1115 lines
48 KiB
TeX
1115 lines
48 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{Comparison: Decoding Performance}
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\captionsetup[subfigure]{font=footnotesize}
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\hspace*{-0.4cm}
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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*{-0.8cm}
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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}[
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grid=both,
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xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
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ymode=log,
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ymax=1.5, ymin=8e-5,
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width=1.2\textwidth,
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height=0.825\textwidth,
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]
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\addplot[scol2, line width=1pt, solid]
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table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
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{res/proximal/2d_ber_fer_dfr_963965.csv};
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\addplot[scol2, only marks, mark=square, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
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{res/hybrid/2d_ber_fer_dfr_963965.csv};
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\addplot[KITorange, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
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%{res/hybrid/2d_ber_fer_dfr_963965.csv};
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{res/admm/ber_2d_963965.csv};
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\addplot[Black, line width=1pt]
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table [col sep=comma, x=SNR, y=FER,]
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{res/generic/fer_ml_9633965.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
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\citereference{Mac24, 96.33.965}}
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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={$E_b / N_0$ (dB)}, ylabel={FER},
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ymode=log,
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ymax=1.5, ymin=8e-5,
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width=1.2\textwidth,
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height=0.825\textwidth,
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]
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\addplot[scol2, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={gamma}{0.05},
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discard if gt={SNR}{5.5}]
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{res/proximal/2d_ber_fer_dfr_20433484.csv};
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\addplot[scol2, only marks, mark=square, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
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{res/hybrid/2d_ber_fer_dfr_20433484.csv};
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\addplot[KITorange, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={mu}{3.0},
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discard if gt={SNR}{5.5}]
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{res/admm/ber_2d_20433484.csv};
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\addplot[Black, line width=1pt]
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table [col sep=comma, x=SNR, y=FER,
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discard if gt={SNR}{5.5}]
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{res/generic/fer_ml_20433484.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
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\citereference{Mac24, 204.33.484}}
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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={$E_b / N_0$ (dB)}, ylabel={FER},
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ymode=log,
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ymax=1.5, ymin=8e-5,
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width=1.2\textwidth,
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height=0.825\textwidth,
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]
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\addplot[scol2, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
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{res/proximal/2d_ber_fer_dfr_40833844.csv};
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\addplot[scol2, only marks, mark=square, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
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{res/hybrid/2d_ber_fer_dfr_40833844.csv};
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\addplot[KITorange, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
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{res/admm/ber_2d_40833844.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
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\citereference{Mac24, 408.33.844}}
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\end{subfigure}%
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\vspace*{-2mm}
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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={$E_b / N_0$ (dB)}, ylabel={FER},
