# 3 GPP 5G V2X Error Correction Coding for Various Propagation Environments: A QoS Approach
## 5 Simulation Results
### FER Simulation Results for 128-Bit Frame Length  
In Figure 2, the FER performance of the simulated system model, i.e., for scenarios S1-S5 in Table 1 is shown. We observe that each decoding algorithm improves the FER as the SNR increases at a rate greater than the uncoded case. Additionally, BCJR and logBCJR have almost the same performance, while the suboptimal maxlogBCJR has a loss of 0.2-0.3 dB [52]. All three BCJR-based algorithms have the same convergence rate, causing FER to null very fast, and this is the main reason why the error floor [53] is not fully revealed, although it is present in the simulation scenarios for the BCJR-based algorithms.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**QoS** & **Description** & **Reliability (\%)** & **End-to-End** & **Data Rate per** & **Communication** \\
**Scenario** & & & **Latency (ms)** & **Vehicle (Kbps)** & **Range** \\ \hline Q1 & Cooperative awareness & 90–95 & 100 to 1000 & 5 to 96 & Short to medium \\ \hline Q2 & Cooperative sensing & \textgreater{}95 & 3 to 1000 & 5 to 25,000 & Short \\ \hline Q3 & Cooperative maneuver & \textgreater{}99 & \textless{}3 to 100 & 10 to 5000 & Short to medium \\ \hline Q4 & Vulner road user & 95 & 100 to 1000 & 5 to 10 & Short \\ \hline Q5 & Traffic efficiency & \textless{}90 & \textgreater{}1000 & 10 to 2000 & Long \\ \hline Q6 & Tele-operated driving & \textgreater{}99 & 5 to 20 & \textgreater{}25,000 & Long \\ \hline \end{tabular}
\end{table}
Table 2: Some 3 GPP 5G QoS scenarios.  
Figure 2: FER vs. SNR for scenarios S1–S5 and 128-bit frame length. **(a)** Highway–LOS scenario (S1); **(b)** highway–NLOS’v scenario (S2); **(c)** urban–LOS scenario (S3); **(d)** urban–NLOS scenario (S4); **(e)** urban–NLOS’v scenario (S5).  
The SOVA is also suboptimal compared to the BCJR-based algorithms [54] and its low rate of convergence prevents it from zeroing in the SNR range between 0 and 10 dB. Furthermore, it has better performance compared to LDPC in the low and middle SNR regions, but eventually, it becomes the worst algorithm in the high SNR region due to its slow convergence rate.  
The FER in LDPC has a very slow rate of convergence initially, but as the SNR increases, the rate increases vastly. Although the slope of the convergence rate in LDPC is comparable to that of the BCJR-based algorithms at the middle SNR region, it slowly diminishes and diverges, specifying the presence of an error floor [55; 56]. This error floor is negligible, and it is more clearly visible in both LOS scenarios.  
Contrariwise, there is no error floor in polar coding [57]. Polar coding has an FER similar to the SOVA algorithm initially, but as the SNR increases, the FER diminishes rapidly in all scenarios. Eventually, the rate of convergence becomes better in polar coding than in the BCJR-based algorithms, but it is not enough for polar coding to obtain optimal performance, since FER in the BCJR-based algorithms nulls very quickly.  
These FER performance results can be fully explained through the theoretical operation framework and characteristics of each coding scheme. According to [36], turbo codes are more effective in small data frames, since the convolutional coding results in dense-information parity bits, unlike LDPC, where block coding creates parity bits with less information. Further, in [36], the authors concluded that polarization is not fully revealed in small data frames, and as a result, polar coding is subordinate to turbo coding. Finally, among the turbo coding schemes, the authors in [52; 54] proved and explained in detail the suboptimality of maxlogBCJR and SOVA, respectively, compared to the optimal performance of the BCJR and logBCJR algorithms.  
From Figure 2, and from the above analysis, we can deduce that the BCJR-based algorithms are the best choice regardless of the FER value we want to achieve and for every system model simulation scenario.