From 0235f3fe35b0e016271356b77d5949e2b5df719d Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Thu, 26 Jan 2023 13:37:01 +0100 Subject: [PATCH] Removed index k; Fixed legend of FER plots; Moved legend of surface plots --- .../midterm/sections/decoding_algorithms.tex | 14 +- .../midterm/sections/examination_results.tex | 590 +++++++++--------- 2 files changed, 306 insertions(+), 298 deletions(-) diff --git a/latex/presentations/midterm/sections/decoding_algorithms.tex b/latex/presentations/midterm/sections/decoding_algorithms.tex index 2e81a9a..2449ca0 100644 --- a/latex/presentations/midterm/sections/decoding_algorithms.tex +++ b/latex/presentations/midterm/sections/decoding_algorithms.tex @@ -69,17 +69,15 @@ &\approx \boldsymbol{x} - \gamma \nabla h\left( \boldsymbol{x} \right), \hspace{5mm} \gamma \text{ small} \end{align*} - \item Iterative decoding process\footnote{In these two equations the parameter $k$ - describes the index of the current iteration, not the dimension of the data word} - : + \item Iterative decoding process: \begin{align*} - \boldsymbol{r}^{\left( k+1 \right) } &= \boldsymbol{s}^{\left( k \right) } - - \omega \nabla L\left( \boldsymbol{y} | \boldsymbol{s}^{\left( k \right) } + \boldsymbol{r} &\leftarrow \boldsymbol{s} + - \omega \nabla L\left( \boldsymbol{y} | \boldsymbol{s} \right), \hspace{5mm} \omega > 0 \hspace{10mm} \text{``Gradient descent step''}\\ - \boldsymbol{s}^{\left( k+1 \right) } &= \boldsymbol{r}^{\left( k+1 \right) } - - \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) - \hspace{22mm} \text{``Code proximal step''} + \boldsymbol{s} &\leftarrow \boldsymbol{r} + - \gamma \nabla h\left( \boldsymbol{r} + \right) \hspace{29mm} \text{``Code proximal step''} \end{align*} \end{itemize} \end{frame} diff --git a/latex/presentations/midterm/sections/examination_results.tex b/latex/presentations/midterm/sections/examination_results.tex index 0421b64..4c85f1b 100644 --- a/latex/presentations/midterm/sections/examination_results.tex +++ b/latex/presentations/midterm/sections/examination_results.tex @@ -11,7 +11,7 @@ \frametitle{Proximal Decoding: Bit Error Rate and Performance} \begin{itemize} \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}} with results of Wadayama and Takabe @@ -162,7 +162,7 @@ \begin{figure}[H] \vspace*{-0.5cm} - \hspace*{-0.5cm} + \hspace*{-0.7cm} \centering \begin{subfigure}[c]{0.33\textwidth} \centering @@ -251,7 +251,7 @@ \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*{-0.5cm} + \hspace*{-0.7cm} \begin{subfigure}[c]{0.33\textwidth} \centering \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] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}] {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{proximal, $\gamma = 0.15$} \addplot[Emerald, mark=triangle, densely dashed] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}] {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}] {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{proximal, $\gamma = 0.01$} \addplot[RoyalPurple, mark=triangle, densely dashed] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}] {res/hybrid/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{hybrid, $\gamma = 0.01$} \addplot[RedOrange, mark=*, solid] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}] {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{proximal, $\gamma = 0.05$} \addplot[red, mark=triangle, densely dashed] table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}] {res/hybrid/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{hybrid, $\gamma = 0.05$} \end{axis} \end{tikzpicture} \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] table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] {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}] {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}] {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}] {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}] {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}] {res/hybrid/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{hybrid, $\gamma = 0.05$} \end{axis} \end{tikzpicture} \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] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}] {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{proximal, $\gamma = 0.15$} \addplot[Emerald, mark=triangle, densely dashed] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}] {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}] {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{proximal, $\gamma = 0.01$} \addplot[RoyalPurple, mark=triangle, densely dashed] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}] {res/hybrid/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{hybrid, $\gamma = 0.01$} \addplot[RedOrange, mark=*, solid] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}] {res/proximal/2d_ber_fer_dfr_20433484.csv}; - \addlegendentry{proximal, $\gamma = 0.05$} \addplot[red, mark=triangle, densely dashed] table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}] {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, $\gamma = 0.05$} \end{axis} \end{tikzpicture} @@ -1124,284 +1131,287 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d \begin{frame}[t] \frametitle{Proximal Decoding: Improvement using ``ML-on-List''} - \begin{figure}[H] - \vspace*{-0.5cm} + \begin{minipage}[c]{0.9\textwidth} \centering - \begin{subfigure}[c]{0.33\textwidth} + \begin{figure}[H] + \vspace*{-0.6cm} + \hspace*{-0.7cm} \centering + \begin{subfigure}[c]{0.33\textwidth} + \centering - \begin{tikzpicture}[scale=0.37] - \begin{axis}[ - grid=both, - xlabel={$E_b / N_0$}, ylabel={FER}, - ymode=log, - legend columns=1, - legend pos=outer north east, - %legend columns=2, - %legend style={at={(0.5,-0.45)},anchor=south}, - ymax=1.5, ymin=8e-4, - ] + \begin{tikzpicture}[scale=0.4] + \begin{axis}[ + grid=both, + xlabel={$E_b / N_0$}, ylabel={FER}, + ymode=log, + legend columns=1, + legend pos=outer north east, + %legend columns=2, + %legend style={at={(0.5,-0.45)},anchor=south}, + ymax=1.5, ymin=8e-5, + ] - \addplot[ForestGreen, mark=*, solid] - table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] - {res/proximal/2d_ber_fer_dfr_963965.csv}; + \addplot[ForestGreen, mark=*, solid] + table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] + {res/proximal/2d_ber_fer_dfr_963965.csv}; + \addplot[Emerald, mark=triangle, densely dashed] + table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}] + {res/hybrid/2d_ber_fer_dfr_963965.csv}; + + \addplot[NavyBlue, mark=*, solid] + table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] + {res/proximal/2d_ber_fer_dfr_963965.csv}; + \addplot[RoyalPurple, mark=triangle, densely dashed] + table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}] + {res/hybrid/2d_ber_fer_dfr_963965.csv}; + + \addplot[RedOrange, mark=*, solid] + table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] + {res/proximal/2d_ber_fer_dfr_963965.csv}; + \addplot[red, mark=triangle, densely dashed] + table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}] + {res/hybrid/2d_ber_fer_dfr_963965.csv}; + \end{axis} + \end{tikzpicture} + \caption{$\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, $\gamma = 0.15$} - \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}; + + \addlegendimage{Emerald, mark=triangle, densely dashed} \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_963965.csv}; + \addlegendimage{NavyBlue, mark=*, solid} \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_963965.csv}; + + \addlegendimage{RoyalPurple, mark=triangle, densely dashed} \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_963965.csv}; + + \addlegendimage{RedOrange, mark=*, solid} \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_963965.csv}; + + \addlegendimage{red, mark=triangle, densely dashed} \addlegendentry{hybrid, $\gamma = 0.05$} \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=0.37] - \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,] - 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}; - \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{figure} + \end{minipage} \end{frame} @@ -1411,14 +1421,14 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d \setcounter{footnote}{0} \begin{figure}[H] - \vspace*{-0.5cm} \centering - \begin{tikzpicture}[scale=0.7] + \begin{tikzpicture}[scale=0.6] \begin{axis}[ grid=both, xlabel={k}, ylabel={Average $\left| \boldsymbol{x}-\boldsymbol{\hat{x}} \right|$}, + legend pos=outer north east, ] \addplot table [col sep=comma, discard if not={omega}{0.0774263682681127},