\section{Examination Results}%
\label{sec:Examination Results}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Proximal Decoder}%
\label{sub:Ex Proximal Decoder}

\begin{frame}[t]
    \frametitle{Proximal Decoder: Examination Results}
    \begin{itemize}
        \item AWGN Channel - LDPC Code with $n=204, k=102$:
            \vspace{2mm} 
            \begin{figure}[H]
                \centering

                \begin{subfigure}{0.5\textwidth}
                    \centering

                    \begin{tikzpicture}[scale=0.45]
                        \begin{axis}[
                            grid=both,
                            xlabel={SNR (dB)}, ylabel={Bit Error Rate},
                            ymode=log,
                            legend style={at={(0.05,0.05)},anchor=south west},
                            width=11.5cm,
                            height=8cm,
                            ytick={0, 10e-1, 10e-2, 10e-3, 10e-4},
                            xtick={1, 2, 3, 4, 5},
                            ymax=1.2, ymin=0.8e-4,
                        ]
                        \addplot table [x=SNR, y=BER,
                                        col sep=comma, discard if not={gamma}{0.15}]
                            {res/2d_ber_fer_dfr_20433484.csv};
                        \addlegendentry{$\gamma = 0.15$}
                        \addplot table [x=SNR, y=BER,
                                        col sep=comma, discard if not={gamma}{0.01}]
                            {res/2d_ber_fer_dfr_20433484.csv};
                        \addlegendentry{$\gamma = 0.01$}
                        \addplot table [x=SNR, y=BER,
                                        col sep=comma, discard if not={gamma}{0.05}]
                            {res/2d_ber_fer_dfr_20433484.csv};
                        \addlegendentry{$\gamma = 0.05$}
                        \end{axis}
                    \end{tikzpicture}
                
                    \caption{Simulation results for $\omega = 0.05, K=100$}
                    \label{fig:sim_results_prox}
                \end{subfigure}%
                \begin{subfigure}{0.5\textwidth}
                    \centering

                    \includegraphics[scale=0.6]{res/ber_paper}

                    \caption{Results from ``Proximal Decoding for LDPC Codes''}
                    \label{fig:sim_results_prox}
                \end{subfigure}%
                
            \end{figure}

        \item Performance: $2800 \text{ transm.} / s$ - Intel Core i7-7700HQ @ 2.80GHz\\
            ($\sim 10s$ for the shown plot)
    \end{itemize}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
    \frametitle{Proximal Decoder: Choice of $\gamma$}
    
            \begin{figure}[H]
            \centering
            
            \begin{subfigure}[c]{0.5\textwidth}
                \centering
           
                \begin{tikzpicture}[scale=0.52]
                    \begin{semilogyaxis}[xlabel={SNR},ylabel={BER}, grid=both, grid style={line width=.1pt}, legend style={at={(0.05,0.05)},anchor=south west}]
                        \foreach \gamma in {0.01, 0.05, 0.15}{
                            \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{\gamma}] {res/2d_ber_fer_dfr_20433484.csv};
                            \legend{\gamma}
                        }
                        \legend{$\gamma=0.01$, $\gamma=0.05$, $\gamma=0.15$}
                    \end{semilogyaxis}
                \end{tikzpicture}
            \end{subfigure}%
            \begin{subfigure}[c]{0.5\textwidth}
                \centering
            
                \begin{tikzpicture}[scale=0.7]
                    \begin{axis}[view={75}{60},
                                 zmode=log,
                                 xlabel={SNR},
                                 ylabel={$\gamma$},
                                 zlabel={BER}]
                        \addplot3[surf, mesh/rows=17, mesh/cols=10, colormap/viridis] table [col sep=comma, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv};
                        \addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
                        \addplot3[red, line width=1.5] table[col sep=comma, discard if not={gamma}{0.05}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv};
                        \addlegendentry{$\gamma = 0.05$}
                        \addplot3[blue, line width=1.5] table[col sep=comma, discard if not={gamma}{0.01}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv};
                        \addlegendentry{$\gamma = 0.01$}
                        \addplot3[brown, line width=1.5] table[col sep=comma, discard if not={gamma}{0.15}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv};
                        \addlegendentry{$\gamma = 0.15$}
                    \end{axis}
                \end{tikzpicture}
            \end{subfigure}

            \caption{BER for $\omega = 0.05, K=100$}
            \label{fig:ber_3d}
        \end{figure}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t, fragile]
    \frametitle{Proximal Decoder: Frame Error Rate}

    \begin{minipage}{.4\textwidth}
        \centering
        
        \begin{algorithm}[caption={}, label={},
            basicstyle=\fontsize{7.5}{9.5}\selectfont
            ]
$\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$
for $k=0$ to $K-1$ do
    $\boldsymbol{r}^{\left( k+1 \right)} = \boldsymbol{s}^{(k)} - \omega \nabla L \left( \boldsymbol{s}^{(k)}; \boldsymbol{y} \right) $
    Compute $\nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right)$
    $\boldsymbol{s}^{\left( k+1 \right)} = \boldsymbol{r}^{(k+1)} - \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) $
    $\boldsymbol{\hat{x}} = \text{sign}\left( \boldsymbol{s}^{\left( k+1 \right) } \right) $
    If $\boldsymbol{\hat{x}}$ passes the parity check condition, break the loop.
end for
Output $\boldsymbol{\hat{x}}$
        \end{algorithm}
    \end{minipage}%
    \begin{minipage}{.6\textwidth}
        \centering

