# 3 GPP 5G V2X Error Correction Coding for Various Propagation Environments: A QoS Approach
## 5 Simulation Results
### Maximum Number of Vehicles  
The results derived from Table 8 can be used in order to find the maximum number of vehicles that can communicate simultaneously in a worst-case scenario, i.e., achieving the minimum end-to-end latency at the maximum typical range for each QoS scenario as presented in Table 2. First, we determine the maximum number of vehicles that can be in the maximum typical range of each QoS scenario. For this purpose, we use the road configuration parameters for urban and highway traffic [9] (p. 36), i.e., we assume that there are four and six lanes in total in urban and highway traffic, respectively. Additionally, we assume that there are only Type 2 vehicles [9] (p. 10), i.e., 5 m length vehicles. Finally, \begin{table}
\begin{tabular}{c c} \hline \hline
**Coding Scheme** & **End-to-End Latency** \\ \hline SOVA & \(t_{SOVA}=t_{prop}+\frac{K}{r_{b}}\times I_{Turbo}\) \\ \hline BCJR & \(t_{BCJR}=t_{prop}+3\times\frac{K}{r_{b}}\times I_{Turbo}\) \\ \hline logBCJR & \(t_{LOG}=t_{prop}+2.8\times\frac{K}{r_{b}}\times I_{Turbo}\) \\ \hline maxlogBCJR & \(t_{MAX}=t_{prop}+1.8\times\frac{K}{r_{b}}\times I_{Turbo}\) \\ \hline LDPC & \(t_{LDPC}=t_{prop}+0.57\times\frac{K}{r_{b}}\times I_{LDPC}\) \\ \hline Polar & \(t_{polar}=t_{prop}+0.47\times log_{2}N\times\frac{K}{r_{b}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: End-to-end latency equation for each decoding scheme. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**QoS** & **Maximum** & **BCJR** & **logBCJR** & **maxlogBCJR** & **SOVA** & **LDPC** & **Polar** \\ \hline Q1 & 1000 & 16.00 & 14.93 & 9.60 & 5.33 & 9.12 & 5.38 \\ \hline Q2 & 1000 & 0.06 & 0.06 & 0.04 & 0.02 & 0.04 & 0.02 \\ \hline Q3 & 100 & 0.31 & 0.29 & 0.19 & 0.10 & 0.18 & 0.10 \\ \hline Q4 & 1000 & 153.60 & 143.36 & 92.16 & 51.20 & 87.55 & 51.65 \\ \hline Q5 & 1000 & 0.77 & 0.72 & 0.46 & 0.26 & 0.44 & 0.26 \\ \hline Q6 & 20 & 0.06 & 0.06 & 0.04 & 0.02 & 0.04 & 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: End-to-end latency (in ms) for each decoding algorithm and QoS scenario. we assume that the distance between the rear bumper of a vehicle and the front bumper of the following vehicle is the minimum possible, i.e., 2 m, according to [9] (p. 10). Taking these parameters into consideration, we determine the maximum number of vehicles using the equation:  
\[max\{Vehicles\}=\frac{Range}{7}\times Number\_of\_lanes. \tag{6}\]  
In Table 9, we present the maximum numbers of vehicles for each QoS scenario in the maximum possible range. These values will be used as an upper bound in the analysis that will follow in this section. Using the results of Tables 8 and 9, we can find the maximum number of vehicles that can communicate simultaneously without exceeding the maximum end-to-end latency requirements for each QoS scenario and decoding algorithm. The results are shown in Tables 10 and 11 for urban and highway environments, respectively. These results clearly show that scenarios Q1, Q2, Q3 and Q5 achieve the maximum possible number of vehicles of Table 9, whereas scenarios Q1 and Q4 fail to achieve the upper bound of Table 9.  
In scenarios Q1 and Q4, the superiority of the SOVA and polar decoding schemes becomes apparent, since the number of vehicles that can communicate without exceeding \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**QoS Scenario** & **Maximum Latency** & **BCJR** & **logBCJR** & **maxlogBCJR** & **SOVA** & **LDPC** & **Polar** \\ \hline Q1 & 1000 & 62 & 66 & 104 & 187 & 109 & 185 \\ \hline Q2 & 1000 & 171 & 171 & 171 & 171 & 171 \\ \hline Q3 & 100 & 321 & 321 & 321 & 321 & 321 \\ \hline Q4 & 1000 & 6 & 6 & 10 & 19 & 11 & 19 \\ \hline Q5 & 1000 & 428 & 428 & 428 & 428 & 428 \\ \hline Q6 & 20 & 325 & 348 & 428 & 428 & 428 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Maximum number of vehicles achieving maximum end-to-end latency requirements for each decoding algorithm and QoS scenario in a highway environment.