# Visible-Light CDMA Communications Using Inverted Spread Sequences
## 2 Optical CDMA with MUI Cancellation
### Conventional EWO Scheme
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{2}{c}{**MPSC (\(q=4\))**} & \multicolumn{3}{c}{**Codeword Assignment**} \\ \hline \multicolumn{2}{c}{**Group**} & **Codeword** & **EWO** & **Shalaby** & **Liu** \\ \hline \multirow{6}{*}{\(i=0\)} & \(\mathbf{c}_{0,0}=(1000\,1000\,1000\,1000)\) & \(\mathbf{w}_{0,0}=\mathbf{c}_{0,0}\) & \(\mathbf{y}_{0}=\mathbf{c}_{0,0}\) & \(\mathbf{w}_{0,1}=(1000\,1000\,1000\,1000\,1000)\) \\ \cline{2-5}  & \(\mathbf{c}_{0,1}=(0100\,0100\,0100\,0100)\) & \(\mathbf{w}_{0,1}=\mathbf{c}_{0,1}\) & \(\mathbf{w}_{0,1}=\mathbf{c}_{0,1}\) & \(\mathbf{w}_{1,1}=(0100\,0100\,0100\,1000)\) \\ \cline{2-5}  & \(\mathbf{c}_{0,2}=(0010\,0010\,0010\,0010)\) & \(\mathbf{w}_{1,0}=\mathbf{c}_{0,2}\) & \(\mathbf{w}_{1,1}=\mathbf{c}_{0,2}\) & \(\mathbf{w}_{2,1}=(0010\,0010\,0010\,1000)\) \\ \cline{2-5}  & \(\mathbf{c}_{0,3}=(0001\,0001\,0001\,0001)\) & \(\mathbf{w}_{1,1}=\mathbf{c}_{0,3}\) & \(\mathbf{w}_{2,1}=\mathbf{c}_{0,3}\) & \(\mathbf{w}_{3,1}=(0001\,0001\,0001\,1000)\) \\ \hline \multirow{6}{*}{\(i=1\)} & \(\mathbf{c}_{1,0}=(1000\,0100\,0010\,0001)\) & \(\mathbf{w}_{2,0}=\mathbf{c}_{1,0}\) & \(\mathbf{y}_{1}=\mathbf{c}_{1,0}\) & \(\mathbf{w}_{4,1}=(1000\,0100\,0010\,0010)\) \\ \cline{2-5}  & \(\mathbf{c}_{1,1}=(0100\,1000\,0001\,0010)\) & \(\mathbf{w}_{2,1}=\mathbf{c}_{1,1}\) & \(\mathbf{w}_{3,1}=\mathbf{c}_{1,1}\) & \(\mathbf{w}_{5,1}=(0100\,1000\,0001\,0010)\) \\ \cline{2-5}  & \(\mathbf{c}_{1,2}=(0010\,0001\,1000\,0100)\) & \(\mathbf{w}_{3,0}=\mathbf{c}_{1,2}\) & \(\mathbf{w}_{5,1}=\mathbf{c}_{1,2}\) & \(\mathbf{w}_{6,1}=(0010\,0001\,1000\,0100)\) \\ \cline{2-5}  & \(\mathbf{c}_{1,3}=(0001\,0010\,0100\,1000)\) & \(\mathbf{w}_{3,1}=\mathbf{c}_{1,3}\) & \(\mathbf{w}_{5,1}=\mathbf{c}_{1,3}\) & \(\mathbf{w}_{7,1}=(0001\,0010\,0100\,1000)\) \\ \hline \multirow{6}{*}{\(i=2\)} & \(\mathbf{c}_{2,0}=(1000\,0010\,0001\,0100)\) & \(\mathbf{w}_{4,0}=\mathbf{c}_{2,0}\) & \(\mathbf{y}_{2}=\mathbf{c}_{2,0}\) & \(\mathbf{w}_{8,1}=(1000\,0010\,0001\,0100\,0100)\) \\ \cline{2-5}  & \(\mathbf{c}_{2,1}=(0100\,0001\,0010\,1000)\) & \(\mathbf{w}_{4,1}=\mathbf{c}_{2,1}\) & \(\mathbf{w}_{6,1}=\mathbf{c}_{2,1}\) & \(\mathbf{w}_{9,1}=(0100\,001\,0010\,1000\,0100)\) \\ \cline{2-5}  & \(\mathbf{c}_{2,2}=(0010\,1000\,0100\,0001)\) & \(\mathbf{w}_{5,0}=\mathbf{c}_{2,2}\) & \(\mathbf{w}_{7,1}=\mathbf{c}_{2,2}\) & \(\mathbf{w}_{10,1}=(0010\,1000\,010\,0001\,0100)\) \\ \cline{2-5}  & \(\mathbf{c}_{2,3}=(0001\,0100\,1000\,0010)\) & \(\mathbf{w}_{5,1}=\mathbf{c}_{2,3}\) & \(\mathbf{w}_{8,1}=\mathbf{c}_{2,3}\) & \(\mathbf{w}_{11,1}=(0001\,0100\,1000\,0010)\) \\ \hline \multirow{6}{*}{\(i=3\)} & \(\mathbf{c}_{3,0}=(1000\,0001\,0100\,0010)\) & \(\mathbf{w}_{6,0}=\mathbf{c}_{3,0}\) & \(\mathbf{y}_{3}=\mathbf{c}_{3,0}\) & \(\mathbf{w}_{12,1}=(1000\,0001\,0100\,010)\) \\ \cline{2-5}  & \(\mathbf{c}_{3,1}=(0100\,0010\,1000\,0001)\) & \(\mathbf{w}_{6,1}=\mathbf{c}_{3,1}\) & \(\mathbf{w}_{9,1}=\mathbf{c}_{3,1}\) & \(\mathbf{w}_{13,1}=(0100\,0010\,1000\,0001\,010)\) \\ \cline{1-1} \cline{2-5}  & \(\mathbf{c}_{3,2}=(0010\,0100\,0001\,1000)\) & \(\mathbf{w}_{7,0}=\mathbf{c}_{3,2}\) & \(\mathbf{w}_{10,1}=\mathbf{c}_{3,2}\) & \(\mathbf{w}_{14,1}=(0010\,010\,0001\,1000\,0100)\) \\ \cline{1-1} \cline{2-5}  & \(\mathbf{c}_{3,3}=(0001\,1000\,0010\,0100)\) & \(\mathbf{w}_{7,1}=\mathbf{c}_{3,3}\) & \(\mathbf{w}_{11,1}=\mathbf{c}_{3,3}\) & \(\mathbf{w}_{15,1}=(0001\,1000\,0010\,0100)\) \\ \hline \end{tabular}
\end{table} 
Table 2: Codeword assignment for MPSC (\(q=4\)). Figure 2: Block diagram of the \(k\)th user’s encoder and decoder. (**a**) Block diagram of the encoder, (**b**) Block diagram of the decoder. is transmitted.