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Moved large figures to appendix

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Andreas Tsouchlos 2023-04-11 00:47:23 +02:00
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latex/thesis/chapters/appendix.tex
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@ -1,5 +1,539 @@
\appendix \appendix
\chapter{A Comparison of the Behaviour of Various Codes}
\begin{figure}[H]
\centering
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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 \ac{LDPC} code with $n=96, k=48$
\cite[\text{96.3.965}]{mackay_enc}}
\end{subfigure}%
\hfill
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b/N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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 \ac{LDPC} code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}}
\end{subfigure}%
\hfill
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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 \ac{LDPC} code with $n=204, k=102$
\cite[\text{204.55.187}]{mackay_enc}}
\end{subfigure}%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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 \ac{LDPC} code with $n=408, k=204$
\cite[\text{408.33.844}]{mackay_enc}}
\end{subfigure}%
\hfill
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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}%
\vspace{1cm}
\begin{subfigure}[c]{\textwidth}
\centering
\begin{tikzpicture}
\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{subfigure}
\caption{BER for $\omega = 0.05, K=100$ (different codes)}
\label{fig:prox:results_3d_multiple}
\end{figure}
\begin{figure}[H]
\centering
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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 \ac{LDPC} code with $n=96, k=48$
\cite[\text{96.3.965}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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 \ac{LDPC} code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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 \ac{LDPC} code with $n=204, k=102$
\cite[\text{204.55.187}]{mackay_enc}}
\end{subfigure}%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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 \ac{LDPC} code with $n=408, k=204$
\cite[\text{408.33.844}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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{\ac{LDPC} code (progressive edge growth construction) with $n=504, k=252$
\cite[\text{PEGReg252x504}]{mackay_enc}}
\label{fig:prox:improved:comp:504}
\end{subfigure}%
\vspace{1cm}
\begin{subfigure}[c]{\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[hide axis,
xmin=10, xmax=50,
ymin=0, ymax=0.4,
legend columns=3,
legend style={draw=white!15!black,legend cell align=left}]
\addlegendimage{ForestGreen, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.15$}
\addlegendimage{NavyBlue, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.01$}
\addlegendimage{RedOrange, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.05$}
\addlegendimage{Emerald, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.15$}
\addlegendimage{RoyalPurple, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.01$}
\addlegendimage{red, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.05$}
\end{axis}
\end{tikzpicture}
\end{subfigure}
\caption{Comparison of improvement in decoding performance for various
codes}
\label{fig:prox:improved:comp}
\end{figure}
\chapter{\acs{LP} Decoding using \acs{ADMM} as a Proximal Algorithm}% \chapter{\acs{LP} Decoding using \acs{ADMM} as a Proximal Algorithm}%
\label{chapter:LD Decoding using ADMM as a Proximal Algorithm} \label{chapter:LD Decoding using ADMM as a Proximal Algorithm}

