## 6 Numerical Results and Discussion  
In this phase, the performance of the 3D-VWZCC code is compared to the 3D-perfect difference (3D-PD), 3D-perfect difference/multi-diagonal (3D-PD/MD), and 3D-dynamic cyclic shift/multi-diagonal (3D-DCS/MD), which are previously published in [13; 14; 15] in terms of BER, SNR, and Q factor as a function of spectral width, number of active users, data rate, and effective source power. In addition, thermal noise, shot noise, and phase-induced intensity noise are taken into account during the simulation; in addition, Table 5 shows the parameters that are used in the MATLAB simulation with lengths \(M=7\), \(N=13\), and \(P=3\) for the spectral, temporal, and spatial components, respectively. Figure 3 shows the variation of BER as a function of the number of simultaneous users, where the effective source power and data rate are equal to \(-10\) dBm and \(1.25\) Gbps, respectively. When the property of the optical requirement is at \(10^{-9}\), the code 3D-PD, 3D-PD/MD, and 3D-DCS/MD provides a user capacity of approximately 86, 98, and 109, respectively, while 1D-VWZCC, 2D-VWZCC, and 3D-VWZCC codes provide a significant number of users equal to 62, 141, and 317, respectively. Furthermore, our 3D-VWZCC code offers a system capacity of 3.686 times the 3D-PD code, 3.234 times the 3D-PD/MD code, and 2.908 times the 3D-DCS/MD code, while 3D-VWZCC offers a capacity of 5.112 times the 1D-VWZCC and 2.248 times the 2D-VWZCC for the same family of this code. Therefore, the results of our 3D-VWZCC system code demonstrate a superiority of 36.86%, 32.34%, and 29.09% compared to the codes 3D-PD, 3D-PD/MD, and 3D-DCS/MD, respectively. In addition, our code has the superiority of 51.12% and 22.48% of one-dimensional and two-dimensional VWZCC code for the same family of this code, respectively. As a result, we explain these results by a small impact of PIIN noise on our code compared to the codes in the three-dimensional domain (3D-PD, 3D-PD/MD, and 3D-DCS/MD) due to zero cross correlation and short code length compared to the 1D-VWZCC code, and less spatial components compared to 2D-VWZCC. Figure 4 shows the variation of the SNR against number of simultaneous users for a data rate of 1.25 Gbps and a source power \(P_{sr}\) of \(-10\) dBm for each transmitter. We note \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbol** & **Value** \\ \hline Photo detector responsivity & \(\mathcal{R}\) & 0.75 \\ Data rate & \(\mathrm{R_{b}}\) & 1.25 Gbp \\ Number of users & K & 150 \\ Electric bandwidth 1D, 2D & \(\mathrm{B_{r1,2}}\) & \(0.5\times\mathrm{R_{b}}\) GHz \\ Electric bandwidth 3D & \(\mathrm{B_{r3}}\) & \(0.5\times\mathrm{N}\times\mathrm{R_{b}}\) GHz \\ Receiver load resistor & \(\mathrm{R_{l}}\) & 1030 \(\Omega\) \\ Spectral width of light & \(\Delta\mathrm{v}\) & 5 THz \\ Effective source power & \(\mathrm{P_{sr}}\) & \(-10\) dBm \\ Receiver noise temperature & \(\mathrm{T_{n}}\) & 300 K \\ Electron charge & E & \(1.6\times 10^{-19}\) c \\ Boltzman’s constant & \(\mathrm{K_{b}}\) & \(1.38\times 10^{-23}\) J/K \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The values of the parameters in the 3D-VWZCC system for numerical calculation. that all codes are affected by PINN noise with different degrees depending on the code, except for the 1D-VWZCC code; the PINN noise of this code is equal to zero due to zero cross correlation properties, for the same length (M = 7, N = 13, P = 3) of all codes except 1D-VWZCC and 2D-VWZCC. We set the number of users at 400, our suggested code has a very high signal to noise ratio, reaching 158, while 3D-PD, 3D-PD-MD, and 3D-DCS/MD codes have a signal to noise ratio up to 35.1, 35.3, and 51, respectively. On the other hand, the codes of the same family, 1D-VWZCC and 2D-VWZCC, offer an SNR up to 6 and 41, respectively. As a result, the 3D-VWZCC code provides an SNR up to 4.5 times the 3D-PD, 4.45 times the 3D-PD/MD, and 3.08 times the 3D-DCS/MD, whereas the 3D-VWZCC code provides an SNR up to 26.3 times the 1D-VWZCC and 3.85 times the 2D-VWZCC.