121 lines
4.8 KiB
TeX
121 lines
4.8 KiB
TeX
\appendix
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\section{Proximal Decoding Time Complexity}%
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\label{app:Proximal Decoding Time Complexity}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{Proximal Decoding: Time Complexity}
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\begin{figure}[H]
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\centering
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\begin{tikzpicture}[scale=0.7]
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\begin{axis}[
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grid=both,
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xlabel={$n$}, ylabel={time per frame (s)},
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legend style={at={(0.05,0.77)},anchor=south west},
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]
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\addplot[only marks, red] table [col sep=comma,
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x=n, y=spf] {res/fps_vs_n_proximal.csv};
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\addlegendentry{proximal}
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\addplot[only marks, blue] table [col sep=comma,
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x=n, y=spf] {res/fps_vs_n_hybrid.csv};
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\addlegendentry{hybrid prox \& ML ($\SI{12}{\bit}$)}
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\end{axis}
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\end{tikzpicture}
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\caption{Time Complexity of Proximal Decoding and Modified Implementation\footnotemark}
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\label{fig:fps_vs_n}
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\end{figure}
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\footnotetext{The points shown were calculated by evaluating the metadata
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of BER simulation results from the following codes:
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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;
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204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
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}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{Proximal Decoding: Visualization of Gradients}
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\begin{figure}[H]
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\centering
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\begin{subfigure}[c]{0.5\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[xmin = -1.25, xmax=1.25,
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ymin = -1.25, ymax=1.25,
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xlabel={$x_1$}, ylabel={$x_2$},
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grid=major, grid style={dotted},
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view={0}{90}]
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\addplot3[point meta=\thisrow{grad_norm},
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point meta min=1,
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point meta max=3,
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quiver={u=\thisrow{grad_0},
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v=\thisrow{grad_1},
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scale arrows=.05,
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every arrow/.append style={%
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line width=.3+\pgfplotspointmetatransformed/1000,
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-{Latex[length=0pt 5,width=0pt 3]}
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},
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},
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quiver/colored = {mapped color},
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colormap/rocket,
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-stealth,
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]
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table[col sep=comma] {res/2d_grad_L.csv};
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\end{axis}
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\end{tikzpicture}
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\caption{$\nabla L \left(\boldsymbol{y} \mid \boldsymbol{x} \right) $ for a repetition code with $n=2$
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\footnotemark}
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\end{subfigure}%
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\begin{subfigure}[c]{0.5\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.8]
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\begin{axis}[xmin = -1.25, xmax=1.25,
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ymin = -1.25, ymax=1.25,
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xlabel={$x_1$}, ylabel={$x_2$},
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grid=major, grid style={dotted},
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view={0}{90}]
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\addplot3[point meta=\thisrow{grad_norm},
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point meta min=1,
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point meta max=4,
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quiver={u=\thisrow{grad_0},
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v=\thisrow{grad_1},
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scale arrows=.03,
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every arrow/.append style={%
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line width=.3+\pgfplotspointmetatransformed/1000,
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-{Latex[length=0pt 5,width=0pt 3]}
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},
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},
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quiver/colored = {mapped color},
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colormap/rocket,
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-stealth,
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]
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table[col sep=comma] {res/2d_grad_rep.csv};
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\end{axis}
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\end{tikzpicture}
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\caption{$\nabla h \left( \boldsymbol{x} \right) $ for a repetition code with $n=2$}
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\end{subfigure}%
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\end{figure}
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\footnotetext{In an AWGN Channel $\nabla L\left( \boldsymbol{y} \mid \boldsymbol{x}\right)
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\propto \left( \boldsymbol{x} - \boldsymbol{y} \right)$
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\cite[Sec. 4.1]{proximal_paper}}
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\end{frame}
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