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\documentclass[10pt, aspectratio=169, usenames, dvipsnames]{beamer}
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\usepackage{tikz}
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\usetikzlibrary{intersections, spy}
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\usepackage{tikz-3dplot}
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\usetikzlibrary{spy, external}
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\tikzexternalize[prefix=build/]
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\usepackage{pgfplots}
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\pgfplotsset{compat=newest}
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\usepackage{listings}
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\usepackage{listings}
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\usepackage{subcaption}
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@ -94,6 +96,7 @@
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\input{sections/theoretical_background.tex}
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\input{sections/lp_dec_using_admm.tex}
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\input{sections/proximal_decoding.tex}
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% \input{sections/comparison.tex}
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\input{sections/question_slide.tex}
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\input{sections/appendix.tex}
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\end{document}
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@ -3,6 +3,504 @@
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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{Mac23, 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{Mac23, 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{Mac23, 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{Mac23, 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{Mac23, 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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\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{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. 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{Mac23, 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{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. 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]
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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{Mac23, 204.33.484}
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||||
\item Minimum number of iterations independent of SNR
|
||||
\end{itemize}
|
||||
|
||||
\smallskip
|
||||
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
|
||||
\begin{subfigure}[t]{0.5\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={Iterations},
|
||||
ylabel={Average $\lVert \boldsymbol{c}-\boldsymbol{\hat{c}} \rVert$},
|
||||
width=0.9\textwidth,
|
||||
height=0.675\textwidth,
|
||||
%legend pos=outer north east,
|
||||
]
|
||||
\addplot [scol0, mark=none, line width=1pt]
|
||||
table [col sep=comma,
|
||||
discard if not={omega}{0.0774263682681127},
|
||||
discard if gt={k}{101},
|
||||
x=k, y=err]
|
||||
{res/proximal/2d_avg_error_20433484_1db.csv};
|
||||
\addlegendentry{$E_b / N_0 = \SI{1}{dB}$}
|
||||
\addplot [scol1, mark=none, line width=1pt]
|
||||
table [col sep=comma, discard if not={omega}{0.0774263682681127},
|
||||
discard if gt={k}{101},
|
||||
x=k, y=err]
|
||||
{res/proximal/2d_avg_error_20433484_3db.csv};
|
||||
\addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
|
||||
\addplot [scol2, mark=none, line width=1pt]
|
||||
table [col sep=comma, discard if not={omega}{0.052233450742668434},
|
||||
discard if gt={k}{101},
|
||||
x=k, y=err]
|
||||
{res/proximal/2d_avg_error_20433484_5db.csv};
|
||||
\addlegendentry{$E_b / N_0 = \SI{5}{dB}$}
|
||||
\addplot [KITorange, mark=none, line width=1pt]
|
||||
table [col sep=comma, discard if not={omega}{0.052233450742668434},
|
||||
discard if gt={k}{101},
|
||||
x=k, y=err]
|
||||
{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{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: Choice of $\gamma$}
|
||||
@ -35,15 +533,15 @@
|
||||
colormap/viridis] table [col sep=comma,
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_963965.csv};
|
||||
\addplot3[NavyBlue, line width=1.5] table [col sep=comma,
|
||||
\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[RedOrange, line width=1.5] table [col sep=comma,
|
||||
\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[ForestGreen, line width=1.5] table [col sep=comma,
|
||||
\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};
