\appendix

\section{Proximal Decoding Time Complexity}%
\label{app:Proximal Decoding Time Complexity}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
    \frametitle{Proximal Decoding: Time Complexity}
   
    \begin{figure}[H]
        \centering
    
        \begin{tikzpicture}[scale=0.7]
            \begin{axis}[
                grid=both,
                xlabel={$n$}, ylabel={time per frame (s)},
                legend style={at={(0.05,0.77)},anchor=south west},
            ]
                \addplot[only marks, red] table [col sep=comma,
                                             x=n, y=spf] {res/fps_vs_n_proximal.csv};
                \addlegendentry{proximal}

                \addplot[only marks, blue] table [col sep=comma,
                                             x=n, y=spf] {res/fps_vs_n_hybrid.csv};
                \addlegendentry{hybrid prox \& ML ($\SI{12}{\bit}$)}
            \end{axis}
        \end{tikzpicture}
    
        \caption{Time Complexity of Proximal Decoding and Modified Implementation\footnotemark}
        \label{fig:fps_vs_n}
    \end{figure}
    
    \footnotetext{The points shown were calculated by evaluating the metadata
                  of BER simulation results from the following codes:
                  BCH $\left( 31, 11 \right)$;
                  BCH $\left( 31, 26 \right) $;
                  \cite[\text{96.3.965; 204.33.484;
                        204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
              }

\end{frame}