Added footnotes mentioning used code; Added Hybrid algorithm
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@ -58,7 +58,7 @@
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\left( \boldsymbol{y} | \boldsymbol{x} \right) \right)
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\end{align*}
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\note{Notational difference between $f$ and $f_X$ or $f_Y$}
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\item Code proximal operator:
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\item Code proximal operator \cite{proximal_algorithms}:
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\begin{align*}
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\text{prox}_{\gamma h} \left( \boldsymbol{x} \right) &\equiv
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arg\min_{\boldsymbol{z}\in\mathbb{R}} \left(
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@ -3,14 +3,17 @@
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Proximal Decoder}%
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\label{sub:Ex Proximal Decoder}
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\subsection{Proximal Decoding}%
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\label{sub:Ex Proximal Decoding}
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\begin{frame}[t]
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\frametitle{Proximal Decoder: Examination Results}
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\frametitle{Proximal Decoding: Bit Error Rate and Performance}
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\begin{itemize}
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\item AWGN Channel - (3,6) regular LDPC Code with $n=204, k=102$:
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\vspace{2mm}
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\item Comparison of simulation
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\footnote{(3,6) regular LDPC Code with $n=204, k=102$
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\cite[Code: 204.33.484]{mackay_enc}}
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with results of Wadayama and Takabe
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\begin{figure}[H]
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\centering
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@ -62,71 +65,90 @@
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\item $\mathcal{O}\left(n \right) $ time complexity - same as BP;
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Only multiplication and addition necessary \cite{proximal_paper}
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\item Measured Performance: Between $\SI{0.5}{\mega\bit / \second}$ and
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$\SI{2.5}{\mega\bit / \second}$ - Intel Core i7-7700HQ @ 2.80GHz\\
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($\sim \SI{10}{\second}$ for the shown plot)
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\todo{Use the shown bitrate, or half?
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($n_{iterations} \cdot n$ or $n_{iterations} \cdot k$?)}
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$\SI{2.5}{\mega\bit / \second}$ - Intel Core i7-7700HQ @ 2.80GHz%
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% \\ ($\sim \SI{10}{\second}$ for the shown plot)
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\end{itemize}
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\vspace{3mm}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t]
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\frametitle{Proximal Decoder: Choice of $\gamma$}
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\frametitle{Proximal Decoding: Choice of $\gamma$}
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\setcounter{footnote}{0}
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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=0.52]
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\begin{semilogyaxis}[xlabel={SNR}, ylabel={BER},
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grid=both, grid style={line width=.1pt},
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legend style={at={(0.05,0.05)},anchor=south west},
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ymin=3e-7, ymax=1.5,]
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\foreach \gamma in {0.01, 0.05, 0.15}{
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\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{\gamma}] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\legend{\gamma}
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}
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\legend{$\gamma=0.01$, $\gamma=0.05$, $\gamma=0.15$}
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\end{semilogyaxis}
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\end{tikzpicture}
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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=0.7]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={SNR},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf, mesh/rows=17, mesh/cols=14, colormap/viridis] table [col sep=comma, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma, discard if not={gamma}{0.05}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma, discard if not={gamma}{0.01}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma, discard if not={gamma}{0.15}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\begin{itemize}
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\item Comparison of simulation
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\footnote{(3,6) regular LDPC Code with $n=204, k=102$
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\cite[Code: 204.33.484]{mackay_enc}}
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results for different values of $\gamma$
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\end{itemize}
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\caption{BER for $\omega = 0.05, K=100$}
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\label{fig:ber_3d}
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\end{figure}
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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=0.52]
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\begin{semilogyaxis}[xlabel={SNR}, ylabel={BER},
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grid=both, grid style={line width=.1pt},
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legend style={at={(0.05,0.05)},anchor=south west},
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ymin=3e-7, ymax=1.5,]
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\foreach \gamma in {0.01, 0.05, 0.15}{
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\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{\gamma}] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\legend{\gamma}
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}
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\legend{$\gamma=0.01$, $\gamma=0.05$, $\gamma=0.15$}
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\end{semilogyaxis}
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\end{tikzpicture}
