From 5af7e62f5d7327e802d8525d7cc4ff2bc5d9ed1a Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Sun, 7 Jan 2024 20:43:26 +0100
Subject: [PATCH] Correct abstract

---
 letter.tex | 25 ++++++++++++-------------
 1 file changed, 12 insertions(+), 13 deletions(-)

diff --git a/letter.tex b/letter.tex
index 839aaf3..eccba13 100644
--- a/letter.tex
+++ b/letter.tex
@@ -32,8 +32,8 @@
 \ifoverleaf
 	\input{common.tex}
 \else
-%	\usetikzlibrary{external}
-%	\tikzexternalize[prefix=build/]
+	\usetikzlibrary{external}
+	\tikzexternalize[prefix=build/]
 	\input{lib/latex-common/common.tex}
 \fi
 
@@ -91,20 +91,19 @@ Hertzstr. 16, 76187 Karlsruhe, Germany, Email: \texttt{\{first.last\}@kit.edu}}
 \begin{abstract}
 In this paper, the proximal decoding algorithm is considered within the
 context of \textit{additive white Gaussian noise} (AWGN) channels.
-An analysis of the convergence behavior of the algorithm shows that it is an
-inherent property of proximal decoding to enter an
-oscillating behavior of the estimate after a number of iterations.
+An analysis of the convergence behavior of the algorithm shows that
+proximal decoding inherently enters an oscillating behavior of the estimate
+after a certain number of iterations.
 Due to this oscillation, frame errors arising during decoding can often
-be attributed to only a few remaining wrongly decoded components.
-
-In this paper, an improvement of the algorithm is proposed by appending an
-additional step, in which these erroneous components are attempted to be
-corrected.
-An empirical rule is suggested, with which the components most likely needing
+be attributed to only a few remaining wrongly decoded bits.
+In this letter, an improvement of the proximal decoding algorithm is proposed
+by appending an additional step, in which these erroneous components are
+attempted to be corrected.
+We suggesst an empirical rule with which the components most likely needing
 correction can be determined.
 Using this insight and performing a subsequent ``ML-in-the-list'' decoding,
-a gain of up to approximately 1 dB is achieved compared to proximal decoding,
-depending on the parameters chosen and the code considered.
+a gain of up to approximately 1 dB is achieved compared to conventional
+proximal decoding, depending on the decoder parameters and the code.
 \end{abstract}
 
 \begin{IEEEkeywords}