\section{Comparison}%
\label{sec:Comparison}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Comparison of Simulation Results}%
\label{sub:Comparison of Simulation Results}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{frame}[t]
%    \frametitle{Comparison: Decoding Performance}
%   
%    \vspace{-0.5cm}
%
%    \begin{itemize}
%        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
%    \end{itemize}
%
%    \begin{figure}[H]
%        \centering
%    
%        \begin{tikzpicture}
%            \begin{axis}[
%                grid=both,
%                xlabel={$E_b / N_0$}, ylabel={BER},
%                ymode=log,
%                legend columns=2,
%                legend style={at={(0.5,-0.45)},anchor=south},
%                ymax=1.5, ymin=3e-8,
%                width=0.45\textwidth,
%                height=0.33\textwidth,
%            ]
%                \addplot[RedOrange, mark=*, line width=1pt]
%                    table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
%                \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
%                    table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
%                
%                \addplot[NavyBlue, line width=1pt, mark=*]
%                    table [x=SNR, y=BER, col sep=comma,
%                           discard if not={mu}{3.0},
%                           %discard if gt={SNR}{4.0}
%                           ]
%                        {res/admm/ber_2d_20433484.csv};
%            
%                \addplot [RoyalPurple, mark=*, line width=1pt]
%                    table [x=SNR, y=BP, col sep=comma] {res/ber_paper.csv};
%            \end{axis}
%        \end{tikzpicture}
%        \begin{tikzpicture}
%            \begin{axis}[
%                grid=both,
%                xlabel={$E_b / N_0$}, ylabel={FER},
%                ymode=log,
%                legend columns=2,
%                legend style={at={(0.5,-0.45)},anchor=south},
%                ymax=1.5, ymin=3e-8,
%                width=0.45\textwidth,
%                height=0.33\textwidth,
%            ]
%
%                \addplot[RedOrange, mark=*, solid, line width=1pt]
%                    table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
%                        {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}]
%                        {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}{4.0}
%                           ]
%                        {res/admm/ber_2d_20433484.csv};
%                \addplot[Black, line width=1pt, mark=*]
%                    table [col sep=comma, x=SNR, y=FER,
%                           %discard if gt={SNR}{3.0}
%                           ]
%                        {res/generic/fer_ml_20433484.csv};
%            \end{axis}
%        \end{tikzpicture}
%        \begin{tikzpicture}
%            \begin{axis}[hide axis,
%                         xmin=10, xmax=50,
%                         ymin=0, ymax=0.4,
%                         legend columns=3,
%                         legend style={draw=white!15!black,legend cell align=left}]
%
%                \addlegendimage{RedOrange, mark=*, line width=1pt}
%                \addlegendentry{Proximal}
%                
%                \addlegendimage{NavyBlue, mark=*, line width=1pt}
%                \addlegendentry{ADMM}
%
%                \addlegendimage{Black, mark=*, line width=1pt}
%                \addlegendentry{ML}
%                
%                \addlegendimage{RedOrange, mark=triangle, densely dashed, line width=1pt}
%                \addlegendentry{Improved ($N$=12)}
%                
%                \addlegendimage{RoyalPurple, mark=*, line width=1pt}
%                \addlegendentry{BP}
%            \end{axis}
%        \end{tikzpicture}
%    \end{figure}
%
%    \smallskip
%    \smallskip
%    \smallskip
%    
%    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
%        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
%\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Theoretical Comparison}%
\label{sub:Theoretical Comparison}