712 lines
34 KiB
TeX
712 lines
34 KiB
TeX
\section{Examination Results}%
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\label{sec:Examination Results}
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\subsection{Proximal Decoding}%
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\label{sub:Ex Proximal Decoding}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{Proximal Decoding: Bit Error Rate and Performance}
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\begin{itemize}
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\item Comparison of simulation
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\footnote{(3,6) regular LDPC Code with $n=204, k=102$
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\cite[Code: 204.33.484]{mackay_enc}}
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with results of Wadayama and Takabe
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\begin{figure}[H]
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\centering
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\begin{subfigure}{0.5\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.45]
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\begin{axis}[
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grid=both,
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xlabel={$E_b / N_0$ (dB)}, ylabel={Bit Error Rate},
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ymode=log,
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legend style={at={(0.05,0.05)},anchor=south west},
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width=11.5cm,
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height=8cm,
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ytick={0, 1e-1, 1e-2, 1e-3, 1e-4},
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xtick={1, 2, 3, 4, 5},
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ymax=1.2, ymin=0.8e-4,
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xmin=0.9, xmax=5.6,
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]
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\addplot table [x=SNR, y=BER,
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col sep=comma, discard if not={gamma}{0.15}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.15$}
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\addplot table [x=SNR, y=BER,
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col sep=comma, discard if not={gamma}{0.01}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot table [x=SNR, y=BER,
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col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.05$}
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\end{axis}
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\end{tikzpicture}
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\caption{Simulation results for $\omega = 0.05, K=100$}
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\label{fig:sim_results_prox}
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\end{subfigure}%
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\begin{subfigure}{0.5\textwidth}
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\centering
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\includegraphics[scale=0.6]{res/ber_paper}
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\caption{Results from ``Proximal Decoding for LDPC Codes''}
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\label{fig:paper_results_prox}
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\end{subfigure}%
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\end{figure}
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\item $\mathcal{O}\left(n \right) $ time complexity - same as BP;
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Only multiplication and addition necessary \cite{proximal_paper}
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\item Measured Performance: $\sim\SI{10000}{frames / \second}$
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- Intel Core i7-7700HQ @ 2.80GHz; $n=204$
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\end{itemize}
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\vspace{3mm}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{Proximal Decoding: Choice of $\gamma$}
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\setcounter{footnote}{0}
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\begin{itemize}
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\item Comparison of simulation
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\footnote{(3,6) regular LDPC Code with $n=204, k=102$
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\cite[Code: 204.33.484]{mackay_enc}}
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results for different values of $\gamma$
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\end{itemize}
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\begin{figure}[H]
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\centering
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\begin{subfigure}[c]{0.5\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.52]
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\begin{semilogyaxis}[xlabel={$E_b / N_0$ (dB)}, ylabel={BER},
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grid=both, grid style={line width=.1pt},
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legend style={at={(0.05,0.05)},anchor=south west},
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ymin=3e-7, ymax=1.5,]
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\foreach \gamma in {0.01, 0.05, 0.15}{
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\addplot table [x=SNR, y=BER,
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col sep=comma, discard if not={gamma}{\gamma}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\legend{\gamma}
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}
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\legend{$\gamma=0.01$, $\gamma=0.05$, $\gamma=0.15$}
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\end{semilogyaxis}
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\end{tikzpicture}
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\end{subfigure}%
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\begin{subfigure}[c]{0.5\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.55]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={$E_b / N_0$ (dB)},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf,
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mesh/rows=17, mesh/cols=14,
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colormap/viridis] table [col sep=comma,
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table [col sep=comma,
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discard if not={gamma}{0.05},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table [col sep=comma,
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discard if not={gamma}{0.01},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table [col sep=comma,
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discard if not={gamma}{0.15},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\caption{BER for $\omega = 0.05, K=100$}
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\label{fig:ber_3d}
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\end{figure}
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\begin{itemize}
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\item Not great benefit in finding the optimal value for $\gamma$
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\end{itemize}
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\vspace{3mm}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{Proximal Decoding: Choice of $\gamma$}
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\begin{figure}[H]
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\vspace*{-0.5cm}
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\centering
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\begin{subfigure}[c]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.35]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={$E_b / N_0$ (dB)},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf,