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ymode=log,
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ymax=1.5, ymin=8e-5,
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width=1.2\textwidth,
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height=0.825\textwidth,
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]
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\addplot[scol2, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
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{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
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\addplot[scol2, only marks, mark=square, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
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{res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
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\addplot[KITorange, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
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{res/admm/ber_2d_bch_31_26.csv};
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\addplot[Black, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if gt={SNR}{5.5},
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discard if lt={SNR}{1},
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]
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{res/generic/fer_ml_bch_31_26.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-2mm}
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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={$E_b / N_0$ (dB)}, ylabel={FER},
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ymode=log,
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ymax=1.5, ymin=8e-5,
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width=1.2\textwidth,
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height=0.825\textwidth,
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]
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\addplot[scol2, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
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{res/proximal/2d_ber_fer_dfr_20455187.csv};
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\addplot[scol2, only marks, mark=square, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
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{res/hybrid/2d_ber_fer_dfr_20455187.csv};
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\addplot[KITorange, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
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{res/admm/ber_2d_20455187.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-2mm}
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\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
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\citereference{Mac24, 204.55.187}}
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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={$E_b / N_0$ (dB)}, ylabel={FER},
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ymode=log,
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ymax=1.5, ymin=8e-5,
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width=1.2\textwidth,
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height=0.825\textwidth,
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]
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\addplot[scol2, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
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{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
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\addplot[scol2, only marks, mark=square, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
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{res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv};
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\addplot[KITorange, line width=1pt]
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table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
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{res/admm/ber_2d_pegreg252x504.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-2mm}
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\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
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\citereference{Mac24, PEGReg252x504}}
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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*{-1.2cm}
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\hspace*{2mm}
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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 columns=1,
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legend style={draw=white!15!black},
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legend cell align={left}]
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\addlegendimage{scol2, line width=1pt, solid}
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\addlegendentry{Proximal}
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\addlegendimage{scol2, line width=1pt, only marks, mark=square}
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\addlegendentry{Improved}
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\addlegendimage{KITorange, line width=1pt}
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\addlegendentry{ADMM}
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\addlegendimage{Black, line width=1pt}
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\addlegendentry{ML}
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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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\vspace*{-1mm}