|
||||
@ -73,15 +571,15 @@
|
||||
colormap/viridis] table [col sep=comma,
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addplot3[NavyBlue, line width=1.5] table [col sep=comma,
|
||||
\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[RedOrange, line width=1.5] table [col sep=comma,
|
||||
\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[ForestGreen, line width=1.5] table [col sep=comma,
|
||||
\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};
|
||||
@ -111,15 +609,15 @@
|
||||
colormap/viridis] table [col sep=comma,
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_40833844.csv};
|
||||
\addplot3[NavyBlue, line width=1.5] table [col sep=comma,
|
||||
\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[RedOrange, line width=1.5] table [col sep=comma,
|
||||
\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[ForestGreen, line width=1.5] table [col sep=comma,
|
||||
\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};
|
||||
@ -152,15 +650,15 @@
|
||||
colormap/viridis] table [col sep=comma,
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
|
||||
\addplot3[NavyBlue, line width=1.5] table [col sep=comma,
|
||||
\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[RedOrange, line width=1.5] table [col sep=comma,
|
||||
\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[ForestGreen, line width=1.5] table [col sep=comma,
|
||||
\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};
|
||||
@ -189,15 +687,15 @@
|
||||
colormap/viridis] table [col sep=comma,
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_20455187.csv};
|
||||
\addplot3[NavyBlue, line width=1.5] table [col sep=comma,
|
||||
\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[RedOrange, line width=1.5] table [col sep=comma,
|
||||
\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[ForestGreen, line width=1.5] table [col sep=comma,
|
||||
\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};
|
||||
@ -227,15 +725,15 @@
|
||||
colormap/viridis] table [col sep=comma,
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
|
||||
\addplot3[NavyBlue, line width=1.5] table [col sep=comma,
|
||||
\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[RedOrange, line width=1.5] table [col sep=comma,
|
||||
\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[ForestGreen, line width=1.5] table [col sep=comma,
|
||||
\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};
|
||||
@ -263,11 +761,11 @@
|
||||
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] $};
|
||||
\addlegendimage{NavyBlue, line width=1.5pt}
|
||||
\addlegendimage{scol1, line width=1.5pt}
|
||||
\addlegendentry{$\gamma = 0.01$};
|
||||
\addlegendimage{RedOrange, line width=1.5pt}
|
||||
\addlegendimage{scol2, line width=1.5pt}
|
||||
\addlegendentry{$\gamma = 0.05$};
|
||||
\addlegendimage{ForestGreen, line width=1.5pt}
|
||||
\addlegendimage{scol0, line width=1.5pt}
|
||||
\addlegendentry{$\gamma = 0.15$};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
@ -280,6 +778,103 @@
|
||||
Jan. 2023. 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{Mac23, 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{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{LP Decoding using ADMM: Choice of $\mu$ and $\rho$}
|
||||
@ -305,15 +900,15 @@
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt]
|
||||
\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[RedOrange, line width=1pt]
|
||||
\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[NavyBlue, line width=1pt]
|
||||
\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};
|
||||
@ -336,15 +931,15 @@
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt]
|
||||
\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[RedOrange, line width=1pt]
|
||||
\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[NavyBlue, line width=1pt]
|
||||
\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};
|
||||
@ -367,15 +962,15 @@
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt]
|
||||
\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[RedOrange, line width=1pt]
|
||||
\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[NavyBlue, line width=1pt]
|
||||
\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};
|
||||
@ -401,15 +996,15 @@
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt]
|
||||
\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[RedOrange, line width=1pt]
|
||||
\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[NavyBlue, line width=1pt]
|
||||
\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};
|
||||
@ -431,15 +1026,15 @@
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt]
|
||||
\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[RedOrange, line width=1pt]