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mesh/rows=17, mesh/cols=10,
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colormap/viridis] table [col sep=comma,
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_963965.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.05},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_963965.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.01},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_963965.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.15},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_963965.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$\\ \cite[Code: 96.3.965]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[c]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.35]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={$E_b/N_0$ (dB)},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf,
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mesh/rows=17, mesh/cols=14,
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colormap/viridis] table [col sep=comma,
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20433484.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.05},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20433484.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.01},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20433484.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.15},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20433484.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$\\ \cite[Code: 204.33.484]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[c]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.35]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={$E_b / N_0$ (dB)},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf,
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mesh/rows=17, mesh/cols=10,
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colormap/viridis] table [col sep=comma,
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_40833844.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.05},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_40833844.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.01},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_40833844.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.15},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_40833844.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$\\ \cite[Code: 408.33.844]{mackay_enc}}
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\end{subfigure}
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\begin{subfigure}[c]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.35]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={$E_b / N_0$ (dB)},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf,
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mesh/rows=17, mesh/cols=10,
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colormap/viridis] table [col sep=comma,
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_bch_31_26.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.05},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_bch_31_26.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.01},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_bch_31_26.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.15},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_bch_31_26.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\caption{BCH code with $n=31, k=26$}
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\end{subfigure}%
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\begin{subfigure}[c]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.35]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={$E_b / N_0$ (dB)},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf,
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mesh/rows=17, mesh/cols=10,
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colormap/viridis] table [col sep=comma,
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20455187.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.05},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20455187.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.01},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20455187.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.15},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_20455187.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$\\ \cite[Code: 204.55.187]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[c]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.35]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={$E_b / N_0$ (dB)},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf,
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mesh/rows=17, mesh/cols=10,
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colormap/viridis] table [col sep=comma,
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_pegreg252x504.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.05},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_pegreg252x504.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.01},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_pegreg252x504.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma,
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discard if not={gamma}{0.15},
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x=SNR, y=gamma, z=BER]
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{res/2d_ber_fer_dfr_pegreg252x504.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\caption{LDPC code (Progressive Edge Growth Construction) with $n=504, k=252$\\ \cite[Code: PEGReg252x504]{mackay_enc}}
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\end{subfigure}%
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\end{figure}
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\end{frame}
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t, fragile]
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\frametitle{Proximal Decoding: Frame Error Rate}
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\setcounter{footnote}{0}
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\begin{itemize}
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\item Comparison of simulated
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\footnote{(3,6) regular LDPC Code with $n=204, k=102$
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\cite[Code: 204.33.484]{mackay_enc}}
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BER and FER
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\end{itemize}
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\begin{minipage}{.4\textwidth}
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\centering
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\begin{figure}[htpb]
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\centering
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\begin{algorithm}[caption={}, label={},
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basicstyle=\fontsize{7.5}{9.5}\selectfont
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]
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$\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$
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for $k=0$ to $K-1$ do
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$\boldsymbol{r}^{\left( k+1 \right)} = \boldsymbol{s}^{(k)} - \omega \nabla L \left( \boldsymbol{s}^{(k)}; \boldsymbol{y} \right) $
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Compute $\nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right)$
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$\boldsymbol{s}^{\left( k+1 \right)} = \boldsymbol{r}^{(k+1)} - \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) $
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$\boldsymbol{\hat{x}} = \text{sign}\left( \boldsymbol{s}^{\left( k+1 \right) } \right) $
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If $\boldsymbol{\hat{x}}$ passes the parity check condition, break the loop.