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\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t, fragile]
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\frametitle{Comparison: Algorithm Structure}
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\vspace*{-1cm}
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\begin{figure}[h]
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\centering
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\begin{subfigure}[b]{0.47\textwidth}
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\centering
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\begin{align*}
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\text{minimize}\hspace{2mm} & \textcolor{KITblue}{\underbrace{L\left(
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\boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right)}_{\text{Likelihood}}}
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+ \textcolor{KITred}{\underbrace{\gamma h\left( \tilde{\boldsymbol{x}}
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\right)} _{\text{Constraints}}} \\
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\text{subject to}\hspace{2mm} &\tilde{\boldsymbol{x}} \in \mathbb{R}^n
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\end{align*}
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\vspace*{-5mm}
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\begin{algorithm}[caption={}, label={},
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basicstyle=\fontsize{10}{18}\selectfont
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]
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Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$
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while stopping critierion unfulfilled do
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$\textcolor{KITblue}{\boldsymbol{r} \leftarrow \boldsymbol{r}
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+ \omega \nabla L\left( \boldsymbol{y} \mid \boldsymbol{s} \right)} $
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$\textcolor{KITred}{\boldsymbol{s} \leftarrow
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\textbf{prox}_{\gamma h}\left( \boldsymbol{r} \right)} $|\Suppressnumber|
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|\Reactivatenumber|
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end while
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return $\hat{\boldsymbol{c}}$
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\end{algorithm}
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\end{subfigure}\hfill%
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\begin{subfigure}[b]{0.5\textwidth}
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\centering
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\begin{align*}
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\text{minimize}\hspace{5mm} &
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\textcolor{KITblue}{\underbrace{\boldsymbol{\gamma}^\text{T}
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\tilde{\boldsymbol{c}}}_{\text{Likelihood}}}
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+ \textcolor{KITred}{\underbrace{\sum\nolimits_{j\in\mathcal{J}}
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g_j\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
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\right)}_{\text{Constraints}}} \\
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\text{subject to}\hspace{5mm} &
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\tilde{\boldsymbol{c}} \in \left[ 0, 1 \right]^n
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\end{align*}
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\vspace*{-5mm}
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\begin{algorithm}[caption={}, label={},
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basicstyle=\fontsize{10}{18}\selectfont
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]
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Initialize $\tilde{\boldsymbol{c}}, \boldsymbol{z}, \boldsymbol{u}, \boldsymbol{\gamma}, \rho$
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while stopping criterion unfulfilled do
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$\textcolor{KITblue}{\tilde{\boldsymbol{c}} \leftarrow \argmin_{\tilde{\boldsymbol{c}}}
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\left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
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+ \frac{\rho}{2}\sum_{j\in\mathcal{J}} \left\Vert
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\boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j
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+ \boldsymbol{u}_j \right\Vert \right)}$
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$\textcolor{KITred}{\boldsymbol{z}_j \leftarrow \textbf{prox}_{g_j}
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\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
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+ \boldsymbol{u}_j \right), \hspace{5mm}\forall j\in\mathcal{J}}$
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$\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j
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+ \tilde{\boldsymbol{c}} - \boldsymbol{z}_j, \hspace{14.5mm}\forall j\in\mathcal{J}$
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end while
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return $\hat{\boldsymbol{c}}$
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\end{algorithm}
