Moved all citations to the respective slides
This commit is contained in:
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@ -300,12 +300,13 @@
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\input{sections/proximal_decoding.tex}
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\input{sections/lp_dec_using_admm.tex}
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\input{sections/comparison.tex}
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\input{sections/conclusion.tex}
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\input{sections/question_slide.tex}
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\begin{frame}[allowframebreaks]
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\frametitle{Bibliography}
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\printbibliography[heading=none]
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\end{frame}
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% \begin{frame}[allowframebreaks]
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% \frametitle{Bibliography}
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% \printbibliography[heading=none]
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% \end{frame}
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\input{sections/appendix.tex}
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@ -27,7 +27,7 @@
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ylabel={$\gamma$},
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zlabel={BER},
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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legend pos=outer north east,]
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\addplot3[surf,
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@ -50,10 +50,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{96.3.965}]{mackay_enc}}
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\citereference{Mac23, 96.3.965}}
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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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@ -65,7 +65,7 @@
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ylabel={$\gamma$},
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zlabel={BER},
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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legend pos=outer north east,]
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\addplot3[surf,
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@ -88,10 +88,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{204.33.484}]{mackay_enc}}
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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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@ -103,7 +103,7 @@
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ylabel={$\gamma$},
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zlabel={BER},
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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legend pos=outer north east,]
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\addplot3[surf,
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@ -126,12 +126,14 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{408.33.844}]{mackay_enc}}
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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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@ -142,7 +144,7 @@
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ylabel={$\gamma$},
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zlabel={BER},
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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legend pos=outer north east,]
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\addplot3[surf,
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@ -165,7 +167,7 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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@ -179,7 +181,7 @@
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ylabel={$\gamma$},
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zlabel={BER},
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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legend pos=outer north east,]
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\addplot3[surf,
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@ -202,10 +204,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{204.55.187}]{mackay_enc}}
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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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@ -217,7 +219,7 @@
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ylabel={$\gamma$},
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zlabel={BER},
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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legend pos=outer north east,]
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\addplot3[surf,
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@ -240,10 +242,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{PEGReg252x504}]{mackay_enc}}
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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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@ -271,6 +273,11 @@
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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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@ -296,7 +303,7 @@
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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@ -313,10 +320,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{96.3.965}]{mackay_enc}}
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\citereference{Mac23, 96.3.965}}
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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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@ -327,7 +334,7 @@
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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@ -344,10 +351,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{204.33.484}]{mackay_enc}}
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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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@ -358,7 +365,7 @@
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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@ -375,12 +382,14 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{408.33.844}]{mackay_enc}}
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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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@ -390,7 +399,7 @@
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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@ -407,7 +416,7 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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@ -420,7 +429,7 @@
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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@ -437,10 +446,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{204.55.187}]{mackay_enc}}
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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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@ -451,7 +460,7 @@
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xlabel={$\rho$}, ylabel={Avg. \# iter.},
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ymode=log,