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end for
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Output $\boldsymbol{\hat{x}}$
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\end{algorithm}
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\caption{Proximal decoding algorithm \cite{proximal_paper}}
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\end{figure}
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\end{minipage}%
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\begin{minipage}{.6\textwidth}
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\centering
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\begin{figure}[H]
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\vspace*{-8mm}
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\centering
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\begin{tikzpicture}[scale=0.42]
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\begin{axis}[
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grid=both,
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xlabel={$E_b / N_0$ (dB)}, ylabel={BER},
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ymode=log,
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legend style={at={(0.05,0.05)},anchor=south west},
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ymax=1.5, ymin=3e-7,
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]
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\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.15$}
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\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
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{res/2d_ber_fer_dfr_20433484_proximal.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_proximal.csv};
|
|
\addlegendentry{$\gamma = 0.05$}
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\begin{tikzpicture}[scale=0.42]
|
|
\begin{axis}[
|
|
grid=both,
|
|
xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
|
|
ymode=log,
|
|
legend style={at={(0.05,0.05)},anchor=south west},
|
|
ymax=1.5, ymin=3e-7,
|
|
]
|
|
\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
|
|
{res/2d_ber_fer_dfr_20433484_proximal.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_proximal.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_proximal.csv};
|
|
\addlegendentry{$\gamma = 0.05$}
|
|
\end{axis}
|
|
\end{tikzpicture}\\
|
|
\begin{tikzpicture}[scale=0.42]
|
|
\begin{axis}[
|
|
grid=both,
|
|
xlabel={$E_b / N_0$ (dB)}, ylabel={Decoding Failure Rate},
|
|
ymode=log,
|
|
legend style={at={(0.05,0.05)},anchor=south west},
|
|
ymax=1.5, ymin=3e-7,
|
|
]
|
|
\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
|
|
{res/2d_ber_fer_dfr_20433484_proximal.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_proximal.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_proximal.csv};
|
|
\addlegendentry{$\gamma = 0.05$}
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\caption{Simulation results for $\omega = 0.05, K=100$}
|
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\label{fig:simulation_results_ber_fer_dfr}
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\end{figure}
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\end{minipage}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\newcommand{\tikzbracemark}[1]{\tikz[overlay,remember picture] \node (#1) {};}
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%
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%\newcommand*{\AddNote}[4]{%
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% \begin{tikzpicture}[overlay, remember picture]
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% \draw [decoration={brace,amplitude=0.5em},decorate,ultra thick]
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% ($(#3)!([yshift=1.5ex]#1)!($(#3)-(0,1)$)$) --
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% ($(#3)!(#2)!($(#3)-(0,1)$)$)
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% node [align=center, text width=2cm, pos=0.5, anchor=west] {#4};
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% \end{tikzpicture}
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%}%
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\begin{frame}[t, fragile]
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% \frametitle{Proximal Decoding: Improvement using ``ML-on-List''}
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% \setcounter{footnote}{0}
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%
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|
% \begin{itemize}
|
|
% \item Comparison of proximal \& hybrid-proximal-ML\\
|
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% decoding simulation
|
|
% \footnote{(3,6) regular LDPC Code with $n=204, k=102$
|
|
% \cite[Code: 204.33.484]{mackay_enc}}
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% results
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|
% \end{itemize}
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%
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% \begin{minipage}{.4\textwidth}
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% \centering
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%
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% \begin{algorithm}[caption={}, label={},
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% basicstyle=\fontsize{6.5}{7.5}\selectfont
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|
% ]
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%$\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$$\hspace{4.185cm}\tikzbracemark{prox-start}$
|
|
%for $k=0$ to $K-1$ do
|
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% $\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) $
