## 5 Simulation Results and Discussion
### Convergence Speed Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(\mathbf{E_{b}/N_{0}}\) (dB) & **2.8** & **3** & **3.2** & **3.4** & **3.6** & **3.8** & **4** \\ \hline \multirow{4}{*}{\(I_{avg}\)} & RC-FAID [11] & 12.76 & 11.65 & 10.26 & 9.01 & 7.99 & 7.21 & 6.59 \\  & RC-MIM-QMS [14] & 12.25 & 11.12 & 9.66 & 8.53 & 7.61 & 6.88 & 6.33 \\  & Conventional QSMS [27] & 12.33 & 10.37 & 8.07 & 6.2 & 4.66 & 3.77 & 3.16 \\  & RD-MIM-QSMS [15] & 8.16 & 6.48 & 5.34 & 4.53 & 3.96 & 3.54 & 3.21 \\  & RC-MIM-QSMS & 7.63 & 6.01 & 4.9 & 4.16 & 3.64 & 3.27 & 2.97 \\ \hline \multirow{4}{*}{\(I_{avg}\)} & \(\mathbf{E_{b}/N_{0}}\) (dB) & **3.6** & **3.8** & **4** & **4.2** & **4.4** & **4.6** & **4.8** \\ \cline{2-10}  & RC-FAID [11] & 10.73 & 9.42 & 8.25 & 7.35 & 6.64 & 6.11 & 5.68 \\  & RC-MIM-QMS [14] & 10.84 & 9.49 & 8.33 & 7.44 & 6.72 & 6.17 & 5.72 \\  & Conventional QSMS [27] & 8.34 & 6.35 & 4.87 & 3.77 & 3.13 & 2.71 & 2.44 \\  & RD-MIM-QSMS [15] & 5.84 & 4.76 & 4.03 & 3.53 & 3.18 & 2.91 & 2.69 \\  & RC-MIM-QSMS & 6.27 & 5 & 4.21 & 3.63 & 3.22 & 2.91 & 2.67 \\ \hline \multirow{4}{*}{\(I_{avg}\)} & \(\mathbf{E_{b}/N_{0}}\) (dB) & **4.4** & **4.6** & **4.8** & **5** & **5.2** & **5.4** & **5.6** \\ \cline{2-10}  & RC-FAID [11] & 8.52 & 7.49 & 6.62 & 5.96 & 5.48 & 5.1 & 4.79 \\ \cline{1-1}  & RC-MIM-QMS [14] & 9.82 & 8.58 & 7.51 & 6.71 & 6.11 & 5.64 & 5.27 \\ \cline{1-1}  & Conventional QSMS [27] & 6.28 & 4.61 & 3.64 & 2.95 & 2.57 & 2.33 & 2.17 \\ \cline{1-1}  & RD-MIM-QSMS [15] & 4.52 & 3.71 & 3.2 & 2.84 & 2.59 & 2.4 & 2.26 \\ \cline{1-1}  & RC-MIM-QSMS & 5.81 & 4.7 & 3.96 & 3.44 & 3.07 & 2.79 & 2.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average number of iterations \(I_{\text{avg}}\) of different LDPC decoders with \(q_{m}=4\) for the 5G LDPC codes. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(\mathbf{E_{b}/N_{0}}\) (dB) & **2** & **2.2** & **2.4** & **2.6** & **2.8** & **3** & **3.2** \\ \hline \multirow{4}{*}{\(I_{\text{avg}}\)} & RC-FAID [11] & 13.01 & 11.49 & 9.82 & 8.22 & 7.05 & 6.15 & 5.45 \\  & RC-MIM-QMS [14] & 13.02 & 11.35 & 9.75 & 8.12 & 6.94 & 6.06 & 5.38 \\  & Conventional QSMS [27] & 13.04 & 10.89 & 7.76 & 5.62 & 4.19 & 3.46 & 2.99 \\  & RD-MIM-QSMS [15] & 9.43 & 7.41 & 5.79 & 4.8 & 4.14 & 3.65 & 3.26 \\  & RC-MIM-QSMS & 9.24 & 7.18 & 5.5 & 4.49 & 3.83 & 3.37 & 3.01 \\ \hline \multirow{4}{*}{\(I_{\text{avg}}\)} & \(\mathbf{E_{b}/N_{0}}\) (dB) & **2.4** & **2.6** & **2.8** & **3** & **3.2** & **3.4** & **3.6** \\ \cline{1-1} \cline{2-10}  & RC-FAID [11] & 13.03 & 11.02 & 9.07 & 7.41 & 6.19 & 5.28 & 4.61 \\ \cline{1-1}  & RC-MIM-QMS [14] & 13.17 & 11.11 & 9.14 & 7.47 & 6.23 & 5.32 & 4.64 \\ \cline{1-1}  & Conventional QSMS [27] & 12.09 & 9.05 & 6.4 & 4.52 & 3.49 & 2.9 & 2.52 \\ \cline{1-1}  & RD-MIM-QSMS [15] & 9.95 & 7.38 & 5.41 & 4.25 & 3.52 & 3.03 & 2.66 \\ \cline{1-1}  & RC-MIM-QSMS & 10.03 & 7.52 & 5.49 & 4.25 & 3.5 & 3.01 & 2.66 \\ \hline \multirow{4}{*}{\(I_{\text{avg}}\)} & \(\mathbf{E_{b}/N_{0}}\) (dB) & **3.2** & **3.4** & **3.6** & **3.8** & **4** & **4.2** & **4.4** \\ \cline{1-1} \cline{2-10}  & RC-FAID [11] & 10.71 & 8.3 & 6.46 & 5.09 & 4.2 & 3.58 & 3.11 \\ \cline{1-1} \cline{2-10}  & RC-MIM-QMS [14] & 11.28 & 8.79 & 6.85 & 5.39 & 4.43 & 3.76 & 3.25 \\ \cline{1-1}  & Conventional QSMS [27] & 10.36 & 7.12 & 4.83 & 3.37 & 2.66 & 2.27 & 2.02 \\ \cline{1-1}  & RD-MIM-QSMS [15] & 7.82 & 5.48 & 3.95 & 3.09 & 2.61 & 2.3 & 2.07 \\ \cline{1-1}  & RC-MIM-QSMS & 8.32 & 5.85 & 4.28 & 3.29 & 2.75 & 2.41 & 2.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average number of iterations \(I_{\text{avg}}\) of different LDPC decoders with \(q_{m}=4\) for the 802.11n LDPC codes.