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width=1.2\textwidth,
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height=0.85\textwidth,
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height=0.825\textwidth,
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]
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\addplot[ForestGreen, line width=1pt]
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table [col sep=comma, x=rho, y=k_avg,
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@ -468,10 +477,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{PEGReg252x504}]{mackay_enc}}
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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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@ -500,5 +509,10 @@
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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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@ -11,8 +11,10 @@
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\begin{frame}[t]
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\frametitle{Comparison: Convergence Behavior}
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\vspace*{-3mm}
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\begin{itemize}
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\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
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\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
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\end{itemize}
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\begin{figure}[H]
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@ -105,6 +107,14 @@
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\begin{itemize}
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\item Minimum number of iterations independant of SNR
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\end{itemize}
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\bigskip
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\smallskip
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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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@ -114,11 +124,11 @@
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\vspace*{-6.5mm}
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\begin{itemize}
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\item The points shown are from the following codes: BCH $\left( 31, 11 \right)$;
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BCH $\left( 31, 26 \right)$; \\
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\cite[\text{96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
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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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\begin{figure}[H]
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@ -130,8 +140,8 @@
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xlabel={$n$}, ylabel={time per frame (s)},
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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=0.45\textwidth,
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height=0.3375\textwidth,
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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[RedOrange, only marks, mark=square*]
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table [col sep=comma, x=n, y=spf]
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\end{tikzpicture}
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\end{figure}
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\begin{itemize}
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\item Both algorithms are $\mathcal{O}\left( n \right)$ on average
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\item LP decoding implementation significantly faster
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\end{itemize}
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\bigskip
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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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\vspace{-0.5cm}
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\begin{itemize}
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\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
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\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
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\end{itemize}
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\begin{figure}[H]
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legend columns=2,
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legend style={at={(0.5,-0.45)},anchor=south},
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ymax=1.5, ymin=3e-8,
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width=0.48\textwidth,
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height=0.35\textwidth,
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width=0.45\textwidth,
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height=0.33\textwidth,
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]
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\addplot[RedOrange, mark=*, line width=1pt]
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table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
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@ -208,8 +220,8 @@
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legend columns=2,
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legend style={at={(0.5,-0.45)},anchor=south},
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ymax=1.5, ymin=3e-8,
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width=0.48\textwidth,
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height=0.35\textwidth,
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width=0.45\textwidth,
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height=0.33\textwidth,
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]
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\addplot[RedOrange, mark=*, solid, line width=1pt]
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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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\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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\centering
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\begin{figure}[H]
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\vspace*{-0.7cm}
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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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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=0.85\textwidth,
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height=0.825\textwidth,
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]
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\addplot[RedOrange, line width=1pt, mark=*, solid]
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@ -351,10 +370,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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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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\cite[\text{96.3.965}]{mackay_enc}}