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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=0.55]
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\begin{axis}[view={75}{60},
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zmode=log,
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xlabel={SNR},
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ylabel={$\gamma$},
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zlabel={BER},]
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\addplot3[surf, mesh/rows=17, mesh/cols=14, colormap/viridis] table [col sep=comma, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma, discard if not={gamma}{0.05}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma, discard if not={gamma}{0.01}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma, discard if not={gamma}{0.15}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.15$}
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\end{axis}
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\end{tikzpicture}
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\end{subfigure}
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\caption{BER for $\omega = 0.05, K=100$}
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\label{fig:ber_3d}
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\end{figure}
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\begin{itemize}
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\item Not great benefit in finding the optimal value for $\gamma$
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\end{itemize}
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\vspace{3mm}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[t, fragile]
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\frametitle{Proximal Decoder: Frame Error Rate}
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\frametitle{Proximal Decoding: Frame Error Rate}
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\setcounter{footnote}{0}
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\begin{itemize}
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\item Comparison of simulated
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\footnote{(3,6) regular LDPC Code with $n=204, k=102$
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\cite[Code: 204.33.484]{mackay_enc}}
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BER and FER
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\end{itemize}
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\begin{minipage}{.4\textwidth}
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\centering
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\begin{algorithm}[caption={}, label={},
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basicstyle=\fontsize{7.5}{9.5}\selectfont
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]
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@ -143,11 +165,11 @@ Output $\boldsymbol{\hat{x}}$
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\end{minipage}%
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\begin{minipage}{.6\textwidth}
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\centering
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\begin{figure}[H]
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\vspace*{-8mm}
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\centering
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\begin{tikzpicture}[scale=0.45]
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\begin{tikzpicture}[scale=0.42]
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\begin{axis}[
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grid=both,
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xlabel={SNR}, ylabel={BER},
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@ -165,8 +187,8 @@ Output $\boldsymbol{\hat{x}}$
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.05$}
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\end{axis}
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\end{tikzpicture}\\
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\begin{tikzpicture}[scale=0.45]
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\end{tikzpicture}
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\begin{tikzpicture}[scale=0.42]
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\begin{axis}[
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grid=both,
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xlabel={SNR}, ylabel={FER},
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@ -184,8 +206,8 @@ Output $\boldsymbol{\hat{x}}$
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{$\gamma = 0.05$}
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\end{axis}
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\end{tikzpicture}
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\begin{tikzpicture}[scale=0.45]
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\end{tikzpicture}\\
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\begin{tikzpicture}[scale=0.42]
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\begin{axis}[
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grid=both,
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xlabel={SNR}, ylabel={Decoding Failure Rate},
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@ -212,84 +234,209 @@ Output $\boldsymbol{\hat{x}}$
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\end{frame}
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\begin{frame}[t]
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\frametitle{title}
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\begin{figure}[H]
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\newcommand{\tikzmarknew}[1]{\tikz[overlay,remember picture] \node (#1) {};}
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\newcommand*{\AddNote}[4]{%
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\begin{tikzpicture}[overlay, remember picture]
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\draw [decoration={brace,amplitude=0.5em},decorate,ultra thick]
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($(#3)!([yshift=1.5ex]#1)!($(#3)-(0,1)$)$) --
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($(#3)!(#2)!($(#3)-(0,1)$)$)
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node [align=center, text width=2cm, pos=0.5, anchor=west] {#4};
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\end{tikzpicture}
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}%
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\begin{frame}[t, fragile]
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\frametitle{Proximal Decoding: Improvement using ``ML-on-List''}
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\setcounter{footnote}{0}
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\begin{itemize}
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\item Comparison of proximal \& hybrid-proximal-ML\\
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decoding simulation
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\footnote{(3,6) regular LDPC Code with $n=204, k=102$
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\cite[Code: 204.33.484]{mackay_enc}}
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results
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\end{itemize}
