From ca345d7d5b2c80e4e533ceb2f81547f4954c5106 Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Mon, 24 Apr 2023 20:57:02 +0200
Subject: [PATCH] Almost almost done with corrections

---
 latex/thesis/chapters/lp_dec_using_admm.tex | 2 +-
 latex/thesis/chapters/proximal_decoding.tex | 9 ++++-----
 2 files changed, 5 insertions(+), 6 deletions(-)

diff --git a/latex/thesis/chapters/lp_dec_using_admm.tex b/latex/thesis/chapters/lp_dec_using_admm.tex
index f85880b..cb5b664 100644
--- a/latex/thesis/chapters/lp_dec_using_admm.tex
+++ b/latex/thesis/chapters/lp_dec_using_admm.tex
@@ -1379,7 +1379,7 @@ using \ac{ADMM} and \ac{BP} are shown for various codes.
 To ensure comparability, in all cases the number of iterations was set to
 $K=200$.
 The values of the other parameters were chosen as $\mu = 5$, $\rho = 1$,
-$\epsilon = 10^{-5}$ and $\epsilon=10^{-5}$.
+$\epsilon_\text{pri} = 10^{-5}$ and $\epsilon_\text{dual}=10^{-5}$.
 Comparing the simulation results for the different codes, it is apparent that
 the difference in decoding performance depends on the code being
 considered.
diff --git a/latex/thesis/chapters/proximal_decoding.tex b/latex/thesis/chapters/proximal_decoding.tex
index 1f3d009..da4140b 100644
--- a/latex/thesis/chapters/proximal_decoding.tex
+++ b/latex/thesis/chapters/proximal_decoding.tex
@@ -1,4 +1,4 @@
-\chapter{Proximal Decoding and Implementation}%
+\chapter{Proximal Decoding}%
 \label{chapter:proximal_decoding}
 
 In this chapter, the proximal decoding algorithm is examined.
@@ -10,7 +10,7 @@ Finally, an improvement on proximal decoding is proposed.
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Decoding Algorithm}%
+\section{Decoding Algorithm and Implementation}%
 \label{sec:prox:Decoding Algorithm}
 
 Proximal decoding was proposed by Wadayama et al. as a novel formulation of
@@ -1265,9 +1265,8 @@ error are strongly correlated, a relationship being depicted in figure
     \label{fig:prox:correlation}
 \end{figure}%
 %
-The y-axis depicts whether there is a bit error and the x-axis the
-variance in $\nabla h\left( \tilde{\boldsymbol{x}} \right)$ after the
-100th iteration.
+The x-axis depicts the variance in $\nabla h\left( \tilde{\boldsymbol{x}} \right)$
+after the 100th iteration, and the y-axis depicts whether there is a bit error.
 While this is not exactly the magnitude of the oscillation, it is
 proportional and easier to compute.
 The datapoints are taken from a single decoding operation.