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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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@ -366,7 +385,7 @@
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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=0.85\textwidth,
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height=0.825\textwidth,
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]
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\addplot[RedOrange, line width=1pt, mark=*]
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@ -390,10 +409,10 @@
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\end{axis}
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\end{tikzpicture}
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\vspace*{-1mm}
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\vspace*{-2mm}
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|
||||
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
|
||||
\cite[\text{204.33.484}]{mackay_enc}}
|
||||
\citereference{Mac23, 204.33.484}}
|
||||
\end{subfigure}%
|
||||
\begin{subfigure}[t]{0.33\textwidth}
|
||||
\centering
|
||||
@ -405,7 +424,7 @@
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.85\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
@ -421,12 +440,14 @@
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-1mm}
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
|
||||
\cite[\text{408.33.844}]{mackay_enc}}
|
||||
\citereference{Mac23, 408.33.844}}
|
||||
\end{subfigure}%
|
||||
|
||||
\vspace*{-2mm}
|
||||
|
||||
\begin{subfigure}[t]{0.33\textwidth}
|
||||
\centering
|
||||
|
||||
@ -437,7 +458,7 @@
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.85\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
@ -459,7 +480,7 @@
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-1mm}
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{BCH code with $n=31, k=26$}
|
||||
\end{subfigure}%
|
||||
@ -473,7 +494,7 @@
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.85\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
@ -488,10 +509,10 @@
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-1mm}
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
|
||||
\cite[\text{204.55.187}]{mackay_enc}}
|
||||
\citereference{Mac23, 204.55.187}}
|
||||
\end{subfigure}%
|
||||
\begin{subfigure}[t]{0.33\textwidth}
|
||||
\centering
|
||||
@ -503,7 +524,7 @@
|
||||
ymode=log,
|
||||
ymax=1.5, ymin=8e-5,
|
||||
width=1.2\textwidth,
|
||||
height=0.85\textwidth,
|
||||
height=0.825\textwidth,
|
||||
]
|
||||
|
||||
\addplot[RedOrange, line width=1pt, mark=*]
|
||||
@ -519,10 +540,10 @@
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\vspace*{-1mm}
|
||||
\vspace*{-2mm}
|
||||
|
||||
\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
|
||||
\cite[\text{PEGReg252x504}]{mackay_enc}}
|
||||
\citereference{Mac23, PEGReg252x504}}
|
||||
\end{subfigure}%
|
||||
\end{figure}
|
||||
\end{minipage}%
|
||||
@ -548,19 +569,17 @@
|
||||
\addlegendimage{NavyBlue, line width=1pt, mark=*}
|
||||
\addlegendentry{ADMM}
|
||||
|
||||
% \addlegendimage{RoyalPurple, line width=1pt, mark=*}
|
||||
% \addlegendentry{BP}
|
||||
|
||||
\addlegendimage{Black, line width=1pt, mark=*}
|
||||
\addlegendentry{ML}
|
||||
|
||||
% \addlegendimage{PineGreen, line width=1pt, mark=triangle*, solid}
|
||||
% \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}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
@ -700,24 +719,3 @@ return $\tilde{\boldsymbol{c}}$
|
||||
\end{figure}%
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}[t]
|
||||
\frametitle{Conclusion}
|
||||
|
||||
\begin{itemize}
|
||||
\item Analysis of the general behavior of the two decoding algorithms
|
||||
\begin{itemize}
|
||||
\item Parameter choice based on decoding performance and time complexity
|
||||
\item Verification of theoretical considerations with simulation results
|
||||
\end{itemize}
|
||||
\item Suggestion for improvement of proximal decoding
|
||||
\begin{itemize}
|
||||
\item Addition of "ML-in-the-List" step
|
||||
\item Up to $\sim \SI{1}{dB}$ gain under certain conditions
|
||||
\end{itemize}
|
||||
\item Comparison
|
||||
\begin{itemize}
|
||||
\item based on simulation results
|
||||
\item based on their theoretical structure
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
26
latex/presentations/final/sections/conclusion.tex
Normal file
26
latex/presentations/final/sections/conclusion.tex
Normal file
@ -0,0 +1,26 @@
|
||||
\section{Conclusion and Outlook}%
|
||||
\label{sec:Comparison}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Conclusion}
|
||||
|
||||
\begin{itemize}
|
||||
\item Analysis of the general behavior of the two decoding algorithms
|
||||
\begin{itemize}
|
||||
\item Parameter choice based on decoding performance and time complexity
|
||||
\item Verification of theoretical considerations with simulation results
|
||||
\end{itemize}
|
||||
\item Suggestion for improvement of proximal decoding
|
||||
\begin{itemize}
|
||||
\item Addition of "ML-in-the-List" step
|
||||
\item Up to $\sim \SI{1}{dB}$ gain under certain conditions
|
||||
\end{itemize}
|
||||
\item Comparison
|
||||
\begin{itemize}
|
||||
\item based on simulation results
|
||||
\item based on their theoretical structure
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
@ -7,7 +7,9 @@
|
||||
\label{sub:LP Decoding using ADMM}
|
||||
|
||||
\begin{frame}[t]
|
||||
\frametitle{LP Decoding \cite{feldman_paper}}
|
||||
\frametitle{LP Decoding \citereference{FWK05}}
|
||||
|
||||
\vspace*{-3mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item General reformulation of ML decoding as a linear program (LP)
|
||||
@ -36,6 +38,13 @@
|
||||
\end{align*}
|
||||
\item Goal: relaxation of constraints to make a practical solution to the problem feasible
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
\bigskip
|
||||
|
||||
\addreference{FWK05}{J. Feldman; M.J. Wainwright; D.R. Karger: \emph{Using linear programming
|
||||
to Decode Binary linear codes}.
|
||||
IEEE Transactions on Information Theory 51.3 (2005), pp. 954–972.}
|
||||
\end{frame}
|
||||
|
||||
|
||||
@ -656,12 +665,16 @@
|
||||
\begin{frame}[t]
|
||||
\frametitle{LP Decoding using ADMM}
|
||||
|
||||
\vspace*{-4mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item Solution using the \textit{alternating direction method of multipliers} (ADMM)
|
||||
\citereference{$\text{Bar}^+\text{13}$}
|
||||
\item Slight reformulation of the LCLP:
|
||||
\begin{align*}
|
||||
\begin{aligned}
|
||||
\text{minimize}\hspace{2mm} &\boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
|
||||
\text{minimize}\hspace{2mm} &\boldsymbol{\gamma}^\text{T}
|
||||
\tilde{\boldsymbol{c}}
|
||||
+ \sum_{j\in\mathcal{J}} g_j\left( \boldsymbol{z}_j \right) \\
|
||||
\text{subject to}\hspace{2mm} &
|
||||
\boldsymbol{T}_j\tilde{\boldsymbol{c}} = \boldsymbol{z}_j, \hspace{2mm}
|
||||
@ -692,6 +705,12 @@
|
||||
% - \boldsymbol{z}_j + \boldsymbol{u}_j\right\Vert \right)
|
||||
\end{alignat*}
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\addreference{$\text{Bar}^+\text{13}$}{Siddharth Barman et al.:
|
||||
\emph{Decomposition Methods for Large Scale LP Decoding}.
|
||||
IEEE Transactions on Information Theory 59.12 (2013), pp. 7870–7886.}
|
||||
\end{frame}
|
||||
|
||||
|
||||
@ -703,12 +722,14 @@
|
||||
|
||||
\begin{itemize}
|
||||
\item Convergence properties enhanced by over-relaxation with parameter $\rho$
|
||||
\item Simplified rules%
|
||||
\footnote{$\left( \boldsymbol{z}_j \right)_i $ is a slight abuse of notation.