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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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\begin{frame}[t]
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\frametitle{Comparison: Time Complexity}
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\vspace*{-6.5mm}
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\begin{itemize}
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\item Codes: BCH $\left( 31, 11 \right)$; BCH $\left( 31, 26 \right)$;
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\citereference{Mac24, 96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}
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\item Measured performance: $\sim\SI{10000}{}$ frames/s
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on Intel Core i7-7700HQ @ 2.80GHz; $n=204$
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\item Both algorithms are $\mathcal{O}\left( n \right)$ on average
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\end{itemize}
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\bigskip
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\begin{figure}[H]
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\centering
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\begin{tikzpicture}
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\begin{axis}[
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grid=both,
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xlabel={$n$}, ylabel={time per frame (ms)},
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legend style={at={(0.05,0.6)},anchor=south west},
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legend cell align={left},
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width=0.43\textwidth,
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height=0.32\textwidth,
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]
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\addplot[scol0, only marks, mark=square*]
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table [col sep=comma, x=n, y=spf,
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y expr=\thisrow{spf} * 1000]
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{res/proximal/fps_vs_n.csv};
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\addlegendentry{proximal}
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\addplot[scol1, only marks, mark=*]
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table [col sep=comma, x=n, y=spf,
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y expr=\thisrow{spf} * 1000]
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{res/hybrid/fps_vs_n.csv};
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\addlegendentry{improved ($N=12$)}
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\addplot[scol2, only marks, mark=triangle*]
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table [col sep=comma, x=n, y=spf,
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y expr=\thisrow{spf} * 1000]
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{res/admm/fps_vs_n.csv};
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\addlegendentry{ADMM}
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\end{axis}
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\end{tikzpicture}
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\end{figure}
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\smallskip
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\smallskip
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\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\end{frame}
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{Comparison: Convergence Behavior}
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\vspace*{-6mm}
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\begin{itemize}
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\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
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\item Minimum number of iterations independent of SNR
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\end{itemize}
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\smallskip
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\begin{figure}[H]
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\centering
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\begin{subfigure}[t]{0.5\textwidth}
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\centering
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|
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\begin{tikzpicture}
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\begin{axis}[
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grid=both,
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xlabel={Iterations},
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ylabel={Average $\lVert \boldsymbol{c}-\boldsymbol{\hat{c}} \rVert$},
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width=0.9\textwidth,
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height=0.675\textwidth,
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%legend pos=outer north east,
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]
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\addplot [scol0, mark=none, line width=1pt]
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table [col sep=comma,
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discard if not={omega}{0.0774263682681127},
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discard if gt={k}{101},
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x=k, y=err]