        \begin{figure}[H]
            \centering
        
            \begin{tikzpicture}[scale=0.45]
                \begin{axis}[
                    grid=both,
                    xlabel={SNR}, ylabel={BER},
                    ymode=log,
                    legend style={at={(0.05,0.05)},anchor=south west},
                    ymax=1.5, ymin=0.8e-4,
                ]
                \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.15$}
                \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.01$}
                \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.05$}
                \end{axis}
            \end{tikzpicture}\\
            \begin{tikzpicture}[scale=0.45]
                \begin{axis}[
                    grid=both,
                    xlabel={SNR}, ylabel={FER},
                    ymode=log,
                    legend style={at={(0.05,0.05)},anchor=south west},
                    ymax=1.5, ymin=0.8e-4,
                ]
                \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.15$}
                \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.01$}
                \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.05$}
                \end{axis}
            \end{tikzpicture}
            \begin{tikzpicture}[scale=0.45]
                \begin{axis}[
                    grid=both,
                    xlabel={SNR}, ylabel={Decoding Failure Rate},
                    ymode=log,
                    legend style={at={(0.05,0.05)},anchor=south west},
                    ymax=1.5, ymin=0.8e-4,
                ]
                \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.15$}
                \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.01$}
                \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
                    {res/2d_ber_fer_dfr_20433484.csv};
                \addlegendentry{$\gamma = 0.05$}
                \end{axis}
            \end{tikzpicture}
        
            \caption{Simulation results for $\omega = 0.05, K=100$}
            \label{fig:simulation_results}
        \end{figure}
    \end{minipage} 
\end{frame}


\begin{frame}[t]
    \frametitle{title}
    \begin{figure}[H]
        \centering
    
        \begin{tikzpicture}[scale=0.45]
            \begin{axis}[
                grid=both,
                xlabel={SNR}, ylabel={BER},
                ymode=log,
                legend style={at={(0.05,0.05)},anchor=south west},
                ymax=1.5, ymin=0.8e-5,
            ]
%            \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
%                {res/2d_ber_fer_dfr_20433484.csv};
%            \addlegendentry{$\gamma = 0.15$}
%            \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
%                {res/2d_ber_fer_dfr_20433484.csv};
%            \addlegendentry{$\gamma = 0.01$}
            \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
                {res/2d_ber_fer_dfr_20433484.csv};
            \addlegendentry{$\gamma = 0.05$}
            \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
                {res/2d_ber_fer_dfr_20433484_hybrid.csv};
            \addlegendentry{hybrid $\gamma = 0.05$}
            \end{axis}
        \end{tikzpicture}\\
        \begin{tikzpicture}[scale=0.45]
            \begin{axis}[
                grid=both,
                xlabel={SNR}, ylabel={FER},
                ymode=log,
                legend style={at={(0.05,0.05)},anchor=south west},
                ymax=1.5, ymin=0.8e-5,
            ]
%            \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
%                {res/2d_ber_fer_dfr_20433484.csv};
%            \addlegendentry{$\gamma = 0.15$}
%            \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
%                {res/2d_ber_fer_dfr_20433484.csv};
%            \addlegendentry{$\gamma = 0.01$}
            \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                {res/2d_ber_fer_dfr_20433484.csv};
            \addlegendentry{$\gamma = 0.05$}
            \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
                {res/2d_ber_fer_dfr_20433484_hybrid.csv};
            \addlegendentry{hybrid $\gamma = 0.05$}
            \end{axis}
        \end{tikzpicture}
        \begin{tikzpicture}[scale=0.45]
            \begin{axis}[
                grid=both,
                xlabel={SNR}, ylabel={Decoding Failure Rate},
                ymode=log,
                legend style={at={(0.05,0.05)},anchor=south west},
                ymax=1.5, ymin=0.8e-5,
            ]
%            \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
%                {res/2d_ber_fer_dfr_20433484.csv};
%            \addlegendentry{$\gamma = 0.15$}
%            \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
%                {res/2d_ber_fer_dfr_20433484.csv};
%            \addlegendentry{$\gamma = 0.01$}
            \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
                {res/2d_ber_fer_dfr_20433484.csv};
            \addlegendentry{$\gamma = 0.05$}
            \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
                {res/2d_ber_fer_dfr_20433484_hybrid.csv};
            \addlegendentry{hybrid $\gamma = 0.05$}
            \end{axis}
        \end{tikzpicture}
    
        \caption{Simulation results for $\omega = 0.05, K=100$}
        \label{fig:simulation_results}
    \end{figure}
    
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{ADMM: Examination Results}%
\label{sub:Ex ADMM}

\begin{frame}[t]
    \frametitle{ADMM}

    \todo{TODO}
\end{frame}