|
||||
\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[NavyBlue, line width=1pt]
|
||||
\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};
|
||||
@ -462,15 +1057,15 @@
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt]
|
||||
\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[RedOrange, line width=1pt]
|
||||
\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[NavyBlue, line width=1pt]
|
||||
\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};
|
||||
@ -499,11 +1094,11 @@
|
||||
legend columns=1,
|
||||
legend style={draw=white!15!black}]
|
||||
|
||||
\addlegendimage{NavyBlue, line width=1pt}
|
||||
\addlegendimage{scol0, line width=1pt}
|
||||
\addlegendentry{$\mu = 9$}
|
||||
\addlegendimage{RedOrange, line width=1pt}
|
||||
\addlegendimage{scol2, line width=1pt}
|
||||
\addlegendentry{$\mu = 5$}
|
||||
\addlegendimage{ForestGreen, line width=1pt}
|
||||
\addlegendimage{scol1, line width=1pt}
|
||||
\addlegendentry{$\mu = 2$}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
@ -7,283 +7,15 @@
|
||||
\label{sub:Comparison of Simulation Results}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Comparison: Convergence Behavior}
|
||||
|
||||
\vspace*{-3mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
\item Minimum number of iterations independent of SNR
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
|
||||
\begin{subfigure}[t]{0.5\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={Iterations},
|
||||
ylabel={Average $\lVert \boldsymbol{c}-\boldsymbol{\hat{c}} \rVert$},
|
||||
width=0.9\textwidth,
|
||||
height=0.675\textwidth,
|
||||
%legend pos=outer north east,
|
||||
]
|
||||
\addplot [ForestGreen, mark=none, line width=1pt]
|
||||
table [col sep=comma,
|
||||
discard if not={omega}{0.0774263682681127},
|
||||
discard if gt={k}{101},
|
||||
x=k, y=err]
|
||||
{res/proximal/2d_avg_error_20433484_1db.csv};
|
||||
\addlegendentry{$E_b / N_0 = \SI{1}{dB}$}
|
||||
\addplot [NavyBlue, mark=none, line width=1pt]
|
||||
table [col sep=comma, discard if not={omega}{0.0774263682681127},
|
||||
discard if gt={k}{101},
|
||||
x=k, y=err]
|
||||
{res/proximal/2d_avg_error_20433484_3db.csv};
|
||||
\addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
|
||||
\addplot [RedOrange, mark=none, line width=1pt]
|
||||
table [col sep=comma, discard if not={omega}{0.052233450742668434},
|
||||
discard if gt={k}{101},
|
||||
x=k, y=err]
|
||||
{res/proximal/2d_avg_error_20433484_5db.csv};
|
||||
\addlegendentry{$E_b / N_0 = \SI{5}{dB}$}
|
||||
\addplot [RoyalPurple, mark=none, line width=1pt]
|
||||
table [col sep=comma, discard if not={omega}{0.052233450742668434},
|
||||
discard if gt={k}{101},
|
||||
x=k, y=err]
|
||||
{res/proximal/2d_avg_error_20433484_8db.csv};
|
||||
\addlegendentry{$E_b / N_0 = \SI{8}{dB}$}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\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[ForestGreen, 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[RedOrange, 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[NavyBlue, 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[RoyalPurple, 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}
|
||||
\end{subfigure}%
|
||||
\end{figure}
|
||||
|
||||
\smallskip
|
||||
\smallskip
|
||||
\smallskip
|
||||
|
||||
\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Comparison: Time Complexity}
|
||||
|
||||
\vspace*{-6.5mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item Codes: BCH $\left( 31, 11 \right)$; BCH $\left( 31, 26 \right)$;
|
||||
\citereference{Mac23, 96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}
|
||||
\item Measured performance: $\sim\SI{10000}{}$ frames/s
|
||||
on Intel Core i7-7700HQ @ 2.80GHz; $n=204$
|
||||
\item Both algorithms are $\mathcal{O}\left( n \right)$ on average
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$n$}, ylabel={time per frame (ms)},
|
||||
legend style={at={(0.05,0.6)},anchor=south west},
|
||||
legend cell align={left},
|
||||
width=0.43\textwidth,
|
||||
height=0.32\textwidth,
|
||||
]
|
||||
\addplot[RedOrange, only marks, mark=square*]
|
||||
table [col sep=comma, x=n, y=spf,
|
||||
y expr=\thisrow{spf} * 1000]
|
||||
{res/proximal/fps_vs_n.csv};
|
||||
\addlegendentry{proximal}
|
||||
|
||||
\addplot[Gray, only marks, mark=*]
|
||||
table [col sep=comma, x=n, y=spf,
|
||||
y expr=\thisrow{spf} * 1000]
|
||||
{res/hybrid/fps_vs_n.csv};
|
||||
\addlegendentry{improved ($N=12$)}
|
||||
|
||||
\addplot[NavyBlue, only marks, mark=triangle*]
|
||||
table [col sep=comma, x=n, y=spf,
|
||||
y expr=\thisrow{spf} * 1000]
|
||||
{res/admm/fps_vs_n.csv};
|
||||
\addlegendentry{ADMM}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{figure}
