\appendix

\section{Supplementary Slides}%
\label{app:Supplementary Slides}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
    \frametitle{Proximal Decoding: Choice of $\gamma$}
    
    \captionsetup[subfigure]{font=footnotesize}

    \hspace*{-0.4cm}
    \begin{minipage}[c]{0.9\textwidth}
        \centering
    
        \begin{figure}[H]
            \vspace*{-0.7cm}
            \centering
        
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
            
                \begin{tikzpicture}[scale=0.8]
                    \begin{axis}[
                        grid=both,
                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
                        ymode=log,
                        ymax=1.5, ymin=8e-5,
                        width=1.2\textwidth,
                        height=0.85\textwidth,
                    ]

                        \addplot[RedOrange, line width=1pt, mark=*, solid]
                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                                {res/proximal/2d_ber_fer_dfr_963965.csv};
                        \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
                            table [x=SNR, y=FER, col sep=comma,
                                   discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
                                {res/hybrid/2d_ber_fer_dfr_963965.csv};
                        \addplot[NavyBlue, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
                                %{res/hybrid/2d_ber_fer_dfr_963965.csv};
                                {res/admm/ber_2d_963965.csv};
                        \addplot[Black, line width=1pt, mark=*]
                            table [col sep=comma, x=SNR, y=FER,]
                                {res/generic/fer_ml_9633965.csv};
                    \end{axis}
                \end{tikzpicture}

                \vspace*{-1mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
                    \cite[\text{96.3.965}]{mackay_enc}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
            
                \begin{tikzpicture}[scale=0.8]
                    \begin{axis}[
                        grid=both,
                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
                        ymode=log,
                        ymax=1.5, ymin=8e-5,
                        width=1.2\textwidth,
                        height=0.85\textwidth,
                    ]
                
                        \addplot[RedOrange, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma,
                                   discard if not={gamma}{0.05},
                                   discard if gt={SNR}{5.5}]
                                {res/proximal/2d_ber_fer_dfr_20433484.csv};
                        \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
                            table [x=SNR, y=FER, col sep=comma,
                                   discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
                                {res/hybrid/2d_ber_fer_dfr_20433484.csv};
                        \addplot[NavyBlue, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma,
                                   discard if not={mu}{3.0},
                                   discard if gt={SNR}{5.5}]
                                {res/admm/ber_2d_20433484.csv};
                        \addplot[Black, line width=1pt, mark=*]
                            table [col sep=comma, x=SNR, y=FER,
                                   discard if gt={SNR}{5.5}]
                                {res/generic/fer_ml_20433484.csv};
                    \end{axis}
                \end{tikzpicture}
            
                \vspace*{-1mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
                    \cite[\text{204.33.484}]{mackay_enc}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
            
                \begin{tikzpicture}[scale=0.8]
                    \begin{axis}[
                        grid=both,
                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
                        ymode=log,
                        ymax=1.5, ymin=8e-5,
                        width=1.2\textwidth,
                        height=0.85\textwidth,
                    ]
                
                        \addplot[RedOrange, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                                {res/proximal/2d_ber_fer_dfr_40833844.csv};
                        \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
                            table [x=SNR, y=FER, col sep=comma,
                                   discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
                                {res/hybrid/2d_ber_fer_dfr_40833844.csv};
                        \addplot[NavyBlue, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
                                {res/admm/ber_2d_40833844.csv};
                    \end{axis}
                \end{tikzpicture}

                \vspace*{-1mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
                    \cite[\text{408.33.844}]{mackay_enc}}
            \end{subfigure}%

            \begin{subfigure}[t]{0.33\textwidth}
                \centering
            
                \begin{tikzpicture}[scale=0.8]
                    \begin{axis}[
                        grid=both,
                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
                        ymode=log,
                        ymax=1.5, ymin=8e-5,
                        width=1.2\textwidth,
                        height=0.85\textwidth,
                    ]
                
                        \addplot[RedOrange, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                                {res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
                        \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
                            table [x=SNR, y=FER, col sep=comma,
                                   discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
                                {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
                        \addplot[NavyBlue, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
                                {res/admm/ber_2d_bch_31_26.csv};
                        \addplot[Black, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma,
                                   discard if gt={SNR}{5.5},
                                   discard if lt={SNR}{1},
                                   ]
                                {res/generic/fer_ml_bch_31_26.csv};
                    \end{axis}
                \end{tikzpicture}
            
                \vspace*{-1mm}
            
                \caption{BCH code with $n=31, k=26$}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
            
                \begin{tikzpicture}[scale=0.8]
                    \begin{axis}[
                        grid=both,
                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
                        ymode=log,
                        ymax=1.5, ymin=8e-5,
                        width=1.2\textwidth,
                        height=0.85\textwidth,
                    ]
                
                        \addplot[RedOrange, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                                {res/proximal/2d_ber_fer_dfr_20455187.csv};
                        \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                                {res/hybrid/2d_ber_fer_dfr_20455187.csv};
                        \addplot[NavyBlue, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
                                {res/admm/ber_2d_20455187.csv};
                    \end{axis}
                \end{tikzpicture}
            
                \vspace*{-1mm}
            
                \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
                    \cite[\text{204.55.187}]{mackay_enc}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
            
                \begin{tikzpicture}[scale=0.8]
                    \begin{axis}[
                        grid=both,
                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
                        ymode=log,
                        ymax=1.5, ymin=8e-5,
                        width=1.2\textwidth,
                        height=0.85\textwidth,
                    ]
                
                        \addplot[RedOrange, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                                {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
                        \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
                            table [x=SNR, y=FER, col sep=comma,
                                   discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
                                {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv};
                        \addplot[NavyBlue, line width=1pt, mark=*]
                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
                                {res/admm/ber_2d_pegreg252x504.csv};
                    \end{axis}
                \end{tikzpicture}
            
                \vspace*{-1mm}
                
                \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
                    \cite[\text{PEGReg252x504}]{mackay_enc}}
            \end{subfigure}%
        \end{figure}
    \end{minipage}%
    \begin{minipage}[c]{0.1\textwidth}
        \centering
    
        \begin{figure}
            \centering
            \vspace*{-1.2cm}
            \hspace*{2mm}
            \begin{tikzpicture}[scale=0.8]
                \begin{axis}[hide axis,
                             xmin=10, xmax=50,
                             ymin=0, ymax=0.4,
                             legend columns=1,
                             legend style={draw=white!15!black}]
                    \addlegendimage{RedOrange, line width=1pt, mark=*, solid}
                    \addlegendentry{Proximal}

                    \addlegendimage{RedOrange, line width=1pt, mark=triangle*, densely dashed}
                    \addlegendentry{Improved}
                   
                    \addlegendimage{NavyBlue, line width=1pt, mark=*}
                    \addlegendentry{ADMM}

%                    \addlegendimage{RoyalPurple, line width=1pt, mark=*}
%                    \addlegendentry{BP}

                    \addlegendimage{Black, line width=1pt, mark=*}
                    \addlegendentry{ML}
                    
%                    \addlegendimage{PineGreen, line width=1pt, mark=triangle*, solid}
%                    \addlegendentry{ML}
                \end{axis}
            \end{tikzpicture}
        \end{figure}
    \end{minipage}

\end{frame}