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{res/proximal/2d_avg_error_20433484_1db.csv};
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\addlegendentry{$E_b / N_0 = \SI{1}{dB}$}
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\addplot [scol1, mark=none, line width=1pt]
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table [col sep=comma, discard if not={omega}{0.0774263682681127},
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discard if gt={k}{101},
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x=k, y=err]
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{res/proximal/2d_avg_error_20433484_3db.csv};
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\addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
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\addplot [scol2, mark=none, line width=1pt]
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table [col sep=comma, discard if not={omega}{0.052233450742668434},
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discard if gt={k}{101},
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x=k, y=err]
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{res/proximal/2d_avg_error_20433484_5db.csv};
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\addlegendentry{$E_b / N_0 = \SI{5}{dB}$}
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\addplot [KITorange, mark=none, line width=1pt]
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table [col sep=comma, discard if not={omega}{0.052233450742668434},
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discard if gt={k}{101},
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x=k, y=err]
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{res/proximal/2d_avg_error_20433484_8db.csv};
|
|
\addlegendentry{$E_b / N_0 = \SI{8}{dB}$}
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\caption{Proximal Decoding}
|
|
\end{subfigure}%
|
|
\begin{subfigure}[t]{0.5\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}
|
|
\begin{axis}[
|
|
grid=both,
|
|
width=0.9\textwidth,
|
|
height=0.675\textwidth,
|
|
% legend pos=outer north east,
|
|
xlabel={Iteration},
|
|
ylabel={Average $\left\Vert \hat{\boldsymbol{c}} - \boldsymbol{c} \right\Vert$}
|
|
]
|
|
\addplot[scol0, line width=1pt]
|
|
table [col sep=comma, x=k, y=err,
|
|
discard if not={SNR}{1.0},
|
|
discard if gt={k}{101}]
|
|
{res/admm/avg_error_20433484.csv};
|
|
\addlegendentry{$E_b / N_0 = \SI{1}{dB}$}
|
|
|
|
\addplot[scol1, line width=1pt]
|
|
table [col sep=comma, x=k, y=err,
|
|
discard if not={SNR}{2.0},
|
|
discard if gt={k}{101}]
|
|
{res/admm/avg_error_20433484.csv};
|
|
\addlegendentry{$E_b / N_0 = \SI{2}{dB}$}
|
|
|
|
\addplot[scol2, line width=1pt]
|
|
table [col sep=comma, x=k, y=err,
|
|
discard if not={SNR}{3.0},
|
|
discard if gt={k}{101}]
|
|
{res/admm/avg_error_20433484.csv};
|
|
\addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
|
|
|
|
\addplot[KITorange, line width=1pt]
|
|
table [col sep=comma, x=k, y=err,
|
|
discard if not={SNR}{4.0},
|
|
discard if gt={k}{101}]
|
|
{res/admm/avg_error_20433484.csv};
|
|
\addlegendentry{$E_b / N_0 = \SI{4}{dB}$}
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\caption{LP Decoding using ADMM}
|
|
\end{subfigure}%
|
|
\end{figure}
|
|
|
|
\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
|
June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
|
\end{frame}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\begin{frame}[t]
|
|
\frametitle{Proximal Decoding: Choice of $\gamma$}
|
|
|
|
\captionsetup[subfigure]{font=footnotesize}
|
|
|
|
\hspace*{-0.5cm}
|
|
\begin{minipage}[c]{0.9\textwidth}
|
|
\centering
|
|
|
|
\begin{figure}[H]
|
|
\vspace*{-0.7cm}
|
|
\centering
|
|
|
|
\begin{subfigure}[t]{0.33\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}[scale=0.8]
|
|
\begin{axis}[view={75}{30},
|
|
zmode=log,
|
|
xlabel={$E_b / N_0$ (dB)},
|
|
ylabel={$\gamma$},
|
|
zlabel={BER},
|
|
width=1.2\textwidth,
|
|
height=0.825\textwidth,
|
|
legend pos=outer north east,]
|
|
|
|
\addplot3[surf,
|
|
mesh/rows=17, mesh/cols=10,
|
|
colormap/viridis] table [col sep=comma,
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_963965.csv};
|
|
\addplot3[scol1, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.01},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_963965.csv};
|
|
\addplot3[scol2, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.05},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_963965.csv};
|
|
\addplot3[scol0, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.15},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_963965.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
|
|
\citereference{Mac24, 96.3.965}}
|
|
\end{subfigure}%
|
|
\begin{subfigure}[t]{0.33\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}[scale=0.8]
|
|
\begin{axis}[view={75}{30},
|
|
zmode=log,
|
|
xlabel={$E_b / N_0$ (dB)},
|
|
ylabel={$\gamma$},
|
|
zlabel={BER},
|
|
width=1.2\textwidth,
|
|
height=0.825\textwidth,
|
|
legend pos=outer north east,]
|
|
|
|
\addplot3[surf,
|
|
mesh/rows=17, mesh/cols=14,
|
|
colormap/viridis] table [col sep=comma,
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
|
\addplot3[scol1, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.01},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
|
\addplot3[scol2, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.05},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
|
\addplot3[scol0, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.15},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
|
|
\citereference{Mac24, 204.33.484}}
|
|
\end{subfigure}%
|
|
