diff --git a/latex/presentations/final/sections/decoding_algorithms.tex b/latex/presentations/final/sections/decoding_algorithms.tex index c5cbfd1..7941cf2 100644 --- a/latex/presentations/final/sections/decoding_algorithms.tex +++ b/latex/presentations/final/sections/decoding_algorithms.tex @@ -762,6 +762,7 @@ return $\boldsymbol{\hat{c}}$ \frametitle{LP Decoding using ADMM} \begin{itemize} + \item Solution using the \textit{alternating direction method of multipliers} (ADMM) \item Slight reformulation of the LCLP: \begin{align*} \begin{aligned} diff --git a/latex/presentations/final/sections/examination_results.tex b/latex/presentations/final/sections/examination_results.tex index 21a0823..2272e6b 100644 --- a/latex/presentations/final/sections/examination_results.tex +++ b/latex/presentations/final/sections/examination_results.tex @@ -171,219 +171,219 @@ \end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}[t] - \frametitle{Proximal Decoding: Choice of $\gamma$} - - \begin{minipage}[c]{0.9\textwidth} - \centering - - \begin{figure}[H] - \vspace*{-0.5cm} - \hspace*{-0.7cm} - \centering - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[view={75}{30}, - zmode=log, - xlabel={$E_b / N_0$ (dB)}, - ylabel={$\gamma$}, - zlabel={BER},] - \addplot3[surf, - mesh/rows=17, mesh/cols=10, - colormap/viridis] table [col sep=comma, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_963965.csv}; - \addplot3[RedOrange, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.05}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_963965.csv}; - \addplot3[NavyBlue, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.01}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_963965.csv}; - \addplot3[ForestGreen, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.15}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_963965.csv}; - \end{axis} - \end{tikzpicture} - \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$ \cite[\text{96.3.965}]{mackay_enc}} - \end{subfigure}% - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[view={75}{30}, - zmode=log, - xlabel={$E_b/N_0$ (dB)}, - ylabel={$\gamma$}, - zlabel={BER},] - \addplot3[surf, - mesh/rows=17, mesh/cols=14, - colormap/viridis] table [col sep=comma, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addplot3[RedOrange, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.05}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addplot3[NavyBlue, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.01}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addplot3[ForestGreen, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.15}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \end{axis} - \end{tikzpicture} - \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}} - \end{subfigure}% - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[view={75}{30}, - zmode=log, - xlabel={$E_b / N_0$ (dB)}, - ylabel={$\gamma$}, - zlabel={BER},] - \addplot3[surf, - mesh/rows=17, mesh/cols=10, - colormap/viridis] table [col sep=comma, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_40833844.csv}; - \addplot3[RedOrange, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.05}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_40833844.csv}; - \addplot3[NavyBlue, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.01}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_40833844.csv}; - \addplot3[ForestGreen, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.15}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_40833844.csv}; - \end{axis} - \end{tikzpicture} - \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ \cite[\text{408.33.844}]{mackay_enc}} - \end{subfigure} - \hspace*{-0.7cm} - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[view={75}{30}, - zmode=log, - xlabel={$E_b / N_0$ (dB)}, - ylabel={$\gamma$}, - zlabel={BER},] - \addplot3[surf, - mesh/rows=17, mesh/cols=10, - colormap/viridis] table [col sep=comma, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; - \addplot3[RedOrange, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.05}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; - \addplot3[NavyBlue, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.01}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; - \addplot3[ForestGreen, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.15}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; - \end{axis} - \end{tikzpicture} - \caption{BCH code with $n=31, k=26$\\[2\baselineskip]} - \end{subfigure}% - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[view={75}{30}, - zmode=log, - xlabel={$E_b / N_0$ (dB)}, - ylabel={$\gamma$}, - zlabel={BER},] - \addplot3[surf, - mesh/rows=17, mesh/cols=10, - colormap/viridis] table [col