# 5G V2X Performance Comparison for Different Channel Coding Schemes and Propagation Models
## 4 Simulation Results
### FER Simulation Results  
Prior to this, we presented and analysed the BER versus SNR simulation results. Another important parameter that must studied is FER versus SNR. The simulations show that the results have qualitative similarities for all the decoding algorithms on average. For that reason, we choose to show the FER performance for highway-LOS scenario (Figure 8a-c) and urban-NLOS scenario (Figure 8d-f) as representatives for the good and poor FER scenarios, respectively.  
The results clearly show the superiority of turbo codes in both good and poor communication systems. In fact, as the data frame size increases, the difference in FER performance from polar and LDPC coding accelerates. The turbo implementations maintain the same correlations between them as in the BER results, since the BCJR and logBCJR performances are identical and the maxlogBCJR maintains an average gap of 0.2 to 0.3 dB. Further, SOVA coding remains, as expected, the least efficient, maintaining a slow rate of convergence across the entire SNR range. From Figure 8, we conclude that turbo coding is the best coding scheme based on FER performance for all scenarios and frame lengths.  
The big qualitative difference between the BER and FER results is that FER is clearly better in polar coding than in LDPC in all simulated scenarios and for all frame sizes. In the case of the FER performance, this superiority extends over the entire SNR range, while, as we highlighted, the BER performance is worse in the low SNR region for all frame sizes and in the high SNR region for 512-bit frame sizes for polar coding. Of course, for the case of 512-bit frames, LDPC has a much higher convergence speed than polar coding, but it does not manage to reach its FER performance because its middle SNR region is characterized by a relatively slow rate of convergence. The difference in polar coding is also evident from the fact that its FER performance is consistently better than that of SOVA in the case of the highway-LOS scenario. This phenomenon can only be explained based on the distribution of binary errors in the data frames after the decoding process. Apparently, after the decoding process in LDPC, the binary errors are more uniformly distributed in the transmitted frames, leading to a large FER, while in polar coding, the errors are concentrated in specific frames. Since the initial errors before decoding are distributed in the same way for each coding scheme, we conclude that polar coding is much better at handling frames with few errors than LDPC and eliminating binary errors completely, producing error-free frames. On the contrary, it is less efficient for frames with a large number of errors, correcting only very few of them. LDPC is not as efficient as polar coding on frames with a small number of errors and, thus, does not produce many error-free frames. On the contrary, it is more efficient in cases of frames with many errors.  
Figure 8: FER vs. SNR. (**a**) highway-LOS scenario 128-bit frames; (**b**) highway-LOS scenario and 256-bit frames; (**c**) highway-LOS scenario and 512-bit frames; (**d**) urban-NLOS scenario and 128-bit frames; (**e**) urban-NLOS scenario and 256-bit frames; (**f**) urban-NLOS scenario and 512-bit frames.