505 lines
25 KiB
TeX
505 lines
25 KiB
TeX
\appendix
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\section{Supplementary Slides}%
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\label{app:Supplementary Slides}
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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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\captionsetup[subfigure]{font=footnotesize}
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\hspace*{-0.5cm}
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\begin{minipage}[c]{0.9\textwidth}
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\centering
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\begin{figure}[H]
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\vspace*{-0.7cm}
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\centering
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[view={75}{30},
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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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width=1.2\textwidth,
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height=0.85\textwidth,
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legend pos=outer north east,]
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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/proximal/2d_ber_fer_dfr_963965.csv};
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\addplot3[NavyBlue, 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/proximal/2d_ber_fer_dfr_963965.csv};
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\addplot3[RedOrange, 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/proximal/2d_ber_fer_dfr_963965.csv};
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\addplot3[ForestGreen, 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/proximal/2d_ber_fer_dfr_963965.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
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\cite[\text{96.3.965}]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[view={75}{30},
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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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width=1.2\textwidth,
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height=0.85\textwidth,
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legend pos=outer north east,]
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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/proximal/2d_ber_fer_dfr_20433484.csv};
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\addplot3[NavyBlue, 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/proximal/2d_ber_fer_dfr_20433484.csv};
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\addplot3[RedOrange, 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/proximal/2d_ber_fer_dfr_20433484.csv};
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\addplot3[ForestGreen, 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/proximal/2d_ber_fer_dfr_20433484.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
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\cite[\text{204.33.484}]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[view={75}{30},
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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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width=1.2\textwidth,
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height=0.85\textwidth,
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legend pos=outer north east,]
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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/proximal/2d_ber_fer_dfr_40833844.csv};
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\addplot3[NavyBlue, 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/proximal/2d_ber_fer_dfr_40833844.csv};
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\addplot3[RedOrange, 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/proximal/2d_ber_fer_dfr_40833844.csv};
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\addplot3[ForestGreen, 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/proximal/2d_ber_fer_dfr_40833844.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
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\cite[\text{408.33.844}]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[view={75}{30},
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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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width=1.2\textwidth,
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height=0.85\textwidth,
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legend pos=outer north east,]
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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/proximal/2d_ber_fer_dfr_bch_31_26.csv};
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\addplot3[NavyBlue, 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/proximal/2d_ber_fer_dfr_bch_31_26.csv};
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\addplot3[RedOrange, 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/proximal/2d_ber_fer_dfr_bch_31_26.csv};
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\addplot3[ForestGreen, 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/proximal/2d_ber_fer_dfr_bch_31_26.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{BCH code with $n=31, k=26$}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[view={75}{30},
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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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width=1.2\textwidth,
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height=0.85\textwidth,
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legend pos=outer north east,]
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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/proximal/2d_ber_fer_dfr_20455187.csv};
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\addplot3[NavyBlue, 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/proximal/2d_ber_fer_dfr_20455187.csv};
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\addplot3[RedOrange, 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/proximal/2d_ber_fer_dfr_20455187.csv};
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\addplot3[ForestGreen, 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/proximal/2d_ber_fer_dfr_20455187.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
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\cite[\text{204.55.187}]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[view={75}{30},
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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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width=1.2\textwidth,
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height=0.85\textwidth,
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legend pos=outer north east,]
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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/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
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\addplot3[NavyBlue, 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/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
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\addplot3[RedOrange, 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/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
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\addplot3[ForestGreen, 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/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
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\cite[\text{PEGReg252x504}]{mackay_enc}}
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\end{subfigure}%