|
||||
What is actually meant is the component of $\boldsymbol{z}_j$ that is associated
|
||||
with the VN $i$, i.e., $\left( \boldsymbol{T}_j^\text{T}
|
||||
\boldsymbol{z}_j \right)_i$.\\
|
||||
The same is true for $\left( \boldsymbol{u}_j \right)_i$}:
|
||||
\item Simplified rules:
|
||||
% \footnote{$\left( \boldsymbol{z}_j \right)_i $ is a slight abuse of notation.
|
||||
% What is actually meant is the component of $\boldsymbol{z}_j$ that is associated
|
||||
% with the VN $i$, i.e., $\left( \boldsymbol{T}_j^\text{T}
|
||||
% \boldsymbol{z}_j \right)_i$.\\
|
||||
% The same is true for $\left( \boldsymbol{u}_j \right)_i$}:
|
||||
|
||||
\vspace*{-3mm}
|
||||
|
||||
\begin{alignat*}{3}
|
||||
\tilde{c}_i &\leftarrow \frac{1}{\left| N_v\left( i \right) \right|} \left(
|
||||
@ -726,12 +747,31 @@
|
||||
- \boldsymbol{z}_j
|
||||
\hspace{5mm} && \forall j\in\mathcal{J}
|
||||
\end{alignat*}
|
||||
|
||||
\vspace*{2mm}
|
||||
|
||||
\item The projections $\Pi_{\mathcal{P}_{d_j}}, \hspace{1mm} j\in\mathcal{J}$
|
||||
are the main computational effort
|
||||
\item Many approaches exist \cite{original_admm}, \cite{efficient_lp_dec_admm},
|
||||
\cite{lautern}
|
||||
\item The approach chosen here is the one described in \cite{original_admm}
|
||||
\item Many approaches exist \citereference{$\text{Bar}^+\text{13}$},
|
||||
\citereference{ZS13}, \citereference{$\text{Gen}^+\text{20}$}
|
||||
\item The approach chosen here is the one described in
|
||||
\citereference{$\text{Bar}^+\text{13}$}
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
\smallskip
|
||||
|
||||
\addreferences
|
||||
{$\text{Bar}^+\text{13}$}{Siddharth Barman et al.:
|
||||
\emph{Decomposition Methods for Large Scale LP Decoding}.
|
||||
IEEE Transactions on Information Theory 59.12 (2013), pp. 7870–7886.}
|
||||
{ZS13}{Xiaojie Zhang; Paul H. Siegel: \emph{Efficient iterative LP decoding
|
||||
of LDPC codes with alternating direction method of multipliers}.
|
||||
2013 IEEE International Symposium on Information Theory. 2013, pp. 1501–1505.}
|
||||
{$\text{Gen}^+\text{20}$}{Florian Gensheimer et al.:
|
||||
\emph{A Reduced-Complexity Projection Algorithm for ADMM-Based LP Decoding}.
|
||||
IEEE Transactions on Information Theory 66.8 (2020), pp. 4819–4833.}
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
|
||||
@ -827,9 +867,11 @@
|
||||
\begin{frame}[t]
|
||||
\frametitle{LP Decoding using ADMM: Frame Error Rate}
|
||||
|
||||
\vspace*{-6mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
|
||||
\cite[\text{Margulis2640.1320.3}]{mackay_enc}
|
||||
\citereference{Mac23, Margulis2640.1320.3}
|
||||
% ; $K=200, \mu = 3.3, \rho=1.9,
|
||||
% \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
|
||||
\end{itemize}
|
||||
@ -852,50 +894,7 @@
|
||||
discard if gt={SNR}{2.2},
|
||||
]
|
||||
{res/admm/fer_paper_margulis.csv};
|
||||
\addlegendentry{ADMM (Barman et al.)}
|
||||
\addplot[RoyalPurple, line width=1pt, mark=*]
|
||||
table [col sep=comma, x=SNR, y=FER, discard if gt={SNR}{2.2},]
|
||||
{res/generic/fer_bp_mackay_margulis.csv};
|
||||
\addlegendentry{BP (Barman et al.)}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{figure}
|
||||
|
||||
\begin{itemize}
|
||||
\item Comparison of simulation with results from Barman et al. \cite{original_admm}
|
||||
\end{itemize}
|
||||
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}[t]
|
||||
\frametitle{LP Decoding using ADMM: Frame Error Rate}
|
||||
|
||||
\begin{itemize}
|
||||
\item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
|
||||
\cite[\text{Margulis2640.1320.3}]{mackay_enc}
|
||||
% ; $K=200, \mu = 3.3, \rho=1.9,
|
||||
% \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[H]
|
||||
\centering
|
||||
|
||||
\begin{tikzpicture}
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$E_b / N_0 \left( \text{dB} \right) $}, ylabel={FER},
