## 4 VLPC Network Based on SICD-OPRC Scheme  
### System Principle of SICD-OPRC  
For the ACDM-OPRC-based VLP system design described in Section 3, OPRC sequences are cyclically broadcasted by LED transmitters. If we substitute plain cyclic OPRC sequences with OPRC-encoded user data at the transmission stage, the cross-correlation outcomes between received signals and OPRC sequences at the receiver can be utilized to encapsulate both RSS information and user data. This dual functionality allows us to extract the necessary RSS information from the cross-correlation results for VLP while also decoding user data for VLC by setting a reasonable threshold to parse the cross-correlation values. This method leverages the OPRC encoding mechanism to integrate VLP and VLC functions into a single system, constructing an integrated VLPC system. Reflecting on the practical deployment of LEDs, we consider a multi-cell VLPC network architecture, as illustrated in Figure 6, with LEDs spaced equidistantly. Within this framework, LEDs in each cell are governed by a dedicated controller, ensuring synchronized signal transmission within the cell. In contrast, LEDs across different cells are managed by their respective controllers, leading to asynchronous signal transmission among them. Based on this architecture, user data are encoded by OPRCs, combined with a DC component to generate the VLPC signals, which are then distributed to every LED transmitter via the controller for broadcast. These VLPC signals traverse the VLC channel and are eventually captured by the PD receiver. The received signal can be expressed as:  
\[\mathbf{R}_{s}(t)=\sum_{i=1}^{N_{\text{LED}}}\beta\delta_{i}P_{i}[\alpha\mathbf{B}_{i} (t+\tau_{i})S_{i}(t+\tau_{i})+1]+N_{\text{AWGN}}(t), \tag{14}\]  
where \(\mathbf{B}_{i}\) and \(\tau_{i}\) represent the user data and time delay of the \(i\)-th VLPC signal emitted from the \(i\)-th LED, respectively. When the PD receives signals from synchronized LED transmitters, \(\tau_{i}=0\) for \(i=1,\ldots,N_{\text{LED}}\). Figure 6: Schematic diagram of the VLPC network based on SICD-OPRC: (**a**) distribution of LED transmitters; (**b**) VLPC system model in the 4-LED cell; (**c**) VLPC signal modulation in the controllers at the LED transmitter side; and (**d**) VLPC signal demodulation in the processor at the PD receiver side. Then, we use the OPRC corresponding to the \(i\)-th LED to decode the received signal, as shown in Figure 7. For the synchronous transmission scenario, the cross-correlation results between the received signal and OPRC for the \(i\)-th LED can be simply expressed as:  
\[ \begin{array}{ll}CV_{Si}(k)&=\alpha\beta P_{t}\frac{1}{L_{S}}\sum\limits_{j=1 }^{N_{\text{LED}}}\sum\limits_{n=1}^{L_{S}}\delta_{j}b_{j}(k)\textbf{S}_{j}(n) \textbf{S}_{i}(n)+\widetilde{N}_{\text{AWGN}}\\ &=\alpha\beta P_{t}\delta_{i}\frac{1}{L_{S}}b_{i}(k)\sum\limits_{n=1}^{L_{S}} \textbf{S}_{i}(n)\textbf{S}_{i}(n)+\widetilde{N}_{\text{AWGN}}\end{array} , \tag{15}\]  
where \(b_{j}(k)\) is the \(k\)-th symbol of the user data from the \(j\)-th LED. As for the asynchronous transmission scenario, the cross-correlation results exhibit a more complex form, which can be expressed as:  
\[ \begin{array}{ll}CV_{ASi}(k)=\alpha\beta P_{t}\frac{1}{L_{S}}\sum\limits_{j =1}^{N_{\text{LED}}}\delta_{j}\left[\begin{array}{c}\sum\limits_{n=1}^{L_{S }-\tau_{j}}b_{j}(k)\textbf{S}_{j}(n+\tau_{j})\textbf{S}_{i}(n)+\\ \sum\limits_{n=L_{S}-\tau_{j}+1}^{L_{S}}b_{j}(k+1)\textbf{S}_{j}(n+\tau_{j}) \textbf{S}_{i}(n)\end{array}\right]+\widetilde{N}_{\text{AWGN}}.\end{array}  \tag{16}\]  
For ease of expression, we assume that when recovering the signal transmitted by the \(i\)-th LED, the system can always accurately identify the start symbol of the signal.