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Removed index k; Fixed legend of FER plots; Moved legend of surface plots

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This commit is contained in:
Andreas Tsouchlos 2023-01-26 13:37:01 +01:00
parent 542733acc6
commit 0235f3fe35
2 changed files with 306 additions and 298 deletions
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14
latex/presentations/midterm/sections/decoding_algorithms.tex
View File

@ -69,17 +69,15 @@
&\approx \boldsymbol{x} - \gamma \nabla h\left( \boldsymbol{x} \right), &\approx \boldsymbol{x} - \gamma \nabla h\left( \boldsymbol{x} \right),
\hspace{5mm} \gamma \text{ small} \hspace{5mm} \gamma \text{ small}
\end{align*} \end{align*}
\item Iterative decoding process\footnote{In these two equations the parameter $k$ \item Iterative decoding process:
describes the index of the current iteration, not the dimension of the data word}
:
\begin{align*} \begin{align*}
\boldsymbol{r}^{\left( k+1 \right) } &= \boldsymbol{s}^{\left( k \right) } \boldsymbol{r} &\leftarrow \boldsymbol{s}
- \omega \nabla L\left( \boldsymbol{y} | \boldsymbol{s}^{\left( k \right) } - \omega \nabla L\left( \boldsymbol{y} | \boldsymbol{s}
\right), \hspace{5mm} \omega > 0 \right), \hspace{5mm} \omega > 0
\hspace{10mm} \text{``Gradient descent step''}\\ \hspace{10mm} \text{``Gradient descent step''}\\
\boldsymbol{s}^{\left( k+1 \right) } &= \boldsymbol{r}^{\left( k+1 \right) } \boldsymbol{s} &\leftarrow \boldsymbol{r}
- \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) - \gamma \nabla h\left( \boldsymbol{r}
\hspace{22mm} \text{``Code proximal step''} \right) \hspace{29mm} \text{``Code proximal step''}
\end{align*} \end{align*}
\end{itemize} \end{itemize}
\end{frame} \end{frame}

586
latex/presentations/midterm/sections/examination_results.tex
View File

@ -11,7 +11,7 @@
\frametitle{Proximal Decoding: Bit Error Rate and Performance} \frametitle{Proximal Decoding: Bit Error Rate and Performance}
\begin{itemize} \begin{itemize}
\item Comparison of simulation \item Comparison of simulation
\footnote{(3,6) regular LDPC Code with $n=204, k=102$ \footnote{(3,6) regular LDPC code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}} \cite[\text{204.33.484}]{mackay_enc}}
with results of Wadayama and Takabe with results of Wadayama and Takabe
@ -162,7 +162,7 @@
\begin{figure}[H] \begin{figure}[H]
\vspace*{-0.5cm} \vspace*{-0.5cm}
\hspace*{-0.5cm} \hspace*{-0.7cm}
\centering \centering
\begin{subfigure}[c]{0.33\textwidth} \begin{subfigure}[c]{0.33\textwidth}
\centering \centering
@ -251,7 +251,7 @@
\end{tikzpicture} \end{tikzpicture}
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ \cite[\text{408.33.844}]{mackay_enc}} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ \cite[\text{408.33.844}]{mackay_enc}}
\end{subfigure} \end{subfigure}
\hspace*{-0.5cm} \hspace*{-0.7cm}
\begin{subfigure}[c]{0.33\textwidth} \begin{subfigure}[c]{0.33\textwidth}
\centering \centering
\begin{tikzpicture}[scale=0.4] \begin{tikzpicture}[scale=0.4]
@ -1012,29 +1012,23 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d
\addplot[ForestGreen, mark=*, solid] \addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.15$}
\addplot[Emerald, mark=triangle, densely dashed] \addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{hybrid $\gamma = 0.15$}
\addplot[NavyBlue, mark=*, solid] \addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.01$}
\addplot[RoyalPurple, mark=triangle, densely dashed] \addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{hybrid, $\gamma = 0.01$}
\addplot[RedOrange, mark=*, solid] \addplot[RedOrange, mark=*, solid]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.05$}
\addplot[red, mark=triangle, densely dashed] \addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{hybrid, $\gamma = 0.05$}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\begin{tikzpicture}[scale=0.55] \begin{tikzpicture}[scale=0.55]
@ -1050,29 +1044,23 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d
\addplot[ForestGreen, mark=*, solid] \addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.15$}
\addplot[Emerald, mark=triangle, densely dashed] \addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{hybrid, $\gamma = 0.15$}
\addplot[NavyBlue, mark=*, solid] \addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.01$}