|
||||
ymode=log,
|
||||
width=0.45\textwidth,
|
||||
height=0.325\textwidth,
|
||||
%legend style={at={(0.03,0.04)},anchor=south west},
|
||||
legend pos=outer north east,
|
||||
]
|
||||
\addplot[Emerald, line width=1pt, mark=*]
|
||||
table [col sep=comma, x=SNR, y=FER,
|
||||
discard if gt={SNR}{2.2},
|
||||
]
|
||||
{res/admm/fer_paper_margulis.csv};
|
||||
\addlegendentry{ADMM (Barman et al.)}
|
||||
\addlegendentry{ADMM \citereference{$\text{Bar}^+\text{13}$}}
|
||||
\addplot[NavyBlue, mark=*, line width=1pt, densely dashed]
|
||||
table [col sep=comma, x=SNR, y=FER,]
|
||||
{res/admm/ber_margulis264013203.csv};
|
||||
@ -903,14 +902,25 @@
|
||||
\addplot[RoyalPurple, line width=1pt, mark=*]
|
||||
table [col sep=comma, x=SNR, y=FER, discard if gt={SNR}{2.2},]
|
||||
{res/generic/fer_bp_mackay_margulis.csv};
|
||||
\addlegendentry{BP (Barman et al.)}
|
||||
\addlegendentry{BP \citereference{$\text{Bar}^+\text{13}$}}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{figure}%
|
||||
|
||||
\begin{itemize}
|
||||
\item Comparison of simulation with results from Barman et al. \cite{original_admm}
|
||||
\item Comparison of simulation with results from Barman et al.
|
||||
\citereference{$\text{Bar}^+\text{13}$}
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\addreferences
|
||||
{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
|
||||
Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
|
||||
{$\text{Bar}^+\text{13}$}{Siddharth Barman et al.:
|
||||
\emph{Decomposition Methods for Large Scale LP Decoding}.
|
||||
IEEE Transactions on Information Theory 59.12 (2013), pp. 7870–7886.}
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
@ -918,8 +928,10 @@
|
||||
\frametitle{LP Decoding using ADMM: Choice of Penalty\\
|
||||
Parameters}
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[H]
|
||||
@ -933,8 +945,8 @@
|
||||
grid=both,
|
||||
xlabel={$\mu$}, ylabel={FER},
|
||||
ymode=log,
|
||||
width=0.9\textwidth,
|
||||
height=0.675\textwidth,
|
||||
width=0.8\textwidth,
|
||||
height=0.6\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
|
||||
table [col sep=comma, x=mu, y=FER,
|
||||
@ -959,8 +971,8 @@
|
||||
grid=both,
|
||||
xlabel={$\rho$}, ylabel={FER},
|
||||
ymode=log,
|
||||
width=0.9\textwidth,
|
||||
height=0.675\textwidth,
|
||||
width=0.8\textwidth,
|
||||
height=0.6\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
|
||||
table [col sep=comma, x=rho, y=FER,
|
||||
@ -1003,6 +1015,11 @@
|
||||
\item Similar to $\gamma$ with proximal decoding: no clear optimum
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
\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}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
@ -1010,8 +1027,10 @@
|
||||
\frametitle{LP Decoding using ADMM: Choice of Penalty\\
|
||||
Parameters}
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[H]
|
||||
@ -1024,8 +1043,8 @@
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$\mu$}, ylabel={Average \# of iterations},
|
||||
width=0.9\textwidth,
|
||||
height=0.675\textwidth,
|
||||
width=0.8\textwidth,
|
||||
height=0.6\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
|
||||
table [col sep=comma, x=mu, y=k_avg,
|
||||
@ -1049,8 +1068,8 @@
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={$\rho$}, ylabel={Average \# of iterations},
|
||||
width=0.9\textwidth,
|
||||
height=0.675\textwidth,
|
||||
width=0.8\textwidth,
|
||||
height=0.6\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
|
||||
table [col sep=comma, x=rho, y=k_avg,
|
||||
@ -1092,5 +1111,13 @@
|
||||
\begin{itemize}
|
||||
\item For lower decoding time, choose low $\mu$ and high $\rho$
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
\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}
|
||||
|
||||
|
||||
