received optical power \(P_{r}\) and (**b**) photon counts \(k_{s}\).  
co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All authors listed have approved the manuscript that is enclosed.