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% If $\boldsymbol{\hat{x}}$ passes the parity check condition, output $\boldsymbol{\hat{x}}$
|
|
%end for $\tikzbracemark{prox-end}$
|
|
%Find $N$ most probably wrong bits $\hspace{2cm}\tikzbracemark{ml-start}$
|
|
%Generate variations $\boldsymbol{\tilde{x}}_n$ of $\boldsymbol{\hat{x}}$ with the $N$ bits modified
|
|
%Compute $d\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right) \forall n \in \left[ 1 : N-1 \right] $
|
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%Output $\boldsymbol{\tilde{x}}_n$ with lowest $d\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right)$ $\tikzbracemark{ml-end}$
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% \end{algorithm}
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%
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|
% \AddNote{prox-start}{prox-end}{prox-start}{\small Proximal\\Decoding}
|
|
% \AddNote{ml-start}{ml-end}{ml-start}{\small ML-on-List}
|
|
% \end{minipage}%
|
|
% \begin{minipage}{.6\textwidth}
|
|
% \centering
|
|
% \begin{figure}[H]
|
|
% \centering
|
|
% \vspace*{-12mm}
|
|
%
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|
% \begin{tikzpicture}[scale=0.42]
|
|
% \begin{axis}[
|
|
% grid=both,
|
|
% xlabel={SNR}, ylabel={BER},
|
|
% ymode=log,
|
|
% legend style={at={(0.05,0.05)},anchor=south west},
|
|
% ymax=1.5, ymin=3e-8,
|
|
% ]
|
|
%
|
|
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
|
|
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
|
|
% \addlegendentry{proximal}
|
|
% \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 prox. \& ML}
|
|
% \end{axis}
|
|
% \end{tikzpicture}
|
|
% \begin{tikzpicture}[scale=0.42]
|
|
% \begin{axis}[
|
|
% grid=both,
|
|
% xlabel={SNR}, ylabel={FER},
|
|
% ymode=log,
|
|
% legend style={at={(0.05,0.05)},anchor=south west},
|
|
% ymax=1.5, ymin=3e-8,
|
|
% ]
|
|
%
|
|
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
|
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
|
|
% \addlegendentry{proximal}
|
|
% \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 prox. \& ML}
|
|
% \end{axis}
|
|
% \end{tikzpicture}\\
|
|
% \begin{tikzpicture}[scale=0.42]
|
|
% \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=3e-8,
|
|
% ]
|
|
%
|
|
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
|
|
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
|
|
% \addlegendentry{proximal}
|
|
% \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 prox. \& ML}
|
|
% \end{axis}
|
|
% \end{tikzpicture}
|
|
%
|
|
% \caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, N=12$}
|
|
% \label{fig:simulation_results_hybrid}
|
|
% \end{figure}
|
|
% \end{minipage}
|
|
%\end{frame}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\begin{frame}[t, fragile]
|
|
\frametitle{Proximal Decoding: Improvement using ``ML-on-List''}
|
|
\setcounter{footnote}{0}
|
|
|
|
\begin{itemize}
|
|
\item Improvement of proximal decoding by adding an ``ML-on-list'' step after iterating
|
|
\end{itemize}
|
|
|
|
\begin{minipage}[t]{.48\textwidth}
|
|
\centering
|
|
|
|
\begin{figure}
|
|
\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}
|
|
|
|
\caption{Proximal decoding algorithm \cite{proximal_paper}}
|
|
\end{figure}
|
|
|
|
\end{minipage}%
|
|
\hfill\begin{minipage}[t]{.48\textwidth}
|
|
\centering
|
|
\begin{figure}
|
|
\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) $
|
|
$\textcolor{KITblue}{\text{If }\boldsymbol{\hat{x}}\text{ passes the parity check condition, output }\boldsymbol{\hat{x}}}$
|
|
end for
|
|
$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$
|
|
$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{x}}_n\text{ of }\boldsymbol{\hat{x}}\text{ with the }N\text{ bits modified.}}$
|
|
$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right) \forall n \in \left[ 1 : N-1 \right]}$
|
|
$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{x}}_n\text{ with lowest }d_H\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right)}$
|
|
\end{algorithm}
|
|
|
|
\caption{Hybrid proximal \& ML decoding algorithm}
|
|
\end{figure}
|
|
\end{minipage}
|
|
\end{frame}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\begin{frame}[t, fragile]
|
|
\frametitle{Proximal Decoding: Improvement using ``ML-on-List''}
|
|
\setcounter{footnote}{0}
|
|
|
|
\begin{itemize}
|
|
\item Improvement of proximal decoding by adding an ``ML-on-list'' step after iterating
|
|
\end{itemize}
|
|
|
|
\begin{minipage}[t]{.48\textwidth}
|
|
\centering
|
|
|
|
\begin{figure}
|
|
\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}
|
|
|
|
\caption{Proximal decoding algorithm \cite{proximal_paper}}
|
|
\end{figure}
|
|
|
|
\end{minipage}%
|
|
\hfill\begin{minipage}[t]{.48\textwidth}
|
|
\centering
|
|
\begin{figure}
|
|
\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) $
|
|
$\textcolor{KITblue}{\text{If }\boldsymbol{\hat{x}}\text{ passes the parity check condition, output }\boldsymbol{\hat{x}}}$
|
|
end for
|
|
$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$
|
|
$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{x}}_n\text{ of }\boldsymbol{\hat{x}}\text{ with the }N\text{ bits modified.}}$
|
|
$\textcolor{KITblue}{\text{Compute }\langle \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \rangle \forall n \in \left[ 1 : N-1 \right]}$
|
|
$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{x}}_n\text{ with lowest }\langle \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \rangle}$
|
|
\end{algorithm}
|
|
|
|
\caption{Hybrid proximal \& ML decoding algorithm}
|
|
\end{figure}
|
|
\end{minipage}
|
|
\end{frame}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\subsection{ADMM: Examination Results}%
|
|
\label{sub:Ex ADMM}
|
|
|
|
\begin{frame}[t]
|
|
\frametitle{ADMM}
|
|
|
|
\todo{TODO}
|
|
\end{frame}
|
|
|