@ -7,9 +7,9 @@
|
||||
\label{sub:Decoding Algorithm}
|
||||
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: General Idea \cite{proximal_paper}}
|
||||
\frametitle{Proximal Decoding: General Idea \citereference{WT22}}
|
||||
|
||||
\vspace*{-0.3cm}
|
||||
\vspace*{-0.7cm}
|
||||
|
||||
\begin{itemize}
|
||||
\item MAP rule as continuous maximization problem:
|
||||
@ -59,6 +59,13 @@
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\end{itemize}
|
||||
|
||||
\smallskip
|
||||
\smallskip
|
||||
|
||||
\addreference{WT22}{Tadashi Wadayama; Satoshi Takabe: \emph{Proximal Decoding for LDPC
|
||||
Codes}. IEICE Transactions on Fundamentals of Electronics, Communications and Computer
|
||||
Sciences advpub (2022), 2022TAP0002.}
|
||||
\end{frame}
|
||||
|
||||
|
||||
@ -66,6 +73,8 @@
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: General Idea}
|
||||
|
||||
\vspace*{-3mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item Objective function:
|
||||
\begin{align*}
|
||||
@ -74,7 +83,7 @@
|
||||
+ \gamma h\left( \tilde{\boldsymbol{x}} \right)
|
||||
\end{align*}
|
||||
\note{Notational difference between $f$ and $f_X$ or $f_Y$}
|
||||
\item Proximal operator \cite{proximal_algorithms}:
|
||||
\item Proximal operator \citereference{PB14}:
|
||||
\begin{align*}
|
||||
\text{prox}_{\gamma h} \left( \tilde{\boldsymbol{x}} \right) &\equiv
|
||||
\argmin_{\boldsymbol{t}\in\mathbb{R}^n}
|
||||
@ -96,6 +105,11 @@
|
||||
\hspace{10mm} \text{``Code proximal step''}
|
||||
\end{align*}
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\addreference{PB14}{Neal Parikh; Stephen Boyd: \emph{Proximal Algorithms}.
|
||||
Found. Trends Optim. 1.3 (Jan. 2014), pp. 127–239.}
|
||||
\end{frame}
|
||||
|
||||
|
||||
@ -103,7 +117,7 @@
|
||||
\begin{frame}[t, fragile]
|
||||
\frametitle{Proximal Decoding: Algorithm}
|
||||
\begin{itemize}
|
||||
\item Iterative decoding algorithm \cite{proximal_paper}:
|
||||
\item Iterative decoding algorithm:
|
||||
\end{itemize}
|
||||
|
||||
\vspace{2mm}
|
||||
@ -130,8 +144,10 @@ return $\boldsymbol{\hat{c}}$
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: Bit Error Rate}
|
||||
|
||||
\vspace*{-7mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[H]
|
||||
@ -159,7 +175,7 @@ return $\boldsymbol{\hat{c}}$
|
||||
\addlegendentry{$\gamma = 0.15$}
|
||||
\addplot [ForestGreen, mark=*, line width=1pt]
|
||||
table [x=SNR, y=gamma_0_15, col sep=comma] {res/ber_paper.csv};
|
||||
\addlegendentry{$\gamma = 0.15$ (Wadayama et al.)}
|
||||
\addlegendentry{$\gamma = 0.15$ \citereference{WT22}}
|
||||
|
||||
\addplot [NavyBlue, mark=triangle, dashed, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma,
|
||||
@ -169,7 +185,7 @@ return $\boldsymbol{\hat{c}}$
|
||||
\addlegendentry{$\gamma = 0.01$}
|
||||
\addplot [NavyBlue, mark=*, line width=1pt]
|
||||
table [x=SNR, y=gamma_0_01, col sep=comma] {res/ber_paper.csv};
|
||||
\addlegendentry{$\gamma = 0.01$ (Wadayama et al.)}
|
||||
\addlegendentry{$\gamma = 0.01$ \citereference{WT22}}
|
||||
|
||||
\addplot [RedOrange, mark=triangle, dashed, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma,
|
||||
@ -179,19 +195,29 @@ return $\boldsymbol{\hat{c}}$
|
||||
\addlegendentry{$\gamma = 0.05$}
|
||||
\addplot [RedOrange, mark=*, line width=1pt]
|
||||
table [x=SNR, y=gamma_0_05, col sep=comma] {res/ber_paper.csv};
|
||||
\addlegendentry{$\gamma = 0.05$ (Wadayama et al.)}
|
||||
\addlegendentry{$\gamma = 0.05$ \citereference{WT22}}
|
||||
|
||||
\addplot [RoyalPurple, mark=*, line width=1pt]
|
||||
table [x=SNR, y=BP, col sep=comma] {res/ber_paper.csv};
|
||||
\addlegendentry{BP}
|
||||
\addlegendentry{BP \citereference{WT22}}
|
||||
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
\end{figure}
|
||||
|
||||