sep=comma, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_20455187.csv}; - \addplot3[RedOrange, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.05}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_20455187.csv}; - \addplot3[NavyBlue, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.01}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_20455187.csv}; - \addplot3[ForestGreen, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.15}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_20455187.csv}; - \end{axis} - \end{tikzpicture} - \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.55.187}]{mackay_enc}} - \end{subfigure}% - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[view={75}{30}, - zmode=log, - xlabel={$E_b / N_0$ (dB)}, - ylabel={$\gamma$}, - zlabel={BER},] - \addplot3[surf, - mesh/rows=17, mesh/cols=10, - colormap/viridis] table [col sep=comma, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; - \addplot3[RedOrange, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.05}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; - \addplot3[NavyBlue, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.01}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; - \addplot3[ForestGreen, line width=1.5] table[col sep=comma, - discard if not={gamma}{0.15}, - x=SNR, y=gamma, z=BER] - {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; - \end{axis} - \end{tikzpicture} - \caption{LDPC code (Progressive Edge Growth Construction) with $n=504, k=252$ \cite[\text{PEGReg252x504}]{mackay_enc}} - \end{subfigure}% - \end{figure} - \end{minipage}% - \begin{minipage}[c]{0.1\textwidth} - \centering - - \begin{figure}[H] - \vspace*{-1.5cm} - \hspace*{-0.75cm} - \centering - \begin{tikzpicture}[scale=0.7] - \begin{axis}[hide axis, - xmin=10, xmax=50, - ymin=0, ymax=0.4, - legend style={draw=white!15!black,legend cell align=left}] - \addlegendimage{surf, colormap/viridis} - \addlegendentry{$\gamma = \left[ 0\text{ : }0.01\text{ : }0.16 \right] $}; - \addlegendimage{NavyBlue, line width=1.5pt} - \addlegendentry{$\gamma = 0.01$}; - \addlegendimage{RedOrange, line width=1.5pt} - \addlegendentry{$\gamma = 0.05$}; - \addlegendimage{ForestGreen, line width=1.5pt} - \addlegendentry{$\gamma = 0.15$}; - \end{axis} - \end{tikzpicture} - \end{figure} - \end{minipage} -\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\begin{frame}[t] +% \frametitle{Proximal Decoding: Choice of $\gamma$} +% +% \begin{minipage}[c]{0.9\textwidth} +% \centering +% +% \begin{figure}[H] +% \vspace*{-0.5cm} +% \hspace*{-0.7cm} +% \centering +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[view={75}{30}, +% zmode=log, +% xlabel={$E_b / N_0$ (dB)}, +% ylabel={$\gamma$}, +% zlabel={BER},] +% \addplot3[surf, +% mesh/rows=17, mesh/cols=10, +% colormap/viridis] table [col sep=comma, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_963965.csv}; +% \addplot3[RedOrange, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.05}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_963965.csv}; +% \addplot3[NavyBlue, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.01}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_963965.csv}; +% \addplot3[ForestGreen, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.15}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_963965.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$ \cite[\text{96.3.965}]{mackay_enc}} +% \end{subfigure}% +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[view={75}{30}, +% zmode=log, +% xlabel={$E_b/N_0$ (dB)}, +% ylabel={$\gamma$}, +% zlabel={BER},] +% \addplot3[surf, +% mesh/rows=17, mesh/cols=14, +% colormap/viridis] table [col sep=comma, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_20433484.csv}; +% \addplot3[RedOrange, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.05}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_20433484.csv}; +% \addplot3[NavyBlue, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.01}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_20433484.csv}; +% \addplot3[ForestGreen, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.15}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_20433484.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}} +% \end{subfigure}% +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[view={75}{30}, +% zmode=log, +% xlabel={$E_b / N_0$ (dB)}, +% ylabel={$\gamma$}, +% zlabel={BER},] +% \addplot3[surf, +% mesh/rows=17, mesh/cols=10, +% colormap/viridis] table [col sep=comma, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_40833844.csv}; +% \addplot3[RedOrange, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.05}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_40833844.csv}; +% \addplot3[NavyBlue, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.01}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_40833844.csv}; +% \addplot3[ForestGreen, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.15}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_40833844.