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\begin{minipage}{.4\textwidth}
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\centering
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\begin{tikzpicture}[scale=0.45]
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\begin{axis}[
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grid=both,
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xlabel={SNR}, ylabel={BER},
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ymode=log,
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legend style={at={(0.05,0.05)},anchor=south west},
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ymax=1.5, ymin=3e-8,
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\begin{algorithm}[caption={}, label={},
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basicstyle=\fontsize{6.5}{7.5}\selectfont
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]
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% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.15$}
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% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.01$}
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\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{proximal}
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\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_hybrid.csv};
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\addlegendentry{hybrid prox. \& ML}
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\end{axis}
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\end{tikzpicture}\\
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\begin{tikzpicture}[scale=0.45]
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\begin{axis}[
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grid=both,
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xlabel={SNR}, ylabel={FER},
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ymode=log,
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legend style={at={(0.05,0.05)},anchor=south west},
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ymax=1.5, ymin=3e-8,
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]
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% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.15$}
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% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.01$}
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\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{proximal}
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\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_hybrid.csv};
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\addlegendentry{hybrid prox. \& ML}
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\end{axis}
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\end{tikzpicture}
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\begin{tikzpicture}[scale=0.45]
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\begin{axis}[
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grid=both,
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xlabel={SNR}, ylabel={Decoding Failure Rate},
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ymode=log,
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legend style={at={(0.05,0.05)},anchor=south west},
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ymax=1.5, ymin=3e-8,
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]
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% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.15$}
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% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.01$}
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\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{proximal}
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\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_hybrid.csv};
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\addlegendentry{hybrid prox. \& ML}
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\end{axis}
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\end{tikzpicture}
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\caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200$}
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\label{fig:simulation_results_hybrid}
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\end{figure}
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$\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$$\hspace{4.185cm}\tikzmarknew{prox-start}$
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for $k=0$ to $K-1$ do
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$\boldsymbol{r}^{\left( k+1 \right)} = \boldsymbol{s}^{(k)} - \omega \nabla L \left( \boldsymbol{s}^{(k)}; \boldsymbol{y} \right) $
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Compute $\nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right)$
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$\boldsymbol{s}^{\left( k+1 \right)} = \boldsymbol{r}^{(k+1)} - \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) $
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$\boldsymbol{\hat{x}} = \text{sign}\left( \boldsymbol{s}^{\left( k+1 \right) } \right) $
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If $\boldsymbol{\hat{x}}$ passes the parity check condition, output $\boldsymbol{\hat{x}}$
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end for $\tikzmarknew{prox-end}$
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Find $N$ most probably wrong bits $\hspace{2cm}\tikzmarknew{ml-start}$
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Generate variations $\boldsymbol{\tilde{x}}_n$ of $\boldsymbol{\hat{x}}$ with the $N$ bits modified
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Compute $d\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right) \forall n \in \left[ 1 : N-1 \right] $
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Output $\boldsymbol{\tilde{x}}_n$ with lowest $d\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right)$ $\tikzmarknew{ml-end}$
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\end{algorithm}
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\AddNote{prox-start}{prox-end}{prox-start}{\small Proximal\\Decoding}
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\AddNote{ml-start}{ml-end}{ml-start}{\small ML-on-List}
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\end{minipage}%
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\begin{minipage}{.6\textwidth}
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\centering
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\begin{figure}[H]
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\centering
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\vspace*{-12mm}
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\begin{tikzpicture}[scale=0.42]
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\begin{axis}[
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grid=both,
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xlabel={SNR}, ylabel={BER},
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ymode=log,
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legend style={at={(0.05,0.05)},anchor=south west},