539
latex/thesis/chapters/proximal_decoding.tex
View File

@ -479,8 +479,8 @@ in each case.
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Visualization of relationship between the decoding performance\protect\footnotemark{} \caption{Visualization of the relationship between the decoding performance
and the parameter $\gamma$} \protect\footnotemark{} and the parameter $\gamma$}
\label{fig:prox:results_3d} \label{fig:prox:results_3d}
\end{figure}% \end{figure}%
% %
@ -542,231 +542,6 @@ certain threshold does not improve the decoding performance.
The choice of $\eta$ is insignificant and the parameter is only relevant as a The choice of $\eta$ is insignificant and the parameter is only relevant as a
means to bring about numerical stability. means to bring about numerical stability.
\begin{figure}[H]
\centering
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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 \ac{LDPC} code with $n=96, k=48$
\cite[\text{96.3.965}]{mackay_enc}}
\end{subfigure}%
\hfill
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b/N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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 \ac{LDPC} code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}}
\end{subfigure}%
\hfill
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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 \ac{LDPC} code with $n=204, k=102$
\cite[\text{204.55.187}]{mackay_enc}}
\end{subfigure}%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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 \ac{LDPC} code with $n=408, k=204$
\cite[\text{408.33.844}]{mackay_enc}}
\end{subfigure}%
\hfill
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[view={75}{30},
zmode=log,
xlabel={$E_b / N_0$ (dB)},
ylabel={$\gamma$},
zlabel={BER},
width=\textwidth,
height=0.75\textwidth,]
\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}%
\vspace{1cm}
\begin{subfigure}[c]{\textwidth}
\centering
\begin{tikzpicture}
\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{subfigure}
\caption{BER for $\omega = 0.05, K=100$ (different codes)}
\label{fig:prox:results_3d_multiple}
\end{figure}
\subsection{Decoding Performance} \subsection{Decoding Performance}
@ -1247,7 +1022,7 @@ gradient of the negative log-likelihood is counteracted.
In conclusion, as a general rule, the proximal decoding algorithm reaches In conclusion, as a general rule, the proximal decoding algorithm reaches
an oscillatory state which it cannot escape as a consequence of its structure. an oscillatory state which it cannot escape as a consequence of its structure.
In this state, the constraints may not be satisfied, leading to the algorithm In this state the constraints may not be satisfied, leading to the algorithm
returning an invalid codeword. returning an invalid codeword.
\begin{figure}[H] \begin{figure}[H]
@ -1418,7 +1193,6 @@ Its only difference to algorithm \ref{alg:prox} is that instead of returning
the last estimate when no valid result is reached, an ML-in-the-List step is the last estimate when no valid result is reached, an ML-in-the-List step is
performed. performed.
\begin{minipage}{\linewidth}
\begin{genericAlgorithm}[caption={Improved proximal decoding algorithm}, \begin{genericAlgorithm}[caption={Improved proximal decoding algorithm},
label={alg:prox:improved},] label={alg:prox:improved},]
$\boldsymbol{s} \leftarrow \boldsymbol{0}$ $\boldsymbol{s} \leftarrow \boldsymbol{0}$
@ -1438,7 +1212,6 @@ $\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{c}}_l,
$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_l\text{ with lowest } $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_l\text{ with lowest }
d_H\left( \boldsymbol{ \tilde{c}}_l, \boldsymbol{\hat{c}} \right)}$ d_H\left( \boldsymbol{ \tilde{c}}_l, \boldsymbol{\hat{c}} \right)}$
\end{genericAlgorithm} \end{genericAlgorithm}
\end{minipage}
\todo{Not hamming distance, correlation} \todo{Not hamming distance, correlation}
@ -1654,309 +1427,3 @@ negligible computational performance penalty.
The improvement is mainly noticable for higher \ac{SNR} values and depends on The improvement is mainly noticable for higher \ac{SNR} values and depends on
the code as well as the chosen parameters. the code as well as the chosen parameters.
\begin{figure}[H]
\centering
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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 \ac{LDPC} code with $n=96, k=48$
\cite[\text{96.3.965}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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 \ac{LDPC} code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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 \ac{LDPC} code with $n=204, k=102$
\cite[\text{204.55.187}]{mackay_enc}}
\end{subfigure}%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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 \ac{LDPC} code with $n=408, k=204$
\cite[\text{408.33.844}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\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,
width=\textwidth,
height=0.75\textwidth,
]
\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{\ac{LDPC} code (progressive edge growth construction) with $n=504, k=252$
\cite[\text{PEGReg252x504}]{mackay_enc}}
\label{fig:prox:improved:comp:504}
\end{subfigure}%
\vspace{1cm}
\begin{subfigure}[c]{\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[hide axis,
xmin=10, xmax=50,
ymin=0, ymax=0.4,
legend columns=3,
legend style={draw=white!15!black,legend cell align=left}]
\addlegendimage{ForestGreen, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.15$}
\addlegendimage{NavyBlue, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.01$}
\addlegendimage{RedOrange, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.05$}
\addlegendimage{Emerald, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.15$}
\addlegendimage{RoyalPurple, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.01$}
\addlegendimage{red, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.05$}
\end{axis}
\end{tikzpicture}
\end{subfigure}
\caption{Comparison of improvement in decoding performance for various
codes}
\label{fig:prox:improved:comp}
\end{figure}