diff --git a/letter.tex b/letter.tex
index 1d1a994..a651373 100644
--- a/letter.tex
+++ b/letter.tex
@@ -89,19 +89,16 @@
 \begin{document}
 
 
-\title{List-based Proximal Decoding for Linear Block Codes}
+\title{List-based Optimization of Proximal Decoding for Linear Block Codes}
 
-\author{Andreas Tsouchlos, Holger Jäkel, and Laurent Schmalen\\
-Communications Engineering Lab (CEL), Karlsruhe Institute of Technology (KIT)\\
-Hertzstr. 16, 76187 Karlsruhe, Germany, Email: \texttt{\{first.last\}@kit.edu}}
+\author{Andreas Tsouchlos, Holger Jäkel, and Laurent Schmalen
+\thanks{The authors are with the Communications Engineering Lab (CEL), Karlsruhe Institute of Technology (KIT), corresponding author: \texttt{holger.jaekel@kit.edu}}}
 
-% TODO
-\markboth{Journal of \LaTeX\ Class Files,~Vol.~14, No.~8, August~2021}%
-{Shell \MakeLowercase{\textit{et al.}}: A Sample Article Using IEEEtran.cls
-    for IEEE Journals}
+\markboth{IEEE Communications Letters}{List-based Optimization of Proximal Decoding for Linear Block Codes}
 
 \maketitle
 
+
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Abstract & Index Terms
@@ -331,7 +328,7 @@ presented in Algorithm \ref{alg:proximal_decoding}.
         \STATE \textbf{for} $K$ iterations \textbf{do}
         \STATE \hspace{5mm} $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \left( \boldsymbol{s} - \boldsymbol{y} \right) $
         \STATE \hspace{5mm} $\boldsymbol{s} \leftarrow \Pi_\eta \left(\boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) \right)$
-		\STATE \hspace{5mm} $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \preceq 0 \right\}}$
+		\STATE \hspace{5mm} $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$
         \STATE \hspace{5mm} \textbf{if} $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ \textbf{do}
         \STATE \hspace{10mm} \textbf{return} $\boldsymbol{\hat{c}}$
         \STATE \hspace{5mm} \textbf{end if}
@@ -631,7 +628,7 @@ the probability that a given component was decoded incorrectly.%
 				ylabel=$P(\hat{c}_{i'} \ne c_{i'})$,
 				xlabel=$i'$,
 				ymode=log,
-				ymin=1e-9,ymax=1e-5,
+				ymin=8e-9,ymax=1e-5,
 				xmin=0,xmax=200,
 				width=0.95\figwidth,
 				height=\figheight,
@@ -709,7 +706,14 @@ algorithm presented here when applied to a $\left( 3,6 \right)$-regular LDPC
 code with $n=204$ and $k=102$ \cite[204.33.484]{mackay}.
 The parameters chosen for the simulation are
 $\gamma = 0.05, \omega=0.05, \eta=1.5, K=200$.
-Again, these parameters were chosen,%
+Again, these parameters were chosen,
+as a preliminary examination
+showed that they provide the best results for proximal decoding as well as
+the improved algorithm.
+All points were generated by simulating at least 100 frame errors.
+The number $N$ of possibly wrong components selected was selected as $8$,
+since this provides reasonable gain without requiring an unreasonable amount
+of memory and computational resources.
 %
 \begin{figure}
     \centering
@@ -717,6 +721,15 @@ Again, these parameters were chosen,%
 	\ifoverleaf
 		\includegraphics{figs/letter-figure5.pdf}
 	\else
+		\newcommand{\lineintext}[1]{%
+			\begin{tikzpicture}
+				\draw[#1] (0,0) -- (1.5em,0);
+
+				% Dummy node taking up the space of a letter to fix spacing
+				\node[outer sep=0, inner sep=0] () at (0.75em,0) {\phantom{a}};
+			\end{tikzpicture}%
+		}
+
 		\begin{tikzpicture}
 			\begin{axis}[
 				grid=both,
@@ -726,39 +739,35 @@ Again, these parameters were chosen,%
 				ymax=1, ymin=1e-6,
 				width=\figwidth,
 				height=\figheight,
-				legend columns=2,
-				legend style={draw=white!15!black,
-					legend cell align=left,
-					at={(0.5,-0.44)},anchor=south}
+				legend pos=north east,
+				ylabel={BER (\lineintext{}) / FER (\lineintext{dashed})},
 			]
 
-				\addplot+[FERPlot, mark=o, mark options={solid}, scol1]
+				\addplot+[FERPlot, mark=o, mark options={solid}, scol1, forget plot]
 					table [x=SNR, y=FER, col sep=comma,
 						   discard if not={gamma}{0.05},
 						   discard if gt={SNR}{9}]
 						{res/proximal_ber_fer_dfr_20433484.csv};
-				\addlegendentry{FER, prox. dec.};
 
 				\addplot+[BERPlot, mark=*, scol1]
 					table [x=SNR, y=BER, col sep=comma,
 						   discard if not={gamma}{0.05},
 						   discard if gt={SNR}{7.5}]
 						{res/proximal_ber_fer_dfr_20433484.csv};
-				\addlegendentry{BER, prox. dec.};
+				\addlegendentry{Prox. dec.};
 
-				\addplot+[FERPlot, mark=triangle, mark options={solid}, scol2]
+				\addplot+[FERPlot, mark=triangle, mark options={solid}, scol2, forget plot]
 					table [x=SNR, y=FER, col sep=comma,
 						   discard if not={gamma}{0.05},
 						   discard if gt={SNR}{7.5}]
 						{res/improved_ber_fer_dfr_20433484.csv};
-				\addlegendentry{FER, improved};
 
 				\addplot+[BERPlot, mark=triangle*, scol2]
 					table [x=SNR, y=BER, col sep=comma,
 						   discard if not={gamma}{0.05},
 						   discard if gt={SNR}{6.5}]
 						{res/improved_ber_fer_dfr_20433484.csv};
-				\addlegendentry{BER, improved};
+				\addlegendentry{Improved};
 			\end{axis}
 		\end{tikzpicture}
 	\fi
@@ -773,13 +782,6 @@ Again, these parameters were chosen,%
     \label{fig:results}
 \end{figure}%
 %
-\noindent as a preliminary examination
-showed that they provide the best results for proximal decoding as well as
-the improved algorithm.
-All points were generated by simulating at least 100 frame errors.
-The number $N$ of possibly wrong components selected was selected as $8$,
-since this provides reasonable gain without requiring an unreasonable amount
-of memory and computational resources.
 
 A noticeable improvement can be observed both in the FER as well as the BER.
 The gain varies significantly
@@ -824,3 +826,4 @@ Ministry of Education and Research (BMBF) within the project Open6GHub
 \printbibliography
 
 \end{document}
+