## 6 Numerical Results and Discussion
According to the figure, the code is tested with three types of noise; the blue curve presents a combination between thermal noise, shot noise, and PIIN noise, the green curve presents a combination between shot noise and PIIN noise, and the red curve presents a combination between thermal noise and PIIN noise. It is clear that the impact of combination between thermal noise, shot noise, and PIIN noise on the system have the same effect as the combination between thermal noise and PIIN noise. In contrast, the combination between shot noise and PIIN noise demonstrates a significant variation compared to the other curves. As a result, the impact of shot noise is totally neglected and the system is mainly affected by thermal noise and PIIN noise. The variation of photocurrent noise against effective source power, where the data rate and number of simultaneous users are equal to 1.25 Gbps and 250 users, respectively, is shown in Figure 9 when the effective source power is lower than \(-\)10 dBm. All codes have a stable value reaching \(10^{-13}\), and during the increase in the effective source power we notice an important variation in the photocurrent noise value between 3D-PD, 3D-PD/MD, and 3D-DCS/MD, as well as 3D-MD and 3D-VWZCC; this is due to the characteristic of zero cross correlation, which reduces the effect of MAI and PIIN noise and direct detection at the receiver. Consequently, the shot noise becomes inefficient in the system and PIIN noise becomes the main noise, which degrades the performance of the optical multiplexing system. Figure 10 shows the variation of phase-induced intensity noise PIIN as a function of received power, where all the codes have the same length (M = 7, N = 13, P = 3) and data rate, and the number of simultaneous users are equal to 1.25 Gbps and 250 users, respectively. It is clear that our 3D-VWZCC code has less PIIN noise power than 3D-PD, 3D-PD/MD, and 3D-DCS/MD codes. Thus, we interpret these results by the zero cross correlation property of the VWZCC code, which requires a simple detection method that reduces the effect of PIIN compared to other codes. Figure 7: BER versus data rate when the number of active users K = 250 and effective source power P\({}_{\rm{sr}}=-\)10 dBm. Figure 8: BER against effective source power when the number of simultaneous users K = 250 and data rate \(\rm R_{b}=1.25\) Gbps. Figure 9: Photo current noise against effective source power when the number of simultaneous users K = 250 and data rate \(\rm R_{b}=1.25\) Gbps. Figure 11 indicates the variation of SNR of our code against the number of simultaneous users with the impact of different combinations of noises, thermal noise + shot noise + PINN noise, shot noise + PINN noise, and thermal noise + PINN noise, where the effective source power equal to \(P_{sr}=-10\) dBm and the data rate \(R_{b}=1.25\) Gbps. We observe that our code is mainly affected by thermal noise and PINN noise, to a lesser degree, and shot noise is neglected due to the thermal agitation of electrons in electronic components; this is what has been proven in Figures 8-10. Figure 12 indicates the variation of the Q factor against the number of simultaneous users where the effective source power equals \(-10\) dBm and the data rate equals 1.25 Gbps. At the value of the quality factor Q satisfying the optical transmission requirements (Q = 6), all codes do not exceed number of users greater than 200 except our code 3D-VWZCC; as a result, the number of users can reach 83, 96, 106 for the codes 3D-PD, 3D-PD/MD, 3D-DCS/MD, respectively, and the passage from 1D and 2D to 3D for our code accommodates a number of users equal to 61,140, and 312, respectively. Hence, the 3D-VWZCC code increased the cardinality by 3.75, 3.25, 2.94, 5.11, and 2.15 times compared to the 3D-PD, 3D-PD/MD, 3D-DCS/MD, 1D-VWZCC, and 2D-VWZCC codes, respectively. Therefore, we explain the superiority of our code compared to others by high multiplexing capacity due to the immunity against the MAI, which allows supporting a very high number of users at higher data rate.