\addplot[RoyalPurple, mark=triangle, densely dashed] \addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{hybrid, $\gamma = 0.01$}
\addplot[RedOrange, mark=*, solid] \addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.05$}
\addplot[red, mark=triangle, densely dashed] \addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{hybrid, $\gamma = 0.05$}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\begin{tikzpicture}[scale=0.55] \begin{tikzpicture}[scale=0.55]
@ -1088,28 +1076,47 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d
\addplot[ForestGreen, mark=*, solid] \addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.15$}
\addplot[Emerald, mark=triangle, densely dashed] \addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{hybrid, $\gamma = 0.15$}
\addplot[NavyBlue, mark=*, solid] \addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.01$}
\addplot[RoyalPurple, mark=triangle, densely dashed] \addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{hybrid, $\gamma = 0.01$}
\addplot[RedOrange, mark=*, solid] \addplot[RedOrange, mark=*, solid]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_20433484.csv}; {res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.05$}
\addplot[red, mark=triangle, densely dashed] \addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv}; {res/hybrid/2d_ber_fer_dfr_20433484.csv};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}[scale=0.7]
\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{hybrid, $\gamma = 0.15$}
\addlegendimage{RoyalPurple, mark=triangle, densely dashed}
\addlegendentry{hybrid, $\gamma = 0.01$}
\addlegendimage{red, mark=triangle, densely dashed}
\addlegendentry{hybrid, $\gamma = 0.05$} \addlegendentry{hybrid, $\gamma = 0.05$}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
@ -1124,284 +1131,287 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d
\begin{frame}[t] \begin{frame}[t]
\frametitle{Proximal Decoding: Improvement using ``ML-on-List''} \frametitle{Proximal Decoding: Improvement using ``ML-on-List''}
\begin{figure}[H] \begin{minipage}[c]{0.9\textwidth}
\vspace*{-0.5cm}
\centering \centering
\begin{subfigure}[c]{0.33\textwidth} \begin{figure}[H]
\vspace*{-0.6cm}
\hspace*{-0.7cm}
\centering \centering
\begin{subfigure}[c]{0.33\textwidth}
\centering
\begin{tikzpicture}[scale=0.37] \begin{tikzpicture}[scale=0.4]
\begin{axis}[ \begin{axis}[
grid=both, grid=both,
xlabel={$E_b / N_0$}, ylabel={FER}, xlabel={$E_b / N_0$}, ylabel={FER},
ymode=log, ymode=log,
legend columns=1, legend columns=1,
legend pos=outer north east, legend pos=outer north east,
%legend columns=2, %legend columns=2,
%legend style={at={(0.5,-0.45)},anchor=south}, %legend style={at={(0.5,-0.45)},anchor=south},
ymax=1.5, ymin=8e-4, ymax=1.5, ymin=8e-5,
] ]
\addplot[ForestGreen, mark=*, solid] \addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_963965.csv}; {res/proximal/2d_ber_fer_dfr_963965.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_963965.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_963965.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\end{axis}
\end{tikzpicture}
\caption{$\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, $\gamma = 0.15$} \addlegendentry{proximal, $\gamma = 0.15$}
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] \addlegendimage{Emerald, mark=triangle, densely dashed}
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\addlegendentry{hybrid, $\gamma = 0.15$} \addlegendentry{hybrid, $\gamma = 0.15$}
\addplot[NavyBlue, mark=*, solid] \addlegendimage{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};
\addlegendentry{proximal, $\gamma = 0.01$} \addlegendentry{proximal, $\gamma = 0.01$}
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] \addlegendimage{RoyalPurple, mark=triangle, densely dashed}
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\addlegendentry{hybrid, $\gamma = 0.01$} \addlegendentry{hybrid, $\gamma = 0.01$}
\addplot[RedOrange, mark=*, solid] \addlegendimage{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};
\addlegendentry{proximal, $\gamma = 0.05$} \addlegendentry{proximal, $\gamma = 0.05$}
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] \addlegendimage{red, mark=triangle, densely dashed}
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\addlegendentry{hybrid, $\gamma = 0.05$} \addlegendentry{hybrid, $\gamma = 0.05$}