|
||||
|
||||
\smallskip
|
||||
\smallskip
|
||||
|
||||
\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Comparison: Decoding Performance}
|
||||
|
||||
\vspace{-0.5cm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$E_b / N_0$}, ylabel={BER},
|
||||
ymode=log,
|
||||
legend columns=2,
|
||||
legend style={at={(0.5,-0.45)},anchor=south},
|
||||
ymax=1.5, ymin=3e-8,
|
||||
width=0.45\textwidth,
|
||||
height=0.33\textwidth,
|
||||
]
|
||||
\addplot[RedOrange, mark=*, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
|
||||
|
||||
\addplot[NavyBlue, line width=1pt, mark=*]
|
||||
table [x=SNR, y=BER, col sep=comma,
|
||||
discard if not={mu}{3.0},
|
||||
%discard if gt={SNR}{4.0}
|
||||
]
|
||||
{res/admm/ber_2d_20433484.csv};
|
||||
|
||||
\addplot [RoyalPurple, mark=*, line width=1pt]
|
||||
table [x=SNR, y=BP, col sep=comma] {res/ber_paper.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$E_b / N_0$}, ylabel={FER},
|
||||
ymode=log,
|
||||
legend columns=2,
|
||||
legend style={at={(0.5,-0.45)},anchor=south},
|
||||
ymax=1.5, ymin=3e-8,
|
||||
width=0.45\textwidth,
|
||||
height=0.33\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, mark=*, solid, line width=1pt]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
|
||||
|
||||
\addplot[NavyBlue, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={mu}{3.0},
|
||||
%discard if gt={SNR}{4.0}
|
||||
]
|
||||
{res/admm/ber_2d_20433484.csv};
|
||||
\addplot[Black, line width=1pt, mark=*]
|
||||
table [col sep=comma, x=SNR, y=FER,
|
||||
%discard if gt={SNR}{3.0}
|
||||
]
|
||||
{res/generic/fer_ml_20433484.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[hide axis,
|
||||
xmin=10, xmax=50,
|
||||
ymin=0, ymax=0.4,
|
||||
legend columns=3,
|
||||
legend style={draw=white!15!black,legend cell align=left}]
|
||||
|
||||
\addlegendimage{RedOrange, mark=*, line width=1pt}
|
||||
\addlegendentry{Proximal}
|
||||
|
||||
\addlegendimage{NavyBlue, mark=*, line width=1pt}
|
||||
\addlegendentry{ADMM}
|
||||
|
||||
\addlegendimage{Black, mark=*, line width=1pt}
|
||||
\addlegendentry{ML}
|
||||
|
||||
\addlegendimage{RedOrange, mark=triangle, densely dashed, line width=1pt}
|
||||
\addlegendentry{Improved ($N$=12)}
|
||||
|
||||
\addlegendimage{RoyalPurple, mark=*, line width=1pt}
|
||||
\addlegendentry{BP}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{figure}
|
||||
|
||||
\smallskip
|
||||
\smallskip
|
||||
\smallskip
|
||||
|
||||
\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%\begin{frame}[t]
|
||||
% \frametitle{Decoding Performance}
|
||||
% \frametitle{Comparison: Decoding Performance}
|
||||
%
|
||||
% \vspace*{-5mm}
|
||||
% \vspace{-0.5cm}
|
||||
%
|
||||
% \begin{itemize}
|
||||
% \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
% \end{itemize}
|
||||
%
|
||||
% \begin{figure}[H]
|
||||
% \centering
|
||||
@ -291,433 +23,99 @@
|
||||
% \begin{tikzpicture}
|
||||
% \begin{axis}[
|
||||
% grid=both,
|
||||
% xlabel={$E_b / N_0 \left( \text{dB} \right) $}, ylabel={FER},
|
||||
% xlabel={$E_b / N_0$}, ylabel={BER},
|
||||
% ymode=log,
|
||||
% ymax=1.5, ymin=5e-5,
|
||||
% legend columns = 3,
|
||||
% legend style={at={(0.5,-0.5)},anchor=south},
|
||||
% legend columns=2,
|
||||
% legend style={at={(0.5,-0.45)},anchor=south},
|
||||
% ymax=1.5, ymin=3e-8,
|
||||
% width=0.45\textwidth,
|
||||
% height=0.3375\textwidth,
|
||||
% height=0.33\textwidth,
|
||||
% ]
|
||||
%
|
||||
% \addplot[RedOrange, line width=1pt, mark=*, solid]
|
||||
% table [x=SNR, y=FER, col sep=comma,
|
||||
% discard if not={gamma}{0.05},
|
||||
% discard if gt={SNR}{5.5}]
|
||||
% \addplot[RedOrange, mark=*, line width=1pt]
|
||||
% table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
% \addlegendentry{Proximal decoding}
|
||||
% \addplot[NavyBlue, line width=1pt, mark=triangle, densely dashed]
|
||||
% table [x=SNR, y=FER, col sep=comma,
|
||||
% \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
% table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/hybrid/2d_ber_fer_dfr_20433484.csv};
|
||||
%
|
||||
% \addplot[NavyBlue, line width=1pt, mark=*]
|
||||
% table [x=SNR, y=BER, col sep=comma,
|
||||
% discard if not={mu}{3.0},
|
||||
% discard if gt={SNR}{4.0}]
|
||||
% %discard if gt={SNR}{4.0}
|
||||
% ]
|
||||
% {res/admm/ber_2d_20433484.csv};
|
||||
% \addlegendentry{ADMM}
|
||||
% \addplot[PineGreen, line width=1pt, mark=triangle, solid]
|
||||
% table [col sep=comma, x=SNR, y=FER,
|
||||
% discard if gt={SNR}{3.0}]
|
||||
% {res/generic/fer_ml_20433484.csv};
|
||||
% \addlegendentry{ML}
|
||||
%
|
||||
% \addplot [RoyalPurple, mark=*, line width=1pt]
|
||||
% table [x=SNR, y=BP, col sep=comma] {res/ber_paper.csv};
|
||||
% \end{axis}
|
||||
