## 4 VLPC Network Based on SICD-OPRC Scheme
### Simulation Results
Notably, OZCZ exhibits slightly lower NECV values compared to the alternatives, likely due to the longer OZCZ codes providing a marginal coding gain that reduces AWGN effects. Overall, MAI-induced NECV is significantly less pronounced than the impact of AWGN. For OPRC and OZCZ schemes, MAI is the primary contributor to CV measurement errors, underscoring the effectiveness of the SICD-OPRC scheme in substantially reducing MAI effects. Figure 10: Color-mapped contour plots of NECV caused by MAI when using: (**a**) SICD-OPRC; (**b**) OPRC; and (**c**) OZCZ; color-mapped contour plots of NECV caused by AWGN when using: (**d**) SICD-OPRC; (**e**) OPRC; and (**f**) OZCZ. Figure 9: Estimated NECV by using different coding mechanisms with varying codeword lengths and SNRs when the receiver is located at (1.25 m, 1.25 m, 0 m). Finally, we compare the VLPC system's performance using the three coding schemes in both synchronous and asynchronous scenarios. We measure the BER and PE of the receiver at each test point and present the results in color-mapped surface plots and contour plots in Figures 11 and 12. In the synchronous setting, Figure 11 illustrates that all three methods deliver similar VLC and VLP performance, achieving BER below the forward error correction (FEC) threshold of \(3.8\times 10^{-3}\) and PE less than 10 cm across most test points. This similarity is due to the ability of these coding mechanisms to maintain signal orthogonality under synchronous conditions. Therefore, the decoding process is mainly affected by AWGN, resulting in a spatial distribution of BER and PE that mirrors the NECV distribution caused by AWGN shown in Figure 10d-f. That is, BER and PE are lower near the center of the model and higher at the edges. In asynchronous scenarios, Figure 12 demonstrates that the system employing the SICD-OPRC scheme sustains stable performance, meeting the FEC standard for VLC and achieving PE below 10 cm at most locations. By contrast, OPRC and OZCZ exhibit significant BER and PE increases, particularly at distant test points from the model's center. The BER for OPRC can rise to \(4.0\times 10^{-2}\) with PE nearing 60 cm, and OZCZ can reach a BER of \(1.0\times 10^{-1}\) with PE approaching 110 cm. This difference is due to SICD-OPRC's effectiveness in mitigating MAI, allowing it to accurately distinguish VLPC signals from different LEDs within complex received signals, thereby preserving performance despite asynchronous transmission-induced MAI. OPRC outperforms OZCZ due to its superior correlation characteristics, offering enhanced MAI resilience and superior VLPC results. Figure 11: For the synchronous VLPC system, the color-mapped surface plots of BER estimated at all test points when using: (**a**) SICD-OPRC; (**b**) OPRC; and (**c**) OZCZ, with the pink plane representing the FEC threshold of \(3.8\times 10^{-3}\), and the color-mapped contour plots of PE estimated at all test points when using: (**d**) SICD-OPRC; (**e**) OPRC; and (**f**) OZCZ. For a quantitative comparison of each scheme's performance, we conduct a statistical analysis of the BER and PE distributions depicted in Figures 11 and 12. The summarized findings are presented in Figure 13. Under ideal synchronous transmission, all schemes perform well, achieving very similar performance levels. Specifically, about 97% of test points achieve a BER below the FEC threshold, while PE is effectively controlled below 5.4 cm for 90% of measurement positions. However, significant performance differences emerge when the transmission environment shifts to asynchronous operation. The system based on the OZCZ scheme exhibits a noticeable decline in performance, maintaining BER within the FEC standard at only 11% of test points, with average BER and PE reaching 4.0 \(\times\) 10\({}^{-2}\) and 32.5 cm, respectively. This is attributed to the OZCZ scheme's limited resistance to MAI induced by asynchronous transmission.