Add stuff from overleaf; FER and BER as ylabel; Remove exessive spacing below 10e-8 figure
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letter.tex
59
letter.tex
@ -89,19 +89,16 @@
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\begin{document}
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\title{List-based Proximal Decoding for Linear Block Codes}
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\title{List-based Optimization of Proximal Decoding for Linear Block Codes}
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\author{Andreas Tsouchlos, Holger Jäkel, and Laurent Schmalen\\
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Communications Engineering Lab (CEL), Karlsruhe Institute of Technology (KIT)\\
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Hertzstr. 16, 76187 Karlsruhe, Germany, Email: \texttt{\{first.last\}@kit.edu}}
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\author{Andreas Tsouchlos, Holger Jäkel, and Laurent Schmalen
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\thanks{The authors are with the Communications Engineering Lab (CEL), Karlsruhe Institute of Technology (KIT), corresponding author: \texttt{holger.jaekel@kit.edu}}}
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% TODO
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\markboth{Journal of \LaTeX\ Class Files,~Vol.~14, No.~8, August~2021}%
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{Shell \MakeLowercase{\textit{et al.}}: A Sample Article Using IEEEtran.cls
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for IEEE Journals}
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\markboth{IEEE Communications Letters}{List-based Optimization of Proximal Decoding for Linear Block Codes}
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\maketitle
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Abstract & Index Terms
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@ -331,7 +328,7 @@ presented in Algorithm \ref{alg:proximal_decoding}.
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\STATE \textbf{for} $K$ iterations \textbf{do}
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\STATE \hspace{5mm} $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \left( \boldsymbol{s} - \boldsymbol{y} \right) $
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\STATE \hspace{5mm} $\boldsymbol{s} \leftarrow \Pi_\eta \left(\boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) \right)$
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\STATE \hspace{5mm} $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \preceq 0 \right\}}$
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\STATE \hspace{5mm} $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$
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\STATE \hspace{5mm} \textbf{if} $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ \textbf{do}
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\STATE \hspace{10mm} \textbf{return} $\boldsymbol{\hat{c}}$
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\STATE \hspace{5mm} \textbf{end if}
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@ -631,7 +628,7 @@ the probability that a given component was decoded incorrectly.%
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ylabel=$P(\hat{c}_{i'} \ne c_{i'})$,
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xlabel=$i'$,
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ymode=log,
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ymin=1e-9,ymax=1e-5,
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ymin=8e-9,ymax=1e-5,
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xmin=0,xmax=200,
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width=0.95\figwidth,
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height=\figheight,
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@ -709,7 +706,14 @@ algorithm presented here when applied to a $\left( 3,6 \right)$-regular LDPC
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code with $n=204$ and $k=102$ \cite[204.33.484]{mackay}.
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The parameters chosen for the simulation are
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$\gamma = 0.05, \omega=0.05, \eta=1.5, K=200$.
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Again, these parameters were chosen,%
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Again, these parameters were chosen,
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as a preliminary examination
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showed that they provide the best results for proximal decoding as well as
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the improved algorithm.
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All points were generated by simulating at least 100 frame errors.
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The number $N$ of possibly wrong components selected was selected as $8$,
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since this provides reasonable gain without requiring an unreasonable amount
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of memory and computational resources.
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%
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\begin{figure}
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\centering
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@ -717,6 +721,15 @@ Again, these parameters were chosen,%
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\ifoverleaf
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\includegraphics{figs/letter-figure5.pdf}
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\else
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\newcommand{\lineintext}[1]{%
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\begin{tikzpicture}
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\draw[#1] (0,0) -- (1.5em,0);
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% Dummy node taking up the space of a letter to fix spacing
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\node[outer sep=0, inner sep=0] () at (0.75em,0) {\phantom{a}};
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\end{tikzpicture}%
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}
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\begin{tikzpicture}
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\begin{axis}[
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grid=both,
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@ -726,39 +739,35 @@ Again, these parameters were chosen,%
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ymax=1, ymin=1e-6,
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width=\figwidth,
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height=\figheight,
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legend columns=2,
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legend style={draw=white!15!black,
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legend cell align=left,
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at={(0.5,-0.44)},anchor=south}
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legend pos=north east,
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ylabel={BER (\lineintext{}) / FER (\lineintext{dashed})},
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]
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\addplot+[FERPlot, mark=o, mark options={solid}, scol1]
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\addplot+[FERPlot, mark=o, mark options={solid}, scol1, forget plot]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={gamma}{0.05},
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discard if gt={SNR}{9}]
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{res/proximal_ber_fer_dfr_20433484.csv};
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\addlegendentry{FER, prox. dec.};
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\addplot+[BERPlot, mark=*, scol1]
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table [x=SNR, y=BER, col sep=comma,
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discard if not={gamma}{0.05},
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discard if gt={SNR}{7.5}]
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{res/proximal_ber_fer_dfr_20433484.csv};
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\addlegendentry{BER, prox. dec.};
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\addlegendentry{Prox. dec.};
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\addplot+[FERPlot, mark=triangle, mark options={solid}, scol2]
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\addplot+[FERPlot, mark=triangle, mark options={solid}, scol2, forget plot]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={gamma}{0.05},
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discard if gt={SNR}{7.5}]
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{res/improved_ber_fer_dfr_20433484.csv};
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\addlegendentry{FER, improved};
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\addplot+[BERPlot, mark=triangle*, scol2]
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table [x=SNR, y=BER, col sep=comma,
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discard if not={gamma}{0.05},
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discard if gt={SNR}{6.5}]
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{res/improved_ber_fer_dfr_20433484.csv};
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\addlegendentry{BER, improved};
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\addlegendentry{Improved};
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\end{axis}
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\end{tikzpicture}
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\fi
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@ -773,13 +782,6 @@ Again, these parameters were chosen,%
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\label{fig:results}
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\end{figure}%
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%
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\noindent as a preliminary examination
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showed that they provide the best results for proximal decoding as well as
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the improved algorithm.
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All points were generated by simulating at least 100 frame errors.
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The number $N$ of possibly wrong components selected was selected as $8$,
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since this provides reasonable gain without requiring an unreasonable amount
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of memory and computational resources.
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A noticeable improvement can be observed both in the FER as well as the BER.
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The gain varies significantly
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@ -824,3 +826,4 @@ Ministry of Education and Research (BMBF) within the project Open6GHub
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\printbibliography
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\end{document}
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