% \end{tikzpicture}
|
||||
% \begin{tikzpicture}
|
||||
% \begin{axis}[
|
||||
% grid=both,
|
||||
% xlabel={$E_b / N_0$}, ylabel={FER},
|
||||
% ymode=log,
|
||||
% legend columns=2,
|
||||
% legend style={at={(0.5,-0.45)},anchor=south},
|
||||
% ymax=1.5, ymin=3e-8,
|
||||
% width=0.45\textwidth,
|
||||
% height=0.33\textwidth,
|
||||
% ]
|
||||
%
|
||||
% \caption{Comparison of FER of proximal decoding and LP decoding using ADMM%
|
||||
% \protect\footnotemark{}}
|
||||
% \end{figure}%
|
||||
% \addplot[RedOrange, mark=*, solid, line width=1pt]
|
||||
% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
% \addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/hybrid/2d_ber_fer_dfr_20433484.csv};
|
||||
%
|
||||
% \footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
|
||||
% \cite[Code: 204.33.484]{mackay_enc}}
|
||||
% \addplot[NavyBlue, line width=1pt, mark=*]
|
||||
% table [x=SNR, y=FER, col sep=comma,
|
||||
% discard if not={mu}{3.0},
|
||||
% %discard if gt={SNR}{4.0}
|
||||
% ]
|
||||
% {res/admm/ber_2d_20433484.csv};
|
||||
% \addplot[Black, line width=1pt, mark=*]
|
||||
% table [col sep=comma, x=SNR, y=FER,
|
||||
% %discard if gt={SNR}{3.0}
|
||||
% ]
|
||||
% {res/generic/fer_ml_20433484.csv};
|
||||
% \end{axis}
|
||||
% \end{tikzpicture}
|
||||
% \begin{tikzpicture}
|
||||
% \begin{axis}[hide axis,
|
||||
% xmin=10, xmax=50,
|
||||
% ymin=0, ymax=0.4,
|
||||
% legend columns=3,
|
||||
% legend style={draw=white!15!black,legend cell align=left}]
|
||||
%
|
||||
% \addlegendimage{RedOrange, mark=*, line width=1pt}
|
||||
% \addlegendentry{Proximal}
|
||||
%
|
||||
% \addlegendimage{NavyBlue, mark=*, line width=1pt}
|
||||
% \addlegendentry{ADMM}
|
||||
%
|
||||
% \addlegendimage{Black, mark=*, line width=1pt}
|
||||
% \addlegendentry{ML}
|
||||
%
|
||||
% \addlegendimage{RedOrange, mark=triangle, densely dashed, line width=1pt}
|
||||
% \addlegendentry{Improved ($N$=12)}
|
||||
%
|
||||
% \addlegendimage{RoyalPurple, mark=*, line width=1pt}
|
||||
% \addlegendentry{BP}
|
||||
% \end{axis}
|
||||
% \end{tikzpicture}
|
||||
% \end{figure}
|
||||
%
|
||||
% \smallskip
|
||||
% \smallskip
|
||||
% \smallskip
|
||||
%
|
||||
% \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
% Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
%\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Comparison: Decoding Performance}
|
||||
|
||||
\captionsetup[subfigure]{font=footnotesize}
|
||||
|
||||
\hspace*{-0.4cm}
|
||||
\begin{minipage}[c]{0.9\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{figure}[H]
|
||||
\vspace*{-0.8cm}
|
||||
\centering
|
||||
|
||||
\begin{subfigure}[t]{0.33\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*, solid]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/proximal/2d_ber_fer_dfr_963965.csv};
|
||||
\addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
|
||||
{res/hybrid/2d_ber_fer_dfr_963965.csv};
|
||||
\addplot[NavyBlue, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
|
||||
%{res/hybrid/2d_ber_fer_dfr_963965.csv};
|
||||
{res/admm/ber_2d_963965.csv};
|
||||
\addplot[Black, line width=1pt, mark=*]
|
||||
table [col sep=comma, x=SNR, y=FER,]
|
||||
{res/generic/fer_ml_9633965.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
|
||||
\citereference{Mac23, 96.33.965}}
|
||||
\end{subfigure}%
|
||||
\begin{subfigure}[t]{0.33\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.05},
|
||||
discard if gt={SNR}{5.5}]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
|
||||
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
|
||||
\addplot[NavyBlue, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={mu}{3.0},
|
||||
discard if gt={SNR}{5.5}]
|
||||
{res/admm/ber_2d_20433484.csv};
|
||||
\addplot[Black, line width=1pt, mark=*]
|
||||
table [col sep=comma, x=SNR, y=FER,
|
||||
discard if gt={SNR}{5.5}]
|
||||
{res/generic/fer_ml_20433484.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
|
||||
\citereference{Mac23, 204.33.484}}
|
||||
\end{subfigure}%
|
||||
\begin{subfigure}[t]{0.33\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/proximal/2d_ber_fer_dfr_40833844.csv};
|
||||
\addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
|
||||
{res/hybrid/2d_ber_fer_dfr_40833844.csv};
|
||||
\addplot[NavyBlue, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
|
||||
{res/admm/ber_2d_40833844.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
|
||||
\citereference{Mac23, 408.33.844}}
|
||||
\end{subfigure}%
|
||||
|
||||
\vspace*{-2mm}
|
||||
|
||||
\begin{subfigure}[t]{0.33\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
|
||||
\addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
|
||||
{res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
