## 6 Numerical Results and Discussion
Therefore, our code has a very high received power compared to the received noise power, and this is due to high immunity against PINN noise thanks to the zero cross correlation property of this code compared to codes 3D-PD, 3D-PD/MD, and 3D-DCS/MD. The variation of BER as a function spectral width is indicated in Figure 5 when the number of users equals 150 users and effective source power \(P_{sr}\) equals to \(-10\)dBm. At the minimum optical transmission value \(10^{-9}\), our proposed system needs a spectral width up to 0.15 THz, while the 3D-PD, 3D-PD/MD, 3D-DCS/MD, and 2D-VWZCC codes need a large spectral width up to 8 THz, 6.3 THz, 5.27 THz, and 3.75 THz, respectively. Therefore, the 3D-VWZCC code saved a spectral width around 8.85 THz from the 3D-PD code, 6.15 THz, 5.12 THz, and 3.6 THz from 3D-PD/MD code, 3D-DCS/MD, and 2D-VWZCC, respectively. Hence, we interpret these results by the zero cross correlation property of our code. Figure 3: BER against number of simultaneous users when the effective power \(P_{sr}=-10\) dBm and data rate \(R_{b}=1.25\) Gbps. Figure 6 shows the variation of BER against effective source power \(P_{sr}\), where a number of simultaneous users equal to 150 and data rate of 1.25 Gbps, for \(P_{sr}\) less than \(-30\) dBm (\(<\)\(-30\) dBm); we note that all the codes have the same BER, and at \(P_{sr}\) greater than \(-30\) dBm (\(>\)\(-30\) dBm) we notice a significant variation in the value of BER. Consequently, in the acceptable BER \(10^{-9}\) our code needs a power up to \(-11\) dBm; on the other hand, the 2D-VWZCC and 1D-VWZCC code of the same code family accommodate an effective power of approximately \(-5.1\) dBm and \(-3.96\) dBm, respectively. In addition, the codes 3D-PD,  
Figure 4: SNR against number of simultaneous users when the effective source power \(P_{\rm sr}=-10\) dBm and data rate \(R_{\rm b}=1.25\) Gbps. Figure 5: BER versus spectral width when the number of active users K = 150 and data rate \(R_{\rm b}=1\) Gbps. 3D-PD/MD, and 3D-DCS/MD have power limited in BER greater than \(10^{-5}\). Therefore, our 3D-VWZCC system gives a better performance and it can save the received power to about \(-5.9\) dBm and \(7.04\) dBm compared to 2D-VWZCC and 1D-VWZCC; this is due to a low power consumption due to short length compared to a one dimensional (1D) code, two dimensional (2D) code, high immunity against PIN noise, and multi-access interference MAI compared to 3D-PD, 3D-PD/MD, and 3D-DCS/MD. Figure 7 shows the variation of BER versus data rate, where the number of simultaneous users equals 250 and spectral width equals 5 THz. According to the figure, all codes provide a data rate less than 0.5 Gbps at an acceptable BER \(10^{-9}\), and approximately 0.38 Gbps, 0.4 Gbps, 0.51 Gbps, and 0.55 Gbps for 3D-PD, 3D-PD/MD, 2D-VWZCC, and 3D-DCS/MD codes, respectively, except for the 1D-VWZCC code, which can provide data rate up to 0.2 Gbps at a BER equal to \(10^{-4}\). Further, when increasing the data rate, the 3D-VWZCC code is the only code that meets the optical transmission requirements with a data rate reaching 2 Gbps. In addition, the 3D-VWZCC system improved the data capacity up to 5.26, 5, and 3.62 times of 3D-PD, 3D-PD/MD, and 3D-DCS/MD code, respectively, whereas the 3D-VWZCC code increased the transmission capacity up to 3.62 times of the passage from two dimension (2D) to the three dimension (3D). As a result, we demonstrate these results by our code's high capacity and immunity against MAI and the effect of PIN noise. Figure 6: BER against effective source power when the number of simultaneous users K = 150 and data rate R\({}_{\text{b}}\) = 1.25 Gbps. Figure 8 shows the variation of BER as a function effective source power where our 3D-VWZCC code is tested with various noises, with the data rate and number of simultaneous users equal to 1.25 Gbps and 250, respectively.