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ \cite[\text{408.33.844}]{mackay_enc}} +% \end{subfigure} +% \hspace*{-0.7cm} +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[view={75}{30}, +% zmode=log, +% xlabel={$E_b / N_0$ (dB)}, +% ylabel={$\gamma$}, +% zlabel={BER},] +% \addplot3[surf, +% mesh/rows=17, mesh/cols=10, +% colormap/viridis] table [col sep=comma, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; +% \addplot3[RedOrange, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.05}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; +% \addplot3[NavyBlue, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.01}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; +% \addplot3[ForestGreen, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.15}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{BCH code with $n=31, k=26$\\[2\baselineskip]} +% \end{subfigure}% +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[view={75}{30}, +% zmode=log, +% xlabel={$E_b / N_0$ (dB)}, +% ylabel={$\gamma$}, +% zlabel={BER},] +% \addplot3[surf, +% mesh/rows=17, mesh/cols=10, +% colormap/viridis] table [col sep=comma, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_20455187.csv}; +% \addplot3[RedOrange, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.05}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_20455187.csv}; +% \addplot3[NavyBlue, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.01}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_20455187.csv}; +% \addplot3[ForestGreen, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.15}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_20455187.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.55.187}]{mackay_enc}} +% \end{subfigure}% +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[view={75}{30}, +% zmode=log, +% xlabel={$E_b / N_0$ (dB)}, +% ylabel={$\gamma$}, +% zlabel={BER},] +% \addplot3[surf, +% mesh/rows=17, mesh/cols=10, +% colormap/viridis] table [col sep=comma, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; +% \addplot3[RedOrange, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.05}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; +% \addplot3[NavyBlue, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.01}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; +% \addplot3[ForestGreen, line width=1.5] table[col sep=comma, +% discard if not={gamma}{0.15}, +% x=SNR, y=gamma, z=BER] +% {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{LDPC code (Progressive Edge Growth Construction) with $n=504, k=252$ \cite[\text{PEGReg252x504}]{mackay_enc}} +% \end{subfigure}% +% \end{figure} +% \end{minipage}% +% \begin{minipage}[c]{0.1\textwidth} +% \centering +% +% \begin{figure}[H] +% \vspace*{-1.5cm} +% \hspace*{-0.75cm} +% \centering +% \begin{tikzpicture}[scale=0.7] +% \begin{axis}[hide axis, +% xmin=10, xmax=50, +% ymin=0, ymax=0.4, +% legend style={draw=white!15!black,legend cell align=left}] +% \addlegendimage{surf, colormap/viridis} +% \addlegendentry{$\gamma = \left[ 0\text{ : }0.01\text{ : }0.16 \right] $}; +% \addlegendimage{NavyBlue, line width=1.5pt} +% \addlegendentry{$\gamma = 0.01$}; +% \addlegendimage{RedOrange, line width=1.5pt} +% \addlegendentry{$\gamma = 0.05$}; +% \addlegendimage{ForestGreen, line width=1.5pt} +% \addlegendentry{$\gamma = 0.15$}; +% \end{axis} +% \end{tikzpicture} +% \end{figure} +% \end{minipage} +%\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -1187,292 +1187,292 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_l\text{ with lowest }d \end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}[t] - \frametitle{Proximal Decoding: Improvement} - - \begin{minipage}[c]{0.9\textwidth} - \centering - \begin{figure}[H] - \vspace*{-0.6cm} - \hspace*{-0.7cm} - \centering - \begin{subfigure}[c]{0.33\textwidth} - \centering - - \begin{tikzpicture}[scale=0.4] - \begin{axis}[ - grid=both, - xlabel={$E_b / N_0$}, ylabel={FER}, - ymode=log, - legend columns=1, - legend pos=outer north east, - %legend columns=2, - %legend style={at={(0.5,-0.45)},anchor=south}, - ymax=1.5, ymin=8e-5, - ] - - \addplot[ForestGreen, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/proximal/2d_ber_fer_dfr_963965.csv}; - \addplot[Emerald, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/hybrid/2d_ber_fer_dfr_963965.csv}; - - \addplot[NavyBlue, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/proximal/2d_ber_fer_dfr_963965.csv}; - \addplot[RoyalPurple, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/hybrid/2d_ber_fer_dfr_963965.csv}; - - \addplot[RedOrange, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/proximal/2d_ber_fer_dfr_963965.csv}; - \addplot[red, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/hybrid/2d_ber_fer_dfr_963965.csv}; - \end{axis} - \end{tikzpicture} - \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$ \cite[\text{96.3.965}]{mackay_enc}} - \end{subfigure}% - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[ - grid=both, - xlabel={$E_b / N_0$}, ylabel={FER}, - ymode=log, - legend columns=1, - legend pos=outer north east, - xmin=0.5, xmax=6, xtick={1, ..., 5}, - ymax=1.5, ymin=8e-5, - ] - - \addplot[ForestGreen, mark=*, solid,] - table [x=SNR, y=FER, col sep=comma, - discard if not={gamma}{0.15}, - discard if gt={SNR}{5.5},] - {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addplot[Emerald, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, - discard if not={gamma}{0.15}, - discard if gt={SNR}{5.5},] - {res/hybrid/2d_ber_fer_dfr_20433484.csv}; - - \addplot[NavyBlue, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, - discard if not={gamma}{0.01}, - discard if gt={SNR}{5.5},] - {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addplot[RoyalPurple, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, - discard if not={gamma}{0.01}, - discard if gt={SNR}{5.5},] - {res/hybrid/2d_ber_fer_dfr_20433484.csv}; - - \addplot[RedOrange, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, - discard if not={gamma}{0.05}, - discard if gt={SNR}{5.5},] - {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addplot[red, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, - discard if not={gamma}{0.05}, - discard if gt={SNR}{5.5},] - {res/hybrid/2d_ber_fer_dfr_20433484.csv}; - \end{axis} - \end{tikzpicture} - \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}} - \end{subfigure}% - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[ - grid=both, - xlabel={$E_b / N_0$}, ylabel={FER}, - ymode=log, - legend columns=1, - legend pos=outer north east, - %legend columns=2, - %legend style={at={(0.5,-0.45)},anchor=south}, - ymax=1.5, ymin=8e-5, - ] - - \addplot[ForestGreen, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/proximal/2d_ber_fer_dfr_40833844.csv}; - \addplot[Emerald, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/hybrid/2d_ber_fer_dfr_40833844.csv}; - - \addplot[NavyBlue, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/proximal/2d_ber_fer_dfr_40833844.csv}; - \addplot[RoyalPurple, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/hybrid/2d_ber_fer_dfr_40833844.csv}; - - \addplot[RedOrange, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/proximal/2d_ber_fer_dfr_40833844.csv}; - \addplot[red, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/hybrid/2d_ber_fer_dfr_40833844.csv}; - \end{axis} - \end{tikzpicture} - \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ \cite[\text{408.33.844}]{mackay_enc}} - \end{subfigure} - \hspace*{-0.7cm} - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[ - grid=both, - xlabel={$E_b / N_0$}, ylabel={FER}, - ymode=log, - legend columns=1, - legend pos=outer north east, - %legend columns=2, - %legend style={at={(0.5,-0.45)},anchor=south}, - ymax=1.5, ymin=8e-5, - ] - - \addplot[ForestGreen, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; - \addplot[Emerald, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv}; - - \addplot[NavyBlue, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; - \addplot[RoyalPurple, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv}; - - \addplot[RedOrange, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; - \addplot[red, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv}; - \end{axis} - \end{tikzpicture} - \caption{BCH code with $n=31, k=26$\\[\baselineskip]} - \end{subfigure}% - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[ - grid=both, - xlabel={$E_b / N_0$}, ylabel={FER}, - ymode=log, - legend columns=1, - legend pos=outer north east, - %legend columns=2, - %legend style={at={(0.5,-0.45)},anchor=south}, - ymax=1.5, ymin=8e-5, - ] - - \addplot[ForestGreen, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/proximal/2d_ber_fer_dfr_20455187.csv}; - \addplot[Emerald, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/hybrid/2d_ber_fer_dfr_20455187.csv}; - - \addplot[NavyBlue, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/proximal/2d_ber_fer_dfr_20455187.csv}; - \addplot[RoyalPurple, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/hybrid/2d_ber_fer_dfr_20455187.csv}; - - \addplot[RedOrange, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/proximal/2d_ber_fer_dfr_20455187.csv}; - \addplot[red, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/hybrid/2d_ber_fer_dfr_20455187.csv}; - \end{axis} - \end{tikzpicture} - \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.55.187}]{mackay_enc}} - \end{subfigure}% - \begin{subfigure}[c]{0.33\textwidth} - \centering - \begin{tikzpicture}[scale=0.4] - \begin{axis}[ - grid=both, - xlabel={$E_b / N_0$}, ylabel={FER}, - ymode=log, - legend columns=1, - legend