|
||||
\addplot[NavyBlue, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
|
||||
{res/admm/ber_2d_bch_31_26.csv};
|
||||
\addplot[Black, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if gt={SNR}{5.5},
|
||||
discard if lt={SNR}{1},
|
||||
]
|
||||
{res/generic/fer_ml_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={$E_b / N_0$ (dB)}, ylabel={FER},
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/proximal/2d_ber_fer_dfr_20455187.csv};
|
||||
\addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/hybrid/2d_ber_fer_dfr_20455187.csv};
|
||||
\addplot[NavyBlue, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
|
||||
{res/admm/ber_2d_20455187.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
|
||||
\citereference{Mac23, 204.55.187}}
|
||||
\end{subfigure}%
|
||||
\begin{subfigure}[t]{0.33\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}[scale=0.8]
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
|
||||
\addplot[RedOrange, mark=triangle, densely dashed, line width=1pt]
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.05}, discard if gt={SNR}{5.5}]
|
||||
{res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv};
|
||||
\addplot[NavyBlue, line width=1pt, mark=*]
|
||||
table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
|
||||
{res/admm/ber_2d_pegreg252x504.csv};
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
|
||||
\citereference{Mac23, PEGReg252x504}}
|
||||
\end{subfigure}%
|
||||
\end{figure}
|
||||
\end{minipage}%
|
||||
\begin{minipage}[c]{0.1\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\vspace*{-1.2cm}
|
||||
\hspace*{2mm}
|
||||
\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{RedOrange, line width=1pt, mark=*, solid}
|
||||
\addlegendentry{Proximal}
|
||||
|
||||
\addlegendimage{RedOrange, line width=1pt, mark=triangle*, densely dashed}
|
||||
\addlegendentry{Improved}
|
||||
|
||||
\addlegendimage{NavyBlue, line width=1pt, mark=*}
|
||||
\addlegendentry{ADMM}
|
||||
|
||||
\addlegendimage{Black, line width=1pt, mark=*}
|
||||
\addlegendentry{ML}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
|
||||
\vspace*{-1mm}
|
||||
|
||||
\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Theoretical Comparison}%
|
||||
\label{sub:Theoretical Comparison}
|
||||
|
||||
\begin{frame}[t, fragile]
|
||||
\frametitle{Comparison: Algorithm Structure}
|
||||
|
||||
\vspace*{-1cm}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
|
||||
\begin{subfigure}[b]{0.47\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{align*}
|
||||
\text{minimize}\hspace{2mm} & \textcolor{KITblue}{\underbrace{L\left(
|
||||
\boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right)}_{\text{Likelihood}}}
|
||||
+ \textcolor{KITred}{\underbrace{\gamma h\left( \tilde{\boldsymbol{x}}
|
||||
\right)} _{\text{Constraints}}} \\
|
||||
\text{subject to}\hspace{2mm} &\tilde{\boldsymbol{x}} \in \mathbb{R}^n
|
||||
\end{align*}
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\begin{algorithm}[caption={}, label={},
|
||||
basicstyle=\fontsize{10}{18}\selectfont
|
||||
]
|
||||
Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$
|
||||
while stopping critierion unfulfilled do
|
||||
$\textcolor{KITblue}{\boldsymbol{r} \leftarrow \boldsymbol{r}
|
||||
+ \omega \nabla L\left( \boldsymbol{y} \mid \boldsymbol{s} \right)} $
|
||||
$\textcolor{KITred}{\boldsymbol{s} \leftarrow
|
||||
\textbf{prox}_{\gamma h}\left( \boldsymbol{r} \right)} $|\Suppressnumber|
|
||||
|\Reactivatenumber|
|
||||
end while
|
||||
return $\hat{\boldsymbol{c}}$
|
||||
\end{algorithm}
|
||||
\end{subfigure}\hfill%
|
||||
\begin{subfigure}[b]{0.5\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{align*}
|
||||
\text{minimize}\hspace{5mm} &
|
||||
\textcolor{KITblue}{\underbrace{\boldsymbol{\gamma}^\text{T}
|
||||
\tilde{\boldsymbol{c}}}_{\text{Likelihood}}}
|
||||
+ \textcolor{KITred}{\underbrace{\sum\nolimits_{j\in\mathcal{J}}
|
||||
g_j\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
|
||||
\right)}_{\text{Constraints}}} \\
|
||||
\text{subject to}\hspace{5mm} &
|
||||
\tilde{\boldsymbol{c}} \in \left[ 0, 1 \right]^n
|
||||
\end{align*}
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\begin{algorithm}[caption={}, label={},
|
||||
basicstyle=\fontsize{10}{18}\selectfont
|
||||
]
|
||||
Initialize $\tilde{\boldsymbol{c}}, \boldsymbol{z}, \boldsymbol{u}, \boldsymbol{\gamma}, \rho$
|
||||
while stopping criterion unfulfilled do
|
||||
$\textcolor{KITblue}{\tilde{\boldsymbol{c}} \leftarrow \argmin_{\tilde{\boldsymbol{c}}}
|
||||
\left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
|
||||
+ \frac{\rho}{2}\sum_{j\in\mathcal{J}} \left\Vert
|
||||
\boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j
