# Visible-Light CDMA Communications Using Inverted Spread Sequences
## 3 MUI Cancellation Schemes with Inverted MPSC
### Inverted MPSC
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Inverted MPSC (\(q=4\))**} & \multicolumn{3}{c}{**Codeword Assignment**} \\ \hline \hline
**Group** & **Codeword** & **EWO** & **Shalaby** & **Modified Liu** \\ \hline \multirow{4}{*}{\(i=0\)} & \(\overline{\epsilon_{0,0}}=(0111\,011\,1011\,011)\) & \(\mathbf{w}^{\prime}_{0,0}=\overline{\epsilon_{0,0}}\) & \(\mathbf{y}_{0}=\epsilon_{0,0}\) & \(\mathbf{w}^{\prime}_{0,1}=(0111\,011\,011\,0111\,011\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{0,1}}=(1011\,1011\,1011\,1011)\) & \(\mathbf{w}^{\prime}_{0,1}=\overline{\epsilon_{0,1}}\) & \(\mathbf{w}^{\prime}_{0,1}=\overline{\epsilon_{0,1}}\) & \(\mathbf{w}^{\prime}_{1,1}=(1011\,1011\,1011\,011\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{0,2}}=(1101\,1101\,1101\,1101)\) & \(\mathbf{w}^{\prime}_{1,0}=\overline{\epsilon_{0,2}}\) & \(\mathbf{w}^{\prime}_{1,1}=\overline{\epsilon_{0,2}}\) & \(\mathbf{w}^{\prime}_{2,1}=(1101\,1101\,1101\,011\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{0,3}}=(1110\,1110\,1110\,1110)\) & \(\mathbf{w}^{\prime}_{1,1}=\overline{\epsilon_{0,3}}\) & \(\mathbf{w}^{\prime}_{2,1}=\overline{\epsilon_{0,3}}\) & \(\mathbf{w}^{\prime}_{3,1}=(1110\,1110\,1110\,111\,1)\) \\ \hline \multirow{4}{*}{\(i=1\)} & \(\overline{\epsilon_{1,0}}=(0111\,1011\,1101\,1110)\) & \(\mathbf{w}^{\prime}_{2,0}=\overline{\epsilon_{1,0}}\) & \(\mathbf{y}_{1}=\mathbf{c}_{1,0}\) & \(\mathbf{w}^{\prime}_{4,1}=(0111\,1011\,1101\,1101\,11)\) \\ \cline{2-6}  & \(\overline{\epsilon_{1,1}}=(1011\,0111\,110\,1101)\) & \(\mathbf{w}^{\prime}_{2,1}=\overline{\epsilon_{1,1}}\) & \(\mathbf{w}^{\prime}_{3,1}=\overline{\epsilon_{1,1}}\) & \(\mathbf{w}^{\prime}_{5,1}=(1011\,011\,1101\,101\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{1,2}}=(1101\,1110\,1011\,011)\) & \(\mathbf{w}^{\prime}_{3,0}=\overline{\epsilon_{1,2}}\) & \(\mathbf{w}^{\prime}_{5,1}=\overline{\epsilon_{1,2}}\) & \(\mathbf{w}^{\prime}_{6,1}=(1101\,110\,011\,1011\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{1,3}}=(1110\,1101\,1011\,011)\) & \(\mathbf{w}^{\prime}_{3,1}=\overline{\epsilon_{1,3}}\) & \(\mathbf{w}^{\prime}_{5,1}=\overline{\epsilon_{1,3}}\) & \(\mathbf{w}^{\prime}_{7,1}=(1110\,1101\,011\,011\,1)\) \\ \hline \multirow{4}{*}{\(i=2\)} & \(\overline{\epsilon_{2,0}}=(0111\,1101\,1101\,011)\) & \(\mathbf{w}^{\prime}_{4,0}=\overline{\epsilon_{2,0}}\) & \(\mathbf{y}_{2}=\mathbf{c}_{2,0}\) & \(\mathbf{w}^{\prime}_{8,1}=(0111\,1101\,1101\,1101\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{2,1}}=(1011\,1110\,101\,0111)\) & \(\mathbf{w}^{\prime}_{4,1}=\overline{\epsilon_{2,1}}\) & \(\mathbf{w}^{\prime}_{6,1}=\overline{\epsilon_{2,1}}\) & \(\mathbf{w}^{\prime}_{9,1}=(1011\,1101\,011\,1101\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{2,2}}=(1101\,011\,1011\,1110)\) & \(\mathbf{w}^{\prime}_{5,0}=\overline{\epsilon_{2,2}}\) & \(\mathbf{w}^{\prime}_{7,1}=\overline{\epsilon_{2,2}}\) & \(\mathbf{w}^{\prime}_{10,1}=(1101\,0111\,1011\,1101\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{2,3}}=(1110\,1011\,11101)\) & \(\mathbf{w}^{\prime}_{5,1}=\overline{\epsilon_{2,3}}\) & \(\mathbf{w}^{\prime}_{8,1}=\overline{\epsilon_{2,3}}\) & \(\mathbf{w}^{\prime}_{11,1}=(1110\,1011\,011\,1101\,1)\) \\ \hline \multirow{4}{*}{\(i=3\)} & \(\overline{\epsilon_{3,0}}=(0111\,1110\,1011\,1101)\) & \(\mathbf{w}^{\prime}_{6,0}=\overline{\epsilon_{3,0}}\) & \(\mathbf{y}_{3}=\mathbf{c}_{3,0}\) & \(\mathbf{w}^{\prime}_{12,1}=(0111\,1101\,1101\,1101\,)\) \\ \cline{2-6}  & \(\overline{\epsilon_{3,1}}=(1011\,1101\,0111\,110)\) & \(\mathbf{w}^{\prime}_{6,1}=\overline{\epsilon_{3,1}}\) & \(\mathbf{w}^{\prime}_{9,1}=\overline{\epsilon_{3,1}}\) & \(\mathbf{w}^{\prime}_{13,1}=(1011\,1101\,0111\,1101\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{3,2}}=(1011\,1011\,110\,0111)\) & \(\mathbf{w}^{\prime}_{7,0}=\overline{\epsilon_{3,2}}\) & \(\mathbf{w}^{\prime}_{10,1}=\overline{\epsilon_{3,2}}\) & \(\mathbf{w}^{\prime}_{14,1}=(1101\,1011\,1110\,0111\,110\,1)\) \\ \cline{2-6}  & \(\overline{\epsilon_{3,3}}=(1110\,0111\,1101\,1011)\) & \(\mathbf{w}^{\prime}_{7,1}=\overline{\epsilon_{3,3}}\) & \(\mathbf{w}^{\prime}_{11,1}=\overline{\epsilon_{3,3}}\) & \(\mathbf{w}^{\prime}_{15,1}=(1110\,0111\,1011\,1101\,1)\) \\ \hline \hline \end{tabular}
\end{table}