# 3 GPP 5G V2X Error Correction Coding for Various Propagation Environments: A QoS Approach
## 5 Simulation Results
### End-to-End Latency
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **QoS** \\ **Scenario** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **System** \\ **Simulation** \\ **Scenario** \\ \end{tabular} } & \multicolumn{3}{c}{**Maximum**} & \multicolumn{6}{c}{**Throughput (Kbps)**} \\ \cline{3-10}  & & & **BCJR** & **logBCJR** & **maxlogBCJR** & **SOVA** & **LDPC** & **Polar** \\ \hline \multirow{2}{*}{Q1} & \multirow{2}{*}{S1, S2, S3, S4, S5} & 96.0 & 96.0 & 96.0 & 96.0 & 96.0 & 96.0 & 96.0 \\ \hline \multirow{2}{*}{Q2} & \multirow{2}{*}{S1, S2, S3, S5} & 25,000.0 & 25,000.0 & 25,000.0 & 25,000.0 & 25,000.0 & 25,000.0 & 25,000.0 \\ \cline{2-10}  & & S4 & 25,000.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline \multirow{2}{*}{Q3} & \multirow{2}{*}{S1, S2, S3, S5} & 5000.0 & 5000.0 & 5000.0 & 5000.0 & 5000.0 & 5000.0 & 5000.0 \\ \cline{2-10}  & & S4 & 5000.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline \multirow{2}{*}{Q4} & \multirow{2}{*}{S1, S2, S3, S4, S5} & 10.0 & 10.0 & 10.0 & 10.0 & 10.0 & 10.0 & 10.0 & 10.0 \\ \hline \multirow{2}{*}{Q5} & \multirow{2}{*}{S1, S2, S3, S5} & 2000.0 & 2000.0 & 2000.0 & 2000.0 & 2000.0 & 2000.0 & 2000.0 & 2000.0 \\ \cline{2-10}  & & S4 & 2000.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline \multirow{2}{*}{Q6} & \multirow{2}{*}{S1, S3, S5} & 25,000.0 & 25,000.0 & 25,000.0 & 25,000.0 & 25,000.0 & 25,000.0 & 25,000.0 \\ \cline{2-10}  & & S2 & 25,000.0 & 24,999.9 & 24,999.8 & 24,999.9 & 24,895.9 & 24,962.8 & 24,994.1 \\ \cline{2-10}  & & S4 & 25,000.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Throughput per QoS scenario (Table 2), simulation scenario (Table 1) and coding scheme. for the end-to-end latency for SOVA (\(t_{SOVA}\)), BCJR (\(t_{BCJR}\)), logBCJR (\(t_{LOG}\)), maxlogBCJ (\(t_{MAX}\)), LDPC (\(t_{LDPC}\)) and polar (\(t_{Polar}\)) are given in Table 7, using the same approach as in [33]. In the above equations, \(K\) is the frame size, \(r_{b}\) is the data rate, \(I_{Turbo}\) is the number of iterations for SOVA- and the BCJR-based algorithms (4 iterations in our simulations) and \(I_{LDPC}\) is the number of iterations for the LDPC decoder (12 iterations in our simulations). From Table 7, we can deduce that the end-to-end latency for a specific data frame length depends on the distance, the data rate and the number of decoding iterations. As a result, the end-to-end latency varies for all QoS scenarios of Table 2. In Table 8, we present the end-to-end latency in ms for each decoding algorithm per QoS scenario, assuming that we have the maximum typical range and data rate for each QoS scenario. From the results presented in Table 8, it is obvious that SOVA and polar have almost the same latency and are by far the best algorithms. LDPC and maxlogBCJR have similar latencies, which are approximately 1.7-2 times higher than SOVA and polar. Finally, BCJR and logBCJR have the highest delay, as expected, since they are the most complex algorithms. However, the main conclusion taken from the table below is that the end-to-end latency does not exceed the maximum latency specified by the specifications of each QoS scenario. From this conclusion, we can infer that, in terms of latency, the BCJR-based algorithms are suitable for 128-bit frame V2X communications.