|
||||
+ \boldsymbol{u}_j \right\Vert \right)}$
|
||||
$\textcolor{KITred}{\boldsymbol{z}_j \leftarrow \textbf{prox}_{g_j}
|
||||
\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
|
||||
+ \boldsymbol{u}_j \right), \hspace{5mm}\forall j\in\mathcal{J}}$
|
||||
$\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j
|
||||
+ \tilde{\boldsymbol{c}} - \boldsymbol{z}_j, \hspace{14.5mm}\forall j\in\mathcal{J}$
|
||||
end while
|
||||
return $\hat{\boldsymbol{c}}$
|
||||
\end{algorithm}
|
||||
\end{subfigure}%
|
||||
\end{figure}%
|
||||
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t, fragile]
|
||||
\frametitle{Comparison: Algorithm Structure}
|
||||
|
||||
\vspace*{-0.6cm}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
|
||||
\begin{subfigure}{0.48\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{algorithm}[caption={}, label={},]
|
||||
Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$
|
||||
while stopping critierion unfulfilled do
|
||||
for $j$ in $\mathcal{J}$ do
|
||||
$p_j \leftarrow \prod_{i\in N_c\left( j \right) } r_i $
|
||||
$\textcolor{KITblue}{M_{j\to i} \leftarrow p_j^2 - p_j}$|\Suppressnumber|
|
||||
|\vspace{0.7mm}\Reactivatenumber|
|
||||
end for
|
||||
for $i$ in $\mathcal{I}$ do
|
||||
$s_i \leftarrow s_i + \gamma \left[ 4\left( s_i^2 - 1 \right)s_i
|
||||
\phantom{\frac{4}{s_i}}\right.$|\Suppressnumber|
|
||||
|\Reactivatenumber|$\left.+ \frac{4}{s_i}\sum_{j\in N_v\left( i \right) }
|
||||
M_{j\to i} \right] $
|
||||
$r_i \leftarrow r_i + \omega \left( s_i - y_i \right)$
|
||||
end for
|
||||
end while
|
||||
return $\hat{\boldsymbol{c}}$
|
||||
\end{algorithm}
|
||||
\end{subfigure}%
|
||||
\hfill
|
||||
\begin{subfigure}{0.48\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{algorithm}[caption={}, label={},]
|
||||
Initialize $\tilde{\boldsymbol{c}}, \boldsymbol{z}, \boldsymbol{u}, \boldsymbol{\gamma}, \rho$
|
||||
while stopping criterion unfulfilled do
|
||||
for $j$ in $\mathcal{J}$ do
|
||||
$\boldsymbol{z}_j \leftarrow \Pi_{P_{d_j}}\left(
|
||||
\boldsymbol{T}_j\tilde{\boldsymbol{c}} + \boldsymbol{u}_j\right)$
|
||||
$\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j + \boldsymbol{T}_j\tilde{\boldsymbol{c}}
|
||||
- \boldsymbol{z}_j$
|
||||
$\textcolor{KITblue}{M_{j\to i} \leftarrow \left( z_j \right)_i - \left( u_j \right)_i,
|
||||
\hspace{3mm} \forall i \in N_c\left( j \right)}$
|
||||
end for
|
||||
for $i$ in $\mathcal{I}$ do
|
||||
$\tilde{c}_i \leftarrow \frac{1}{d_i}
|
||||
\left(\sum_{j\in N_v\left( i \right) } M_{j\to i}
|
||||
- \frac{\gamma_i}{\mu} \right)$|\Suppressnumber|
|
||||
|\vspace{7mm}\Reactivatenumber|
|
||||
end for
|
||||
end while
|
||||
return $\hat{\boldsymbol{c}}$
|
||||
\end{algorithm}
|
||||
\end{subfigure}%
|
||||
\end{figure}%
|
||||
\end{frame}
|
||||
|
||||
|
||||
@ -828,104 +828,6 @@
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
% TODO: Move this to appendix (or remove it if other slide contains this
|
||||
% information anyway)
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{LP Decoding using ADMM: Choice of Penalty\\
|
||||
Parameters}
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 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{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
\end{frame}
|
||||
%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%\begin{frame}[t]
|
||||
|
||||
@ -7,7 +7,7 @@
|
||||
\label{sub:Decoding Algorithm}
|
||||
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: General Idea \citereference{WT22}}
|
||||
\frametitle{Proximal Decoding: General Approach \citereference{WT22}}
|
||||
|
||||
\vspace*{-0.7cm}
|
||||
|
||||
@ -71,7 +71,7 @@
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: General Idea}
|
||||
\frametitle{Proximal Decoding: General Approach}
|
||||
|
||||
\vspace*{-3mm}
|
||||
|
||||
@ -137,8 +137,7 @@ return $\boldsymbol{\hat{c}}$
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Analysis of Simulation Results}%
|
||||
\label{sub:Analysis of Simulation Results}
|
||||
\subsection{Simulation Results}%
|
||||
|
||||
|
||||
\begin{frame}[t]
|
||||
@ -169,27 +168,27 @@ return $\boldsymbol{\hat{c}}$
|
||||
]
|
||||
|
||||
\addplot [scol0, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma,
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.15},
|
||||
discard if gt={SNR}{5.5},]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.15$}
|
||||
\addplot [scol1, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma,
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.01},
|
||||
discard if gt={SNR}{5.5},]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.01$}
|
||||
|
||||
\addplot [scol2, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma,
|
||||