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\end{figure}
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\end{minipage}%
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\begin{minipage}[c]{0.1\textwidth}
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\centering
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\begin{figure}
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\centering
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\vspace*{-2cm}
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\hspace*{-3mm}
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[hide axis,
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xmin=10, xmax=50,
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ymin=0, ymax=0.4,
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legend style={draw=white!15!black,legend cell align=left}]
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\addlegendimage{surf, colormap/viridis}
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\addlegendentry{$\gamma = \left[ 0\text{:}0.01\text{:}0.16 \right] $};
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\addlegendimage{NavyBlue, line width=1.5pt}
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\addlegendentry{$\gamma = 0.01$};
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\addlegendimage{RedOrange, line width=1.5pt}
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\addlegendentry{$\gamma = 0.05$};
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\addlegendimage{ForestGreen, line width=1.5pt}
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\addlegendentry{$\gamma = 0.15$};
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\end{axis}
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\end{tikzpicture}
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\end{figure}
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\end{minipage}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{LP Decoding using ADMM: Choice of $\mu$ and $\rho$}
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\captionsetup[subfigure]{font=footnotesize}
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\begin{minipage}[c]{0.9\textwidth}
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\centering
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\hspace*{-4mm}
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\begin{figure}[H]
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\centering
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\vspace*{-7mm}
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[
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grid=both,
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{2.0},]
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{res/admm/mu_rho_kavg_963965.csv};
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\addplot[RedOrange, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{5.0},]
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{res/admm/mu_rho_kavg_963965.csv};
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\addplot[NavyBlue, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{9.0},]
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{res/admm/mu_rho_kavg_963965.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
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\cite[\text{96.3.965}]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[
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grid=both,
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{2.0},]
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{res/admm/mu_rho_kavg_20433484.csv};
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\addplot[RedOrange, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{5.0},]
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{res/admm/mu_rho_kavg_20433484.csv};
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\addplot[NavyBlue, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{9.0},]
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{res/admm/mu_rho_kavg_20433484.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
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\cite[\text{204.33.484}]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[
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grid=both,
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{2.0},]
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{res/admm/mu_rho_kavg_40833844.csv};
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\addplot[RedOrange, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{5.0},]
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{res/admm/mu_rho_kavg_40833844.csv};
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\addplot[NavyBlue, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{9.0},]
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{res/admm/mu_rho_kavg_40833844.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
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\cite[\text{408.33.844}]{mackay_enc}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[
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grid=both,
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{2.0},]
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{res/admm/mu_rho_kavg_bch_31_26.csv};
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\addplot[RedOrange, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{5.0},]
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{res/admm/mu_rho_kavg_bch_31_26.csv};
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\addplot[NavyBlue, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{9.0},]
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{res/admm/mu_rho_kavg_bch_31_26.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{BCH code with $n=31, k=26$}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[
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grid=both,
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{2.0},]
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{res/admm/mu_rho_kavg_20455187.csv};
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\addplot[RedOrange, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{5.0},]
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{res/admm/mu_rho_kavg_20455187.csv};
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\addplot[NavyBlue, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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discard if not={mu}{9.0},]
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{res/admm/mu_rho_kavg_20455187.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
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|
\cite[\text{204.55.187}]{mackay_enc}}
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|
\end{subfigure}%
|
|
\begin{subfigure}[t]{0.33\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}[scale=0.8]
|
|
\begin{axis}[
|
|
grid=both,
|
|
xlabel={$\rho$}, ylabel={Avg. \# iter.},
|
|
ymode=log,
|
|
width=1.2\textwidth,
|
|
height=0.85\textwidth,
|
|
]
|
|
\addplot[ForestGreen, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{2.0},]
|
|
{res/admm/mu_rho_kavg_pegreg252x504.csv};
|
|
\addplot[RedOrange, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{5.0},]
|
|
{res/admm/mu_rho_kavg_pegreg252x504.csv};
|
|
\addplot[NavyBlue, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{9.0},]
|
|
{res/admm/mu_rho_kavg_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*{-1cm}
|
|
\hspace*{3mm}
|
|
\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{NavyBlue, line width=1pt}
|
|
\addlegendentry{$\mu = 9$}
|
|
\addlegendimage{RedOrange, line width=1pt}
|
|
\addlegendentry{$\mu = 5$}
|
|
\addlegendimage{ForestGreen, line width=1pt}
|
|
\addlegendentry{$\mu = 2$}
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\end{figure}
|
|
\end{minipage}
|
|
\end{frame}
|
|
|