## 4 Simulation Results
This is due to higher noise levels in the VLC channel over longer distances, resulting in a decline in transmission quality;  
_(2)._ When tested at different heights within the room, the VLC system that utilizes polar codes demonstrates a substantially lower BER compared to an uncoded system. Overall, the improvement in BER becomes more significant as communication distances increase. Thus, we conclude that polar codes have the potential to extend the range of reliable communication and significantly boost the performance of the VLC system. Figure 14 presents the calculated results for the reliable communication area of the VLC system at various communication heights. It is clear that implementing the polar code scheme examined in this study significantly expands the reliable communication area of the VLC system, especially at communication heights of 1.5 m and 2.5 m, where it encompasses the entire room. Thus, the proposed scheme notably bolsters the communication reliability of the VLC system. Figure 11: A comparison of the BER performance for the VLC system with a code length of 1024 and code rates of 0.125, 0.5, and 0.75. Figure 15 shows the improvement effects of the studied scheme on the reliable communication area of the VLC system. At a communication height of 0.5 m, the BER of the VLC system exceeds \(10^{-3}\), indicating a reliable communication area of 0. For the ease of calculation, 0.1 is taken as a representative value. From the simulation outcomes, it is evident that the reliable communication area, for both encoded and uncoded scenarios, steadily increases with the rise in communication heights. As the communication distance extends, the improvement brought by the proposed scheme becomes more pronounced. This implies that the expansion effect on the effective communication range is more significant. Figure 12: The BER slice figure of the uncoded VLC system at varying heights—specifically, at 0.5 m, 1.5 m, and 2.5 m.  
Figure 13: The BER slice figure of the coded VLC system at varying heights—specifically, at 0.5 m, 1.5 m, and 2.5 m.  
cant for greater communication distances. The calculation results affirm the effectiveness of the studied encoding scheme. We then evaluate the BER performance of the collaborative coding schemes introduced earlier. In the simulation setup, A and B each encode 512 information bits using a polar encoder with a code rate of 1/2, producing coded words of length 1024. For the DNC-Polar relay scheme, the network-coded results are treated as the information bits and are also encoded using the polar coding with a code rate of 1/2. In contrast, for the PNC-Polar relay  
Figure 14: The statistical results for reliable communication area. Figure 15: The improvement effects for reliable communication area. scheme, the encoded results from the mapped superimposed VLC signals are used as input for the encoding process. The results of the simulations demonstrate that, in comparison to cooperative coding relay schemes, the conventional relay approach exhibits a lower BER. Traditionally, the relay node independently decodes the optical signals received from the source nodes, with the aim of correcting errors. Following this decoding process, the relay forwards the corrected signals to the destination nodes, thereby effectively minimizing errors and achieving greater signal gain. However, this scheme processes the VLC signals individually at the relay node, causing a significant transmission delay. As a result, it may not be ideal for wireless communication systems. In contrast, cooperative coding schemes reduce the number of time slots required, potentially improving the throughput rate of the VLC system. As shown in Figure 16, in low-SNR scenarios, a noticeable performance gap is observed between the DNC-Polar and PNC-Polar relay schemes. Specifically, at a BER of \(10^{-3}\), the PNC-Polar scheme exhibits a performance gap of approximately 1 dB. However, the BER curve for the PNC-Polar relay scheme shows a steeper decline.