\vspace*{-2mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item Comparison of simulation with results of Wadayama et al. \cite{proximal_paper}
|
||||
\item Comparison of simulation with results of Wadayama et al. \citereference{WT22}
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\addreference{WT22}{Tadashi Wadayama; Satoshi Takabe: \emph{Proximal Decoding for LDPC
|
||||
Codes}. IEICE Transactions on Fundamentals of Electronics, Communications and Computer
|
||||
Sciences advpub (2022), 2022TAP0002.}
|
||||
\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}
|
||||
|
||||
|
||||
@ -199,8 +225,10 @@ return $\boldsymbol{\hat{c}}$
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: Choice of $\gamma$}
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[H]
|
||||
@ -273,6 +301,12 @@ return $\boldsymbol{\hat{c}}$
|
||||
\begin{itemize}
|
||||
\item Not great benefit in finding the optimal value for $\gamma$
|
||||
\end{itemize}
|
||||
|
||||
\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}
|
||||
|
||||
|
||||
@ -495,12 +529,14 @@ return $\boldsymbol{\hat{c}}$
|
||||
\begin{frame}[t, fragile]
|
||||
\frametitle{Proximal Decoding: Frame Error Rate}
|
||||
|
||||
\vspace*{-3mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204$,\\
|
||||
$k=102$ \cite[\text{204.33.484}]{mackay_enc}
|
||||
$k=102$ \citereference{Mac23, 204.33.484}
|
||||
\end{itemize}
|
||||
|
||||
\vspace*{-5mm}
|
||||
\vspace*{-2mm}
|
||||
|
||||
\begin{minipage}{.4\textwidth}
|
||||
\centering
|
||||
@ -521,6 +557,11 @@ end for
|
||||
return $\boldsymbol{\hat{c}}$
|
||||
\end{algorithm}
|
||||
\end{figure}
|
||||
|
||||
\vspace*{-4mm}
|
||||
\hspace*{-4mm}
|
||||
\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{minipage}%
|
||||
\begin{minipage}{.6\textwidth}
|
||||
\centering
|
||||
@ -854,8 +895,8 @@ return $\boldsymbol{\hat{c}}$
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{$\nabla L \left(\boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right)$
|
||||
for a repetition code with $n=2$\footnotemark}
|
||||
\caption{$\nabla L \left(\boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right)$%
|
||||
\footnotemark{} for a repetition code with $n=2$}
|
||||
\end{subfigure}%
|
||||
\begin{subfigure}[c]{0.5\textwidth}
|
||||
\centering
|
||||
@ -894,9 +935,7 @@ return $\boldsymbol{\hat{c}}$
|
||||
|
||||
\footnotetext{In an AWGN Channel $\nabla L\left( \boldsymbol{y} \mid
|
||||
\tilde{\boldsymbol{x}}\right)
|
||||
\propto \left( \tilde{\boldsymbol{x}} - \boldsymbol{y} \right)$
|
||||
\cite[Sec. 4.1]{proximal_paper}}
|
||||
|
||||
\propto \left( \tilde{\boldsymbol{x}} - \boldsymbol{y} \right)$}
|
||||
\end{frame}
|
||||
|
||||
|
||||
@ -904,9 +943,11 @@ return $\boldsymbol{\hat{c}}$
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoder: Oscillation of $\nabla h\left( \tilde{\boldsymbol{x}} \right) $}
|
||||
|
||||
\vspace*{-3mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item Single decoding using a (3,6) regular LDPC code with $n=204, k=102$
|
||||
\cite[\text{204.33.484}]{mackay_enc}
|
||||
\citereference{Mac23, 204.33.484}
|
||||
% ; $\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$
|
||||
\end{itemize}
|
||||
|
||||
@ -969,6 +1010,12 @@ return $\boldsymbol{\hat{c}}$
|
||||
\item For larger $n$, the gradient itself starts to oscillate
|
||||
\item Dynamic range of oscillation highly correlated with probability of bit error
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
\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}
|
||||
|
||||
|
||||
@ -1086,7 +1133,7 @@ return $\boldsymbol{\hat{c}}$
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t, fragile]
|
||||
\frametitle{Proximal Decoding: Improvement using \\``ML-in-the-List''}
|
||||
\frametitle{Proximal Decoding: Improvement}
|
||||
|
||||
\vspace*{-0.5cm}
|
||||
|
||||
