## 4 VLPC Network Based on SICD-OPRC Scheme
### Simulation Setup  
To assess the coverage performance of the proposed SICD-OPRC-based VLPC scheme over a wide range of positions, we extend the model to a 5 m \(\times\) 5 m \(\times\) 3 m space, as shown in Figure 6b, which is different from our OPRC-VLP system. Due to the limited experimental space and equipment, we only conduct the simulation to validate the effectiveness of our proposed scheme. In the simulation model, four LED light sources are evenly positioned on the ceiling: \(Tx_{1}\) at (\(-\)1.25 m, 1.25 m, 3 m), \(Tx_{2}\) at (1.25 m, 1.25 m, 3 m), \(Tx_{3}\) at (\(-\)1.25 m, \(-\)1.25 m, 3 m), and \(Tx_{4}\) at (1.25 m, \(-\)1.25 m, 3 m). Each LED utilizes a distinct OPRC code for encoding user data. Next, we place 2601 test points evenly on the receiving plane, with each point separated by 10 cm. The receiver is placed on these test points, with its plane remaining parallel to the LED's plane, at a constant vertical distance of 2.15 m. During simulations, the LED transmission power is set at 10 W, the system bandwidth is 1 GHz, and the decision threshold of the SICD algorithm is set at zero. Other parameters follow the settings in Table 1. We conduct a comprehensive evaluation of the performance of the SICD-OPRC-based VLPC scheme under both synchronous and asynchronous transmission environments. In synchronous mode, a single controller coordinates all LEDs for synchronized signal transmission. In contrast, asynchronous mode features each LED controlled independently, leading to varied signal transmission delays. The OPRC code and the OZCZ code from [26] are also adopted as benchmarks, and we compare them to evaluate how different coding schemes affect overall performance. These schemes are labeled as (i) SICD-OPRC, (ii) OPRC, and (iii) OZCZ.  
We monitor and record the key performance parameters of the VLPC system under various conditions. First, we focus on assessing the efficacy of OPRC and OZCZ codes with varying lengths in mitigating MAI under asynchronous transmission conditions. This assessment is based on the computation of the normalized MAI generated by interfering codewords at different chip offsets relative to the target codeword. The formula for calculating this normalized MAI is given by:  
\[\xi(\tau)=\frac{1}{L_{S}}\sum_{\begin{subarray}{c}j=1,\\ j\
eq i\end{subarray}}^{N_{\text{LED}}}\left[\sum_{n=1}^{L_{S}-\tau}b_{+}S_{j} \langle n+\tau\rangle S_{i}(n)+\sum_{n=L_{S}-\tau+1}^{L_{S}}b_{-}S_{j}\langle n +\tau\rangle S_{i}(n)\right], \tag{24}\]  
where \(b_{+}\) and \(b_{-}\) represent the \"+1\" and \"\(-\)1\" symbols, respectively, while \(S_{i}\) and \(S_{j}\) represent the target codeword and interfering codeword, respectively. This equation quantifies the interference caused by the interfering codeword at different offsets, enabling us to evaluate the MAI suppression capabilities of the OPRC and OZCZ codes. Based on Equations (20) and (21), the performance of VLC and VLP is directly related to the accuracy of the measured CV values, i.e., the cross-correlation values \(CV_{m}(k)\). Therefore, we further investigate the effectiveness of different coding schemes in combating MAI by evaluating the measurement error of the CV values. This is quantified by calculating the normalized error of CV (NECV) using the following formula:  
\[\zeta=\sum_{i=1}^{N_{\text{LED}}}\frac{E(CV_{i})}{|CV_{i}|}, \tag{25}\]  
where \(E(CV_{i})\) is the absolute difference between the measured and ideal CV values for the \(i\)-th VLPC signal. This deviation is caused by MAI and AWGN. Finally, to achieve a thorough assessment, we conduct performance evaluations considering specific metrics including BER and PE.