From ad354f8f02a946890de7098b452053f6fa1dc51a Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Sun, 7 Jan 2024 22:27:36 +0100
Subject: [PATCH] Correct Algorithm 1

---
 letter.tex | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/letter.tex b/letter.tex
index 8d88d8d..5e04c63 100644
--- a/letter.tex
+++ b/letter.tex
@@ -8,6 +8,7 @@
 \usepackage{siunitx}
 \usepackage{dsfont}
 \usepackage{mleftright}
+\usepackage{bbm}
 
 \usepackage{tikz}
 \usetikzlibrary{spy, arrows.meta,arrows}
@@ -303,7 +304,7 @@ The resulting decoding process as described in \cite{proximal_paper} is
 presented in Algorithm \ref{alg:proximal_decoding}.
 
 \begin{algorithm}
-    \caption{Proximal decoding algorithm for an AWGN channel.}
+	\caption{Proximal decoding algorithm for an AWGN channel \cite{proximal_paper}.}
     \label{alg:proximal_decoding}
 
     \begin{algorithmic}
@@ -311,7 +312,7 @@ 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} $\boldsymbol{\hat{c}} \leftarrow \mathds{1} \left\{ \text{sign}\left( \boldsymbol{s} \right) = -1 \right\}$
+		\STATE \hspace{5mm} $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \preceq 0 \right\}}$
         \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}