\begin{subfigure}[t]{0.33\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}[scale=0.8]
|
|
\begin{axis}[view={75}{30},
|
|
zmode=log,
|
|
xlabel={$E_b / N_0$ (dB)},
|
|
ylabel={$\gamma$},
|
|
zlabel={BER},
|
|
width=1.2\textwidth,
|
|
height=0.825\textwidth,
|
|
legend pos=outer north east,]
|
|
|
|
\addplot3[surf,
|
|
mesh/rows=17, mesh/cols=10,
|
|
colormap/viridis] table [col sep=comma,
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_40833844.csv};
|
|
\addplot3[scol1, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.01},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_40833844.csv};
|
|
\addplot3[scol2, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.05},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_40833844.csv};
|
|
\addplot3[scol0, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.15},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_40833844.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
|
|
\citereference{Mac24, 408.33.844}}
|
|
\end{subfigure}%
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\begin{subfigure}[t]{0.33\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}[scale=0.8]
|
|
\begin{axis}[view={75}{30},
|
|
zmode=log,
|
|
xlabel={$E_b / N_0$ (dB)},
|
|
ylabel={$\gamma$},
|
|
zlabel={BER},
|
|
width=1.2\textwidth,
|
|
height=0.825\textwidth,
|
|
legend pos=outer north east,]
|
|
|
|
\addplot3[surf,
|
|
mesh/rows=17, mesh/cols=10,
|
|
colormap/viridis] table [col sep=comma,
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
|
|
\addplot3[scol1, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.01},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
|
|
\addplot3[scol2, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.05},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
|
|
\addplot3[scol0, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.15},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{BCH code with $n=31, k=26$}
|
|
\end{subfigure}%
|
|
\begin{subfigure}[t]{0.33\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}[scale=0.8]
|
|
\begin{axis}[view={75}{30},
|
|
zmode=log,
|
|
xlabel={$E_b / N_0$ (dB)},
|
|
ylabel={$\gamma$},
|
|
zlabel={BER},
|
|
width=1.2\textwidth,
|
|
height=0.825\textwidth,
|
|
legend pos=outer north east,]
|
|
|
|
\addplot3[surf,
|
|
mesh/rows=17, mesh/cols=10,
|
|
colormap/viridis] table [col sep=comma,
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_20455187.csv};
|
|
\addplot3[scol1, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.01},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_20455187.csv};
|
|
\addplot3[scol2, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.05},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_20455187.csv};
|
|
\addplot3[scol0, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.15},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_20455187.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
|
|
\citereference{Mac24, 204.55.187}}
|
|
\end{subfigure}%
|
|
\begin{subfigure}[t]{0.33\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}[scale=0.8]
|
|
\begin{axis}[view={75}{30},
|
|
zmode=log,
|
|
xlabel={$E_b / N_0$ (dB)},
|
|
ylabel={$\gamma$},
|
|
zlabel={BER},
|
|
width=1.2\textwidth,
|
|
height=0.825\textwidth,
|
|
legend pos=outer north east,]
|
|
|
|
\addplot3[surf,
|
|
mesh/rows=17, mesh/cols=10,
|
|
colormap/viridis] table [col sep=comma,
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
|
|
\addplot3[scol1, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.01},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
|
|
\addplot3[scol2, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.05},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
|
|
\addplot3[scol0, line width=1.5] table [col sep=comma,
|
|
discard if not={gamma}{0.15},
|
|
x=SNR, y=gamma, z=BER]
|
|
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
|
|
\citereference{Mac24, PEGReg252x504}}
|
|
\end{subfigure}%
|
|
\end{figure}
|
|
\end{minipage}%
|
|
\begin{minipage}[c]{0.1\textwidth}
|
|
\centering
|
|
|
|
\begin{figure}
|
|
\centering
|
|
\vspace*{-2cm}
|
|
\hspace*{-3mm}
|
|
\begin{tikzpicture}[scale=0.8]
|
|
\begin{axis}[hide axis,
|
|
xmin=10, xmax=50,
|
|
ymin=0, ymax=0.4,
|
|
legend style={draw=white!15!black,legend cell align=left}]
|
|
\addlegendimage{surf, colormap/viridis}
|
|
\addlegendentry{$\gamma = \left[ 0\text{:}0.01\text{:}0.16 \right] $};
|
|
\addlegendimage{scol1, line width=1.5pt}
|
|
\addlegendentry{$\gamma = 0.01$};
|
|
\addlegendimage{scol2, line width=1.5pt}
|
|
\addlegendentry{$\gamma = 0.05$};
|
|
\addlegendimage{scol0, line width=1.5pt}
|
|
\addlegendentry{$\gamma = 0.15$};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\end{figure}
|
|
\end{minipage}
|
|
|
|
\vspace*{-1mm}
|
|
|
|
\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
|
June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
|
\end{frame}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\begin{frame}[t]
|
|
\frametitle{LP Decoding using ADMM: Choice of $\mu$ and $\rho$}
|
|
|
|
\vspace*{-5mm}
|
|
|
|
\begin{itemize}
|
|
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
|
|
\item No clear optimum value
|
|
\end{itemize}
|
|
|
|
\bigskip
|
|
|
|
\begin{figure}[H]
|
|
\centering
|
|
|
|
\begin{subfigure}[c]{0.48\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}
|
|
\begin{axis}[
|
|
grid=both,
|
|
xlabel={$\mu$}, ylabel={FER},
|
|
ymode=log,
|
|
width=0.8\textwidth,
|
|
height=0.6\textwidth,
|
|
]
|
|
\addplot[scol0, line width=1pt]
|
|
table [col sep=comma, x=mu, y=FER,
|
|
discard if not={SNR}{2.0},]
|
|
{res/admm/ber_2d_20433484.csv};
|
|
\addplot[scol1, line width=1pt]
|
|
table [col sep=comma, x=mu, y=FER,
|
