295 lines
13 KiB
TeX
295 lines
13 KiB
TeX
\section{Examination Results}%
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\label{sec:Examination Results}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Proximal Decoder}%
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\label{sub:Ex Proximal Decoder}
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\begin{frame}[t]
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\frametitle{Proximal Decoder: Examination Results}
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\begin{itemize}
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\item AWGN Channel - LDPC Code with $n=204, k=102$:
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\vspace{2mm}
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\begin{figure}[H]
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\centering
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\begin{subfigure}{0.5\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 (dB)}, ylabel={Bit Error 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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width=11.5cm,
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height=8cm,
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ytick={0, 10e-1, 10e-2, 10e-3, 10e-4},
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xtick={1, 2, 3, 4, 5},
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ymax=1.2, ymin=0.8e-4,
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]
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\addplot table [x=SNR, y=BER,
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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,
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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,
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col sep=comma, discard if not={gamma}{0.05}]
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{res/2d_ber_fer_dfr_20433484.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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\caption{Simulation results for $\omega = 0.05, K=100$}
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\label{fig:sim_results_prox}
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\end{subfigure}%
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\begin{subfigure}{0.5\textwidth}
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\centering
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\includegraphics[scale=0.6]{res/ber_paper}
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\caption{Results from ``Proximal Decoding for LDPC Codes''}
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\label{fig:sim_results_prox}
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\end{subfigure}%
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\end{figure}
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\item Performance: $2800 \text{ transm.} / s$ - Intel Core i7-7700HQ @ 2.80GHz\\
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($\sim 10s$ for the shown plot)
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\end{itemize}
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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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\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}, grid=both, grid style={line width=.1pt}, legend style={at={(0.05,0.05)},anchor=south west}]
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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.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=10, colormap/viridis] table [col sep=comma, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv};
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\addlegendentry{$\gamma = \left[ 0\text{:}.01\text{:}.16 \right] $}
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\addplot3[red, line width=1.5] table[col sep=comma, discard if not={gamma}{0.05}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv};
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\addlegendentry{$\gamma = 0.05$}
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\addplot3[blue, line width=1.5] table[col sep=comma, discard if not={gamma}{0.01}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv};
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\addlegendentry{$\gamma = 0.01$}
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\addplot3[brown, line width=1.5] table[col sep=comma, discard if not={gamma}{0.15}, x=SNR, y=gamma, z=BER] {res/2d_ber_fer_dfr_20433484.csv};
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\addlegendentry{$\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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\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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\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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$\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$
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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, break the loop.
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end for
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Output $\boldsymbol{\hat{x}}$
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\end{algorithm}
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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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\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=0.8e-4,
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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.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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\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=0.8e-4,
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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.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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\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=0.8e-4,
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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.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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\caption{Simulation results for $\omega = 0.05, K=100$}
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\label{fig:simulation_results}
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\end{figure}
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\end{minipage}
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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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\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=0.8e-5,
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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.csv};
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\addlegendentry{$\gamma = 0.05$}
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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 $\gamma = 0.05$}
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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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\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=0.8e-5,
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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.csv};
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\addlegendentry{$\gamma = 0.05$}
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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 $\gamma = 0.05$}
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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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\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=0.8e-5,
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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.csv};
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\addlegendentry{$\gamma = 0.05$}
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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 $\gamma = 0.05$}
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\end{axis}
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\end{tikzpicture}
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\caption{Simulation results for $\omega = 0.05, K=100$}
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\label{fig:simulation_results}
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\end{figure}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{ADMM: Examination Results}%
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\label{sub:Ex ADMM}
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\begin{frame}[t]
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\frametitle{ADMM}
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\todo{TODO}
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\end{frame}
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