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ymax=1.5, ymin=3e-8,
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]
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% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.15$}
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% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.01$}
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\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_proximal.csv};
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\addlegendentry{proximal}
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\addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484_hybrid.csv};
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\addlegendentry{hybrid prox. \& ML}
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\end{axis}
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\end{tikzpicture}
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\begin{tikzpicture}[scale=0.42]
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\begin{axis}[
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grid=both,
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xlabel={SNR}, ylabel={FER},
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ymode=log,
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legend style={at={(0.05,0.05)},anchor=south west},
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ymax=1.5, ymin=3e-8,
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]
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% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
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% {res/2d_ber_fer_dfr_20433484.csv};
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% \addlegendentry{$\gamma = 0.15$}
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% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
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% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
% \addlegendentry{$\gamma = 0.01$}
|
||||
\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/2d_ber_fer_dfr_20433484_proximal.csv};
|
||||
\addlegendentry{proximal}
|
||||
\addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/2d_ber_fer_dfr_20433484_hybrid.csv};
|
||||
\addlegendentry{hybrid prox. \& ML}
|
||||
\end{axis}
|
||||
\end{tikzpicture}\\
|
||||
\begin{tikzpicture}[scale=0.42]
|
||||
\begin{axis}[
|
||||
grid=both,
|
||||
xlabel={SNR}, ylabel={Decoding Failure Rate},
|
||||
ymode=log,
|
||||
legend style={at={(0.05,0.05)},anchor=south west},
|
||||
ymax=1.5, ymin=3e-8,
|
||||
]
|
||||
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
|
||||
% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
% \addlegendentry{$\gamma = 0.15$}
|
||||
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
|
||||
% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
% \addlegendentry{$\gamma = 0.01$}
|
||||
\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/2d_ber_fer_dfr_20433484_proximal.csv};
|
||||
\addlegendentry{proximal}
|
||||
\addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
|
||||
{res/2d_ber_fer_dfr_20433484_hybrid.csv};
|
||||
\addlegendentry{hybrid prox. \& ML}
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
|
||||
\caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, N=12$}
|
||||
\label{fig:simulation_results_hybrid}
|
||||
\end{figure}
|
||||
\end{minipage}
|
||||
\end{frame}
|
||||
|
||||
%\begin{frame}[t]
|
||||
% \frametitle{Proximal Decoding: Improvement}
|
||||
% \begin{figure}[H]
|
||||
% \centering
|
||||
%
|
||||
% \begin{tikzpicture}[scale=0.45]
|
||||
% \begin{axis}[
|
||||
% grid=both,
|
||||
% xlabel={SNR}, ylabel={BER},
|
||||
% ymode=log,
|
||||
% legend style={at={(0.05,0.05)},anchor=south west},
|
||||
% ymax=1.5, ymin=3e-8,
|
||||
% ]
|
||||
%% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
|
||||
%% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
%% \addlegendentry{$\gamma = 0.15$}
|
||||
%% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
|
||||
%% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
%% \addlegendentry{$\gamma = 0.01$}
|
||||
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
|
||||
% \addlegendentry{proximal}
|
||||
% \addplot table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/2d_ber_fer_dfr_20433484_hybrid.csv};
|
||||
% \addlegendentry{hybrid prox. \& ML}
|
||||
% \end{axis}
|
||||
% \end{tikzpicture}
|
||||
% \begin{tikzpicture}[scale=0.45]
|
||||
% \begin{axis}[
|
||||
% grid=both,
|
||||
% xlabel={SNR}, ylabel={FER},
|
||||
% ymode=log,
|
||||
% legend style={at={(0.05,0.05)},anchor=south west},
|
||||
% ymax=1.5, ymin=3e-8,
|
||||
% ]
|
||||
%% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
|
||||
%% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
%% \addlegendentry{$\gamma = 0.15$}
|
||||
%% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
|
||||
%% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
%% \addlegendentry{$\gamma = 0.01$}
|
||||
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
|
||||
% \addlegendentry{proximal}
|
||||
% \addplot table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/2d_ber_fer_dfr_20433484_hybrid.csv};
|
||||
% \addlegendentry{hybrid prox. \& ML}
|
||||
% \end{axis}
|
||||
% \end{tikzpicture}\\
|
||||
% \begin{tikzpicture}[scale=0.45]
|
||||
% \begin{axis}[
|
||||
% grid=both,
|
||||
% xlabel={SNR}, ylabel={Decoding Failure Rate},
|
||||
% ymode=log,
|
||||
% legend style={at={(0.05,0.05)},anchor=south west},
|
||||
% ymax=1.5, ymin=3e-8,
|
||||
% ]
|
||||
%% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
|
||||
%% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
%% \addlegendentry{$\gamma = 0.15$}
|
||||
%% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
|
||||
%% {res/2d_ber_fer_dfr_20433484.csv};
|
||||
%% \addlegendentry{$\gamma = 0.01$}
|
||||
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/2d_ber_fer_dfr_20433484_proximal.csv};
|
||||
% \addlegendentry{proximal}
|
||||
% \addplot table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
|
||||
% {res/2d_ber_fer_dfr_20433484_hybrid.csv};
|
||||
% \addlegendentry{hybrid prox. \& ML}
|
||||
% \end{axis}
|
||||
% \end{tikzpicture}
|
||||
%
|
||||
% \caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, \SI{12}{\bit}$}
|
||||
% \label{fig:simulation_results_hybrid}
|
||||
% \end{figure}
|
||||
%
|
||||
%\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\subsection{ADMM: Examination Results}%
|
||||
|
||||
@ -11,11 +11,11 @@
|
||||
\begin{itemize}
|
||||
\item The general [ML] decoding problem for linear codes and the general problem
|
||||
of finding the weights of a linear code are both NP-complete. \cite{ml_np_hard_proof}
|
||||
\item The standard message-passing algorithms used for decoding [LDPC and turbo codes]
|
||||
are often difficult to analyze. \cite{feldman_thesis}
|
||||
\item The iterative message–passing algorithms preffered in practice do not guarantee
|
||||
optimality and may fail to decode correctly when the graph contains cycles
|
||||
\cite{ldpc_conv}
|
||||
\item The standard message-passing algorithms used for decoding [LDPC and turbo codes]
|
||||
are often difficult to analyze. \cite{feldman_thesis}
|
||||
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user