## 4 Simulation Results  
To validate the VLC system model, we simulate and analyze the illumination conditions and luminous power on the plane where the receiver is positioned. In this investigation, the distance between the receiving plane and the light source is set at 2.15 m.  
Figures 5 and 6 show the illumination condition of the indoor VLC system. It is evident that the area near the light source experiences higher illumination levels. From the center towards the periphery, the illumination intensity gradually diminishes. Overall, the illumination ranges between 300 lux and 1100 lux, aligning with the regulations of the International Organization for Standardization and adequately meeting practical lighting requirements. with [PERSON]'s law. This analysis affirms the validity of the model's layout, effectively striking a balance between communication and illumination. Thus, the constructed model stands as an accurate and rational representation. Subsequently, we delve into the technical advantages offered by the proposed scheme by employing polar codes for VLC. In our simulations, we use a polar code with a length of 1024 and a code rate of 0.5. The Bhattacharyya parameters of the polarized channels within the VLC model are calculated using Equation (12), and the scatter plot is displayed in Figure 9. The x-axis represents the indices of the polarized channels, while the y-axis shows the values of the Bhattacharyya parameters \(Z(W_{N}^{(i)})\). By examining the relationship between  
Figure 8: The contour map of luminous power. Figure 7: The luminous power distribution diagram. the Bhattacharyya parameters and channel symmetric capacity, a significant polarization phenomenon is observed. Specifically, some channels' symmetric capacities trend towards 0, while others approach 1, indicating that the channel reliability estimation is ideal. Figure 10 illustrates the BER of the VLC system. In this analysis, polar codes with a code rate of 0.5 and different code lengths are used in the simulations. When the SNR exceeds a certain threshold, it becomes clear that the BER curve for the coded VLC system consistently outperforms that of the uncoded scenario, with a noticeable gap between the two. Furthermore, when the code rate remains fixed, the error-resistance performance of the polar codes improves with increasing code length. This enhancement is due to the stronger polarization effect observed in the sub-channels as the code length increases. Thus, it is evident that the use of polar codes significantly enhances the communication quality of the VLC system. Figure 10: A comparison of the BER performance for the VLC system with a code rate of 0.5 and code lengths of 512, 1024, and 2048. Figure 9: The distribution diagram of Bhattacharyya parameter. Figure 11 illustrates the BER of the VLC system utilizing polar codes with a code length of 1024 and code rates of 0.75, 0.5, and 0.125. At a BER of \(10^{-2}\), the proposed scheme achieves coding gains of approximately 2.5 dB, 5 dB, and 7 dB, compared to the uncoded scenario across the different code rates. In summary, when the code length remains constant, lower code rates exhibit superior error correction capabilities, while higher code rates are comparatively less effective. With respect to different code rates, distinct ranges of SNR are required to facilitate reliable communication in the VLC system. Telecommunication performance may decline if the SNR falls below a certain threshold. With practical VLC applications in mind, we then examine the BER distribution in an indoor VLC system at various communication heights. Our experimentation involves polar codes with a code length of 1024 and a code rate of 0.5, comparing the results to an uncoded system. Figures 12 and 13 illustrate the following:  
_(1)._ As the communication distance increases, both coded and uncoded VLC systems experience an increase in BER.