pos=outer north east, - ymax=1.5, ymin=8e-5, - ] - - \addplot[ForestGreen, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; - \addplot[Emerald, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv}; - - \addplot[NavyBlue, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; - \addplot[RoyalPurple, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] - {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv}; - - \addplot[RedOrange, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; - \addplot[red, mark=triangle, densely dashed] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] - {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv}; - \end{axis} - \end{tikzpicture} - \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$ \cite[\text{PEGReg252x504}]{mackay_enc}} - \end{subfigure}% - \end{figure} - \end{minipage}% - \begin{minipage}[c]{0.1\textwidth} - \centering - - \begin{figure} - \vspace*{-1.5cm} - \hspace*{-0.7cm} - \centering - \begin{tikzpicture}[scale=0.7] - \begin{axis}[hide axis, - xmin=10, xmax=50, - ymin=0, ymax=0.4, - legend style={draw=white!15!black,legend cell align=left}] - \addlegendimage{ForestGreen, mark=*, solid} - \addlegendentry{proximal, $\gamma = 0.15$} - - \addlegendimage{Emerald, mark=triangle, densely dashed} - \addlegendentry{improved, $\gamma = 0.15$} - - \addlegendimage{NavyBlue, mark=*, solid} - \addlegendentry{proximal, $\gamma = 0.01$} - - \addlegendimage{RoyalPurple, mark=triangle, densely dashed} - \addlegendentry{improved, $\gamma = 0.01$} - - \addlegendimage{RedOrange, mark=*, solid} - \addlegendentry{proximal, $\gamma = 0.05$} - - \addlegendimage{red, mark=triangle, densely dashed} - \addlegendentry{improved, $\gamma = 0.05$} - \end{axis} - \end{tikzpicture} - - \end{figure} - \end{minipage} -\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\begin{frame}[t] +% \frametitle{Proximal Decoding: Improvement} +% +% \begin{minipage}[c]{0.9\textwidth} +% \centering +% \begin{figure}[H] +% \vspace*{-0.6cm} +% \hspace*{-0.7cm} +% \centering +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[ +% grid=both, +% xlabel={$E_b / N_0$}, ylabel={FER}, +% ymode=log, +% legend columns=1, +% legend pos=outer north east, +% %legend columns=2, +% %legend style={at={(0.5,-0.45)},anchor=south}, +% ymax=1.5, ymin=8e-5, +% ] +% +% \addplot[ForestGreen, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/proximal/2d_ber_fer_dfr_963965.csv}; +% \addplot[Emerald, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/hybrid/2d_ber_fer_dfr_963965.csv}; +% +% \addplot[NavyBlue, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/proximal/2d_ber_fer_dfr_963965.csv}; +% \addplot[RoyalPurple, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/hybrid/2d_ber_fer_dfr_963965.csv}; +% +% \addplot[RedOrange, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/proximal/2d_ber_fer_dfr_963965.csv}; +% \addplot[red, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/hybrid/2d_ber_fer_dfr_963965.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$ \cite[\text{96.3.965}]{mackay_enc}} +% \end{subfigure}% +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[ +% grid=both, +% xlabel={$E_b / N_0$}, ylabel={FER}, +% ymode=log, +% legend columns=1, +% legend pos=outer north east, +% xmin=0.5, xmax=6, xtick={1, ..., 5}, +% ymax=1.5, ymin=8e-5, +% ] +% +% \addplot[ForestGreen, mark=*, solid,] +% table [x=SNR, y=FER, col sep=comma, +% discard if not={gamma}{0.15}, +% discard if gt={SNR}{5.5},] +% {res/proximal/2d_ber_fer_dfr_20433484.csv}; +% \addplot[Emerald, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, +% discard if not={gamma}{0.15}, +% discard if gt={SNR}{5.5},] +% {res/hybrid/2d_ber_fer_dfr_20433484.csv}; +% +% \addplot[NavyBlue, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, +% discard if not={gamma}{0.01}, +% discard if gt={SNR}{5.5},] +% {res/proximal/2d_ber_fer_dfr_20433484.csv}; +% \addplot[RoyalPurple, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, +% discard if not={gamma}{0.01}, +% discard if gt={SNR}{5.5},] +% {res/hybrid/2d_ber_fer_dfr_20433484.csv}; +% +% \addplot[RedOrange, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, +% discard if not={gamma}{0.05}, +% discard if gt={SNR}{5.5},] +% {res/proximal/2d_ber_fer_dfr_20433484.csv}; +% \addplot[red, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, +% discard if not={gamma}{0.05}, +% discard if gt={SNR}{5.5},] +% {res/hybrid/2d_ber_fer_dfr_20433484.