table [x=SNR, y=FER, col sep=comma,
|
||||
discard if not={gamma}{0.05},
|
||||
discard if gt={SNR}{5.5},]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.05$}
|
||||
|
||||
\addplot [KITorange, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma] {res/generic/bp_20433484.csv};
|
||||
table [x=SNR, y=FER, col sep=comma] {res/generic/bp_20433484.csv};
|
||||
\addlegendentry{BP}
|
||||
|
||||
\end{axis}
|
||||
@ -208,94 +207,6 @@ return $\boldsymbol{\hat{c}}$
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: Choice of $\gamma$}
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
\item Observation: not great benefit in finding the optimal value for $\gamma$
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
\hspace*{-3.5cm}
|
||||
\begin{subfigure}[c]{0.4\textwidth}
|
||||
\centering
|
||||
\begin{tikzpicture}
|
||||
\begin{semilogyaxis}[xlabel={$E_b / N_0$ (dB)}, ylabel={BER},
|
||||
grid=both, grid style={line width=.1pt},
|
||||
width=\textwidth,
|
||||
height=0.75\textwidth,
|
||||
legend style={at={(0.05,0.05)},anchor=south west},
|
||||
ymin=3e-7, ymax=1.5,]
|
||||
\addplot [scol0, line width=1pt] table [x=SNR, y=BER,
|
||||
col sep=comma, discard if not={gamma}{0.15}]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.15$}
|
||||
\addplot [scol1, line width=1pt] table [x=SNR, y=BER,
|
||||
col sep=comma, discard if not={gamma}{0.01}]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.01$}
|
||||
\addplot [scol2, line width=1pt] table [x=SNR, y=BER,
|
||||
col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.05$}
|
||||
\end{semilogyaxis}
|
||||
\end{tikzpicture}
|
||||
\end{subfigure}%
|
||||
\hspace{5mm}
|
||||
\begin{subfigure}[c]{0.4\textwidth}
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[view={75}{30},
|
||||
zmode=log,
|
||||
xlabel={$E_b / N_0$ (dB)},
|
||||
ylabel={$\gamma$},
|
||||
zlabel={BER},
|
||||
width=\textwidth,
|
||||
height=0.75\textwidth,
|
||||
legend pos=outer north east,]
|
||||
|
||||
\addplot3[surf,
|
||||
mesh/rows=17, mesh/cols=14,
|
||||
colormap name={viridis}] table [col sep=comma,
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = \left[ 0\text{:}0.01\text{:}0.16 \right] $}
|
||||
\addplot3[scol1, line width=1.5] table [col sep=comma,
|
||||
discard if not={gamma}{0.01},
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.01$}
|
||||
\addplot3[scol2, line width=1.5] table [col sep=comma,
|
||||
discard if not={gamma}{0.05},
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.05$}
|
||||
\addplot3[scol0, line width=1.5] table [col sep=comma,
|
||||
discard if not={gamma}{0.15},
|
||||
x=SNR, y=gamma, z=BER]
|
||||
{res/proximal/2d_ber_fer_dfr_20433484.csv};
|
||||
\addlegendentry{$\gamma = 0.15$}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{subfigure}
|
||||
\end{figure}
|
||||
|
||||
\bigskip
|
||||
|
||||
\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}}
|
||||
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%\begin{frame}[t]
|
||||
% \frametitle{Proximal Decoding: Choice of $\gamma$}
|
||||
@ -512,6 +423,7 @@ return $\boldsymbol{\hat{c}}$
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Improved Algorithm}%
|
||||
\begin{frame}[t, fragile]
|
||||
\frametitle{Proximal Decoding: Frame Error Rate}
|
||||
|
||||
|
||||
@ -3,8 +3,8 @@
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Motivation}%
|
||||
\label{sub:Motivation}
|
||||
%\subsection{Motivation}%
|
||||
%\label{sub:Motivation}
|
||||
|
||||
\begin{frame}[t]
|
||||
\frametitle{Motivation}
|
||||
@ -31,8 +31,8 @@
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Presumptions}%
|
||||
\label{sub:Presumptions}
|
||||
%\subsection{Presumptions}%
|
||||
%\label{sub:Presumptions}
|
||||
|
||||
\begin{frame}[t]
|
||||
\frametitle{Presumptions: Channel \& Modulation}
|
||||
@ -88,8 +88,8 @@
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{Optimization as a Decoding Method}%
|
||||
\label{sub:Optimization as a Decoding Method}
|
||||
%\subsection{Optimization as a Decoding Method}%
|
||||
%\label{sub:Optimization as a Decoding Method}
|
||||
|
||||
\begin{frame}[t]
|
||||
\frametitle{Optimization as a Decoding Method}
|
||||
|
||||
@ -53,7 +53,7 @@
|
||||
| 33 | Comparison: FER and BER | S |
|
||||
| 34 | Comparison: FER and BER for more codes | S |
|
||||
| 35 | Comparison: Algorithm structure | - |
|
||||
| 36 | Comparison: Algorithm structure: Message passing | S |
|
||||
| 36 | Comparison: Algorithm structure: Message passing | X |
|
||||
| 38 | Conclusion and outlook | R |
|
||||
| 41 | Supplementary slides: Choice of gamma for more codes | - |
|
||||
| 42 | Supplementary slides: Choice of mu and rho for more codes | - |
|
||||
|
||||
Loading…
Reference in New Issue
Block a user