\end{axis} \end{axis}
\end{tikzpicture} \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=0.37]
\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,] \end{figure}
table [x=SNR, y=FER, col sep=comma, \end{minipage}
discard if not={gamma}{0.15},
discard if gt={SNR}{5.5},]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addlegendentry{proximal, $\gamma = 0.15$}
\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};
\addlegendentry{hybrid, $\gamma = 0.15$}
\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};
\addlegendentry{proximal, $\gamma = 0.01$}
\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};
\addlegendentry{hybrid, $\gamma = 0.01$}
\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};
\addlegendentry{proximal, $\gamma = 0.05$}
\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};
\addlegendentry{hybrid, $\gamma = 0.05$}
\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=0.37]
\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};
\addlegendentry{proximal, $\gamma = 0.15$}
\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};
\addlegendentry{hybrid, $\gamma = 0.15$}
\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};
\addlegendentry{proximal, $\gamma = 0.01$}
\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};
\addlegendentry{hybrid, $\gamma = 0.01$}
\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};
\addlegendentry{proximal, $\gamma = 0.05$}
\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};
\addlegendentry{hybrid, $\gamma = 0.05$}
\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}
\begin{subfigure}[c]{0.33\textwidth}
\centering
\begin{tikzpicture}[scale=0.37]
\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};
\addlegendentry{proximal, $\gamma = 0.15$}
\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};
\addlegendentry{hybrid, $\gamma = 0.15$}
\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};
\addlegendentry{proximal, $\gamma = 0.01$}
\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};
\addlegendentry{hybrid, $\gamma = 0.01$}
\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};
\addlegendentry{proximal, $\gamma = 0.05$}
\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};
\addlegendentry{hybrid, $\gamma = 0.05$}
\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=0.37]
\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};
\addlegendentry{proximal, $\gamma = 0.15$}
\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};
\addlegendentry{hybrid, $\gamma = 0.15$}
\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};
\addlegendentry{proximal, $\gamma = 0.01$}
\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};
\addlegendentry{hybrid, $\gamma = 0.01$}
\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};
\addlegendentry{proximal, $\gamma = 0.05$}
\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};
\addlegendentry{hybrid, $\gamma = 0.05$}
\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=0.37]
\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};
\addlegendentry{proximal, $\gamma = 0.15$}
\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};
\addlegendentry{hybrid, $\gamma = 0.15$}
\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};
\addlegendentry{proximal, $\gamma = 0.01$}
\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};
\addlegendentry{hybrid, $\gamma = 0.01$}
\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};
\addlegendentry{proximal, $\gamma = 0.05$}
\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};
\addlegendentry{hybrid, $\gamma = 0.05$}
\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{frame} \end{frame}
@ -1411,14 +1421,14 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d
\setcounter{footnote}{0} \setcounter{footnote}{0}
\begin{figure}[H] \begin{figure}[H]
\vspace*{-0.5cm}
\centering \centering
\begin{tikzpicture}[scale=0.7] \begin{tikzpicture}[scale=0.6]
\begin{axis}[ \begin{axis}[
grid=both, grid=both,
xlabel={k}, xlabel={k},
ylabel={Average $\left| \boldsymbol{x}-\boldsymbol{\hat{x}} \right|$}, ylabel={Average $\left| \boldsymbol{x}-\boldsymbol{\hat{x}} \right|$},
legend pos=outer north east,
] ]
\addplot table [col sep=comma, \addplot table [col sep=comma,
discard if not={omega}{0.0774263682681127}, discard if not={omega}{0.0774263682681127},