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}} +% \end{subfigure}% +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[ +% grid=both, +% xlabel={$E_b / N_0$}, ylabel={FER}, +% ymode=log, +% legend columns=1, +% legend pos=outer north east, +% %legend columns=2, +% %legend style={at={(0.5,-0.45)},anchor=south}, +% ymax=1.5, ymin=8e-5, +% ] +% +% \addplot[ForestGreen, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/proximal/2d_ber_fer_dfr_40833844.csv}; +% \addplot[Emerald, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/hybrid/2d_ber_fer_dfr_40833844.csv}; +% +% \addplot[NavyBlue, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/proximal/2d_ber_fer_dfr_40833844.csv}; +% \addplot[RoyalPurple, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/hybrid/2d_ber_fer_dfr_40833844.csv}; +% +% \addplot[RedOrange, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/proximal/2d_ber_fer_dfr_40833844.csv}; +% \addplot[red, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/hybrid/2d_ber_fer_dfr_40833844.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ \cite[\text{408.33.844}]{mackay_enc}} +% \end{subfigure} +% \hspace*{-0.7cm} +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[ +% grid=both, +% xlabel={$E_b / N_0$}, ylabel={FER}, +% ymode=log, +% legend columns=1, +% legend pos=outer north east, +% %legend columns=2, +% %legend style={at={(0.5,-0.45)},anchor=south}, +% ymax=1.5, ymin=8e-5, +% ] +% +% \addplot[ForestGreen, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; +% \addplot[Emerald, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv}; +% +% \addplot[NavyBlue, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; +% \addplot[RoyalPurple, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv}; +% +% \addplot[RedOrange, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/proximal/2d_ber_fer_dfr_bch_31_26.csv}; +% \addplot[red, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{BCH code with $n=31, k=26$\\[\baselineskip]} +% \end{subfigure}% +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[ +% grid=both, +% xlabel={$E_b / N_0$}, ylabel={FER}, +% ymode=log, +% legend columns=1, +% legend pos=outer north east, +% %legend columns=2, +% %legend style={at={(0.5,-0.45)},anchor=south}, +% ymax=1.5, ymin=8e-5, +% ] +% +% \addplot[ForestGreen, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/proximal/2d_ber_fer_dfr_20455187.csv}; +% \addplot[Emerald, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/hybrid/2d_ber_fer_dfr_20455187.csv}; +% +% \addplot[NavyBlue, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/proximal/2d_ber_fer_dfr_20455187.csv}; +% \addplot[RoyalPurple, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/hybrid/2d_ber_fer_dfr_20455187.csv}; +% +% \addplot[RedOrange, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/proximal/2d_ber_fer_dfr_20455187.csv}; +% \addplot[red, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/hybrid/2d_ber_fer_dfr_20455187.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.55.187}]{mackay_enc}} +% \end{subfigure}% +% \begin{subfigure}[c]{0.33\textwidth} +% \centering +% \begin{tikzpicture}[scale=0.4] +% \begin{axis}[ +% grid=both, +% xlabel={$E_b / N_0$}, ylabel={FER}, +% ymode=log, +% legend columns=1, +% legend pos=outer north east, +% ymax=1.5, ymin=8e-5, +% ] +% +% \addplot[ForestGreen, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; +% \addplot[Emerald, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] +% {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv}; +% +% \addplot[NavyBlue, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; +% \addplot[RoyalPurple, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] +% {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv}; +% +% \addplot[RedOrange, mark=*, solid] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv}; +% \addplot[red, mark=triangle, densely dashed] +% table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] +% {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv}; +% \end{axis} +% \end{tikzpicture} +% \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$ \cite[\text{PEGReg252x504}]{mackay_enc}} +% \end{subfigure}% +% \end{figure} +% \end{minipage}% +% \begin{minipage}[c]{0.1\textwidth} +% \centering +% +% \begin{figure} +% \vspace*{-1.5cm} +% \hspace*{-0.7cm} +% \centering +% \begin{tikzpicture}[scale=0.7] +% \begin{axis}[hide axis, +% xmin=10, xmax=50, +% ymin=0, ymax=0.4, +% legend style={draw=white!15!black,legend cell align=left}] +% \addlegendimage{ForestGreen, mark=*, solid} +% \addlegendentry{proximal, $\gamma = 0.15$} +% +% \addlegendimage{Emerald, mark=triangle, densely dashed} +% \addlegendentry{improved, $\gamma = 0.15$} +% +% \addlegendimage{NavyBlue, mark=*, solid} +% \addlegendentry{proximal, $\gamma = 0.01$} +% +% \addlegendimage{RoyalPurple, mark=triangle, densely dashed} +% \addlegendentry{improved, $\gamma = 0.01$} +% +% \addlegendimage{RedOrange, mark=*, solid} +% \addlegendentry{proximal, $\gamma = 0.05$} +% +% \addlegendimage{red, mark=triangle, densely dashed} +% \addlegendentry{improved, $\gamma = 0.05$} +% \end{axis} +% \end{tikzpicture} +% +% \end{figure} +% \end{minipage} +%\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%