|
discard if not={SNR}{3.0},]
|
|
{res/admm/ber_2d_20433484.csv};
|
|
\addplot[scol2, line width=1pt]
|
|
table [col sep=comma, x=mu, y=FER,
|
|
discard if not={SNR}{4.0},]
|
|
{res/admm/ber_2d_20433484.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\end{subfigure}%
|
|
\begin{subfigure}[c]{0.48\textwidth}
|
|
\centering
|
|
|
|
\begin{tikzpicture}
|
|
\begin{axis}[
|
|
grid=both,
|
|
xlabel={$\rho$}, ylabel={FER},
|
|
ymode=log,
|
|
width=0.8\textwidth,
|
|
height=0.6\textwidth,
|
|
]
|
|
\addplot[scol0, line width=1pt]
|
|
table [col sep=comma, x=rho, y=FER,
|
|
discard if not={SNR}{2.0},]
|
|
{res/admm/ber_2d_20433484_rho.csv};
|
|
\addplot[scol1, line width=1pt]
|
|
table [col sep=comma, x=rho, y=FER,
|
|
discard if not={SNR}{3.0},]
|
|
{res/admm/ber_2d_20433484_rho.csv};
|
|
\addplot[scol2, line width=1pt]
|
|
table [col sep=comma, x=rho, y=FER,
|
|
discard if not={SNR}{4.0},]
|
|
{res/admm/ber_2d_20433484_rho.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\end{subfigure}%
|
|
|
|
\begin{subfigure}[t]{\textwidth}
|
|
\centering
|
|
|
|
\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{scol0, line width=1pt}
|
|
\addlegendentry{$E_b / N_0 = \SI{2}{dB}$}
|
|
\addlegendimage{scol1, line width=1pt}
|
|
\addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
|
|
\addlegendimage{scol2, line width=1pt}
|
|
\addlegendentry{$E_b / N_0 = \SI{4}{dB}$}
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\end{subfigure}
|
|
\end{figure}%
|
|
|
|
\bigskip
|
|
|
|
\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
|
June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
|
\end{frame}
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\begin{frame}[t]
|
|
\frametitle{LP Decoding using ADMM: Choice of $\mu$ and $\rho$}
|
|
|
|
\captionsetup[subfigure]{font=footnotesize}
|
|
|
|
\begin{minipage}[c]{0.9\textwidth}
|
|
\centering
|
|
\hspace*{-4mm}
|
|
|
|
\begin{figure}[H]
|
|
\centering
|
|
\vspace*{-7mm}
|
|
|
|
\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=0.825\textwidth,
|
|
]
|
|
\addplot[scol1, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{2.0},]
|
|
{res/admm/mu_rho_kavg_963965.csv};
|
|
\addplot[scol2, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{5.0},]
|
|
{res/admm/mu_rho_kavg_963965.csv};
|
|
\addplot[scol0, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{9.0},]
|
|
{res/admm/mu_rho_kavg_963965.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
|
|
\citereference{Mac24, 96.3.965}}
|
|
\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=0.825\textwidth,
|
|
]
|
|
\addplot[scol1, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{2.0},]
|
|
{res/admm/mu_rho_kavg_20433484.csv};
|
|
\addplot[scol2, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{5.0},]
|
|
{res/admm/mu_rho_kavg_20433484.csv};
|
|
\addplot[scol0, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{9.0},]
|
|
{res/admm/mu_rho_kavg_20433484.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
|
|
\citereference{Mac24, 204.33.484}}
|
|
\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=0.825\textwidth,
|
|
]
|
|
\addplot[scol1, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{2.0},]
|
|
{res/admm/mu_rho_kavg_40833844.csv};
|
|
\addplot[scol2, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{5.0},]
|
|
{res/admm/mu_rho_kavg_40833844.csv};
|
|
\addplot[scol0, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{9.0},]
|
|
{res/admm/mu_rho_kavg_40833844.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
|
|
\citereference{Mac24, 408.33.844}}
|
|
\end{subfigure}%
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\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=0.825\textwidth,
|
|
]
|
|
\addplot[scol1, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{2.0},]
|
|
{res/admm/mu_rho_kavg_bch_31_26.csv};
|
|
\addplot[scol2, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{5.0},]
|
|
{res/admm/mu_rho_kavg_bch_31_26.csv};
|
|
\addplot[scol0, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{9.0},]
|
|
{res/admm/mu_rho_kavg_bch_31_26.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{BCH code with $n=31, k=26$}
|
|
\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=0.825\textwidth,
|
|
]
|
|
\addplot[scol1, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{2.0},]
|
|
{res/admm/mu_rho_kavg_20455187.csv};
|
|
\addplot[scol2, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{5.0},]
|
|
{res/admm/mu_rho_kavg_20455187.csv};
|
|
\addplot[scol0, line width=1pt]
|
|
table [col sep=comma, x=rho, y=k_avg,
|
|
discard if not={mu}{9.0},]
|
|
{res/admm/mu_rho_kavg_20455187.csv};
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
|
|
\vspace*{-2mm}
|
|
|
|
\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
|
|
\citereference{Mac24, 204.55.187}}
|
|
\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=0.825\textwidth,
|
|
]
|
|
\addplot[scol1, 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[scol2, 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[scol0, 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*{-2mm}
|
|
|
|
\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
|
|
\citereference{Mac24, PEGReg252x504}}
|
|
\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{scol0, line width=1pt}
|
|
\addlegendentry{$\mu = 9$}
|
|
\addlegendimage{scol2, line width=1pt}
|
|
\addlegendentry{$\mu = 5$}
|
|
\addlegendimage{scol1, line width=1pt}
|
|
\addlegendentry{$\mu = 2$}
|
|
\end{axis}
|
|
\end{tikzpicture}
|
|
\end{figure}
|
|
\end{minipage}
|
|
|
|
\vspace*{-1mm}
|
|
|
|
\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
|
June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
|
\end{frame}
|
|
|