@ -1147,12 +1194,12 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Proximal Decoding: Improvement using \\``ML-in-the-List''}
|
||||
\frametitle{Proximal Decoding: Improvement}
|
||||
|
||||
\vspace{-0.5cm}
|
||||
\vspace{-0.6cm}
|
||||
|
||||
\begin{itemize}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
|
||||
\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[H]
|
||||
@ -1166,8 +1213,8 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d
|
||||
legend columns=2,
|
||||
legend style={at={(0.5,-0.45)},anchor=south},
|
||||
ymax=1.5, ymin=3e-8,
|
||||
width=0.48\textwidth,
|
||||
height=0.33\textwidth,
|
||||
width=0.45\textwidth,
|
||||
height=0.3\textwidth,
|
||||
]
|
||||
\addplot[ForestGreen, mark=*, line width=1pt]
|
||||
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
|
||||
@ -1199,8 +1246,8 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d
|
||||
legend columns=2,
|
||||
legend style={at={(0.5,-0.45)},anchor=south},
|
||||
ymax=1.5, ymin=3e-8,
|
||||
width=0.48\textwidth,
|
||||
height=0.33\textwidth,
|
||||
width=0.45\textwidth,
|
||||
height=0.3\textwidth,
|
||||
]
|
||||
|
||||
\addplot[ForestGreen, mark=*, solid, line width=1pt]
|
||||
@ -1256,6 +1303,11 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d
|
||||
\begin{itemize}
|
||||
\item Up to $\sim \SI{1}{dB}$ improvement
|
||||
\end{itemize}
|
||||
|
||||
\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}
|
||||
|
||||
|
||||
|
||||
@ -9,18 +9,37 @@
|
||||
\begin{frame}[t]
|
||||
\frametitle{Motivation}
|
||||
\begin{itemize}
|
||||
\item The general ML decoding problem is NP-complete \cite{ml_np_hard_proof}
|
||||
\item The iterative message–passing algorithms preferred in practice do not guarantee
|
||||
optimality when the graph contains cycles \cite{ldpc_conv}
|
||||
\item The standard message-passing algorithms are often difficult to
|
||||
analyze \cite{feldman_thesis}
|
||||
\item General ML decoding problem NP-complete \citereference{BMT78}
|
||||
\item Iterative message–passing algorithms preferred in practice do not guarantee
|
||||
optimality when the graph contains cycles \citereference{KTP19}
|
||||
\item Standard message-passing algorithms difficult to analyze \citereference{FEL03}
|
||||
\end{itemize}
|
||||
|
||||
\vspace{3.5cm}
|
||||
|
||||
\addreferences
|
||||
{BMT78}{E. Berlekamp; R. McEliece; H. van Tilborg: \emph{On the inherent intractability
|
||||
of certain coding problems (Corresp.)}.
|
||||
IEEE Transactions on Information Theory 24.3 (May 1978), pp. 384–386.}
|
||||
{KTP19}{Banu Kabakulak; Z. Caner Taşkın; Ali Emre Pusane: \emph{Optimization–based
|
||||
decoding algorithms for LDPC convolutional codes in communication systems}.
|
||||
IISE Transactions 51.10 (2019), pp. 1061–1074.}
|
||||
{FEL03}{Jon Feldman: \emph{Decoding error-correcting codes via linear programming}.
|
||||
PhD thesis. MIT, 2003.}
|
||||
\stopreferences
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}[t]
|
||||
\frametitle{Previous Work}
|
||||
|
||||
\vspace*{-5mm}
|
||||
|
||||
\begin{itemize}
|
||||
\item Bachelor's thesis by Yanixa Lu \citereference{Lu22}
|
||||
\end{itemize}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
|
||||
@ -39,14 +58,17 @@
|
||||
|
||||
\fbox{\includegraphics[page=60,width=.6\textwidth]{res/Bachelor_Thesis_Yanxia_Lu}}
|
||||
\end{subfigure}%
|
||||
|
||||
\caption{Bachelor's Thesis by Yanxia Lu \cite{yanxia_lu_thesis}}
|
||||
\end{figure}
|
||||
|
||||
\begin{itemize}
|
||||
\item Analysis of ``Proximal Decoding''
|
||||
\item Analysis of ``Interior Point Decoding''
|
||||
\end{itemize}
|
||||
|
||||
\bigskip
|
||||
|
||||
\addreference{Lu22}{Yanxia Lu: \emph{Realization of Channel Decoding Using Optimization
|
||||
Techniques}. Bachelor’s Thesis. KIT, 2022.}
|
||||
\end{frame}
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user