# BICM-ID with Physical Layer Network Coding in TWR Free Space Optical Communication Links +
## 4 Simulation Results
### Iterative Process  
The transmitted source of data bits is encoded with a rate \(R_{c}\) 0.5 NSC encoder of a constraint length of five and generator polynomials of [23 35]s. Consider that \(L_{d}\) is two kilometres (km); \(V\) in a clear weather condition is 10 km; \(\lambda\) is 1550 nanometes (nm); and \(R_{s}\) is one ampere per watt (A/W). For weak and strong turbulence, \(\sigma_{R}^{2}\) and \(C_{n}^{2}\) are 0.5, 1.6 and 0.75 \(\times\) 10\({}^{-14}\) m\({}^{-2/3}\), 1.00 \(\times\) 10\({}^{-13}\) m\({}^{-2/3}\), respectively. The encoded bits are anti-Gray mapped to a QPSK constellation. Figures 5 and 6 show the BER performance of BICM-ID with PNC over a log-normal (weak) and a gamma-gamma (strong) channels for various numbers of decoder iterations, respectively. As can be seen from the figures, the BER performance has to have the same behaviour after Iteration Number 2. In order to confirm the accuracy and usefulness of the system, the Monte Carlo method is adopted. Specifically, in Figures 7 and 8, we get the results of the BICM-ID TWR-FSO PNC system under weak and strong turbulence conditions. This is mainly due to the fact that the system under the strong turbulence model causes a degradation in the error performance. Consequently, the TWR-FSO with PNC can be compared with the log-normal and the gamma-gamma channels in terms of uncoded, system employed E2E non-iterative code as the convolutional code and the system employing E2E BICM-ID code, as shown in Figures 9 and 10 for a log-normal and a gamma-gamma channel model, respectively. Hence, for  
Figure 4: The decoder setup for TWR-FSO PNC system employing BICM-ID code to generate the ExIT function.  
weak and strong turbulence fading channels, we observe that the BER performance of the proposed system with BICM-ID outperforms the uncoded and non-iterative convolutional code systems. As we can see in Figure 9, the system with BICM-ID shows an improvement when adopting iterative demapping and decoding. For instance, there is an improvement of about 12 dB of \(E_{b}/N_{0}\) at a BER of \(10^{-4}\) for the proposed system compared to that of uncoded as distinguished for weak turbulence. Whereas for a system with a convolutional code, the improvement is approximately 6 dB of \(E_{b}/N_{0}\) at a BER of \(10^{-4}\). However, for the systems in Figure 10 with BICM-ID, the BER improves slightly for the iterative demapping and decoding. For example, at a BER of \(10^{-2}\), the \(E_{b}/N_{0}\) difference is about 8 dB for the proposed system compared to that of uncoded TWR-FSO PNC system. At a BER of \(10^{-4}\), the \(E_{b}/N_{0}\) for the system with convolutional code is 40 dB and for system with BICM-ID code is about 37.5 dB. Therefore, the effects of iterative decoding are detected within an atmospheric turbulence fading channel. Nevertheless, the results show that BICM-ID codes with trellis-based decoding algorithms are suited to TWR-FSO PNC networks. This is mainly because in an atmospheric turbulence fading channel, introducing the interleaver produces a higher degree of diversity order and therefore guarantees significant improvement.  
Figure 5: BER performance of BICM-ID with PNC over a log-normal channel for various numbers of decoder iterations.  
Figure 6: BER performance of BICM-ID with PNC over a gamma-gamma channel for various numbers of decoder iterations.  
Figure 8: Monte Carlo method applied to the BICM-ID TWR-FSO with PNC system over a strong turbulence link.  
Figure 7: Monte Carlo method applied to the BICM-ID TWR-FSO with PNC system over a weak turbulence link.  
Figure 9: BER performance of TWR-FSO with PNC over a log-normal channel when employing uncoded, E2E convolutional code and E2E BICM-ID codes.