# LDPC Coded Massive MIMO Systems
## 5 Numerical Results
### Performance Comparison without Complexity Constraint
\begin{table}
\begin{tabular}{c c c c c|c c c c} \hline \multicolumn{2}{c}{**Channels**} & \multicolumn{3}{c|}{\(\mathbf{16\times 16}\)} & \multicolumn{3}{c}{\(64\times 64\)} \\ \hline \multicolumn{2}{c}{**JDD Strategy**} & \multicolumn{2}{c}{**GIO**} & \multicolumn{2}{c|}{**Proposed**} & \multicolumn{2}{c}{**GIO**} & \multicolumn{2}{c}{**Proposed**} \\ \hline \(d_{v,\text{max}}\) & 3 & 24 & 12 & 24 & 3 & 24 & 12 & 24 \\ \(\lambda_{2}\) & & & 0.30583 & 0.25299 & & & & 0.30486 & 0.25777 \\ \(\lambda_{3}\) & 1.0 & 0.98521 & 0.38338 & 0.33001 & 1.0 & 0.98401 & 0.37864 & 0.32276 \\ \(\lambda_{9}\) & & & & 0.06158 & & & & 0.05931 \\ \(\lambda_{12}\) & & & 0.31079 & & & & & 0.31650 & \\ \(\lambda_{24}\) & & 0.01479 & & & 0.35542 & & & 0.01599 & & 0.36016 \\ \(\rho_{6}\) & 0.99762 & 0.90687 & 0.42250 & & & 0.98853 & 0.89048 & 0.40215 & \\ \(\rho_{7}\) & 0.00238 & 0.09313 & 0.57750 & 0.18756 & 0.01147 & 0.10952 & 0.59785 & 0.21765 \\ \(\rho_{8}\) & & & & 0.81244 & & & & & 0.78235 \\ \(N_{dec}\) & \(N_{g}\) & 1 & 15 & 1 & 15 & 21 & 11 & 18 & 11 & 15 & 15 & 35 & 13 & 29 & 13 \\ \((\frac{E_{b}}{N_{0}})_{dB}^{*}\) & 3.24 & 3.23 & 1.91 & 1.86 & & 3.20 & 3.19 & 1.82 & 1.69 \\ \(\Gamma_{dB}^{*}\) & & & & 1.35 & & & & 1.35 & & & \\ \((\frac{E_{b}}{N_{0}})_{dB}^{*}-\Gamma_{dB}^{*}\) & 1.89 & 1.88 & 0.56 & 0.51 & 1.85 & 1.84 & 0.47 & 0.34 \\ \hline \end{tabular}
\end{table} 
Table 4: Optimal parameters of LDPC codes and JDD strategy for a coded massive MIMO system with \(R=0.5\) over \(16\times 16\) and \(64\times 64\) channels, where GIO JDD with \(N_{g}^{GIO}=15\) was used in a reference system. \begin{table}
\begin{tabular}{c c c|c c|c c} \hline \multicolumn{2}{c}{**Channels**} & \multicolumn{2}{c|}{\(\mathbf{16\times 16}\)} & \multicolumn{3}{c}{\(\mathbf{256\times 256}\)} \\ \hline \multicolumn{2}{c}{**JDD Strategy**} & \multicolumn{2}{c|}{**GIO**} & \multicolumn{2}{c|}{**Proposed**} & \multicolumn{2}{c}{**GIO**} & \multicolumn{2}{c}{**Proposed**} \\ \hline \(d_{v,\text{max}}\) & 3 & 3 & 20 & 3 & 3 & 20 \\ \(\lambda_{2}\) & 0.00339 & 0.18128 & 0.15084 & 0.00772 & 0.18124 & 0.15360 \\ \(\lambda_{3}\) & 0.99661 & 0.81872 & 0.65081 & 0.99228 & 0.81876 & 0.66624 \\ \(\lambda_{20}\) & & & 0.19835 & & & 0.18017 \\ \(\rho_{11}\) & & 0.96429 & & & & 0.96186 & \\ \(\rho_{12}\) & 1.0 & 0.03571 & & & 1.0 & 0.03814 & \\ \(\rho_{13}\) & & & 0.72658 & & & 0.97718 \\ \(\rho_{14}\) & & & 0.27342 & & & 0.02282 \\ \(N_{dec}\) & \(N_{g}\) & 1 & 15 & 11 & 13 & 9 & 13 \\ \((\frac{E_{b}}{N_{0}})_{dB}^{*}\) & 4.20 & 3.66 & 3.65 & 4.10 & 3.45 & 3.44 \\ \(\Gamma_{dB}^{*}\) & & & 3.12 & & & 3.12 & \\ \((\frac{E_{b}}{N_{0}})_{dB}^{*}-\Gamma_{dB}^{*}\) & 1.08 & 0.54 & 0.53 & 0.98 & 0.33 & 0.32 \\ \hline \end{tabular}
\end{table} 
Table 5: Optimal parameters of LDPC codes and JDD strategy for a coded massive MIMO system with \(R=0.75\) over \(16\times 16\) and \(256\times 256\) channels, where GIO JDD with \(N_{g}^{GIO}=15\) was used in a reference system. Figure 8: BER performances of LDPC coded massive MIMO systems equipped with the proposed JDD strategy and with GIO JDD over 16\(\times\)16 channel, where \(N=4096\) and \(N=10,\)240 with \(R=0.5\) and \(R=0.75\), respectively, were considered. Figure 9: BER performances of coded massive MIMO systems with the proposed LDPC codes and JDD strategy and with the conventional LDPC codes and GIO JDD, where \(R=0.5\) and \(N=4096\) over \(16\times 16\) and \(64\times 64\) channels were considered.