From 848ec4469f4bd58ae1ebcec7891d14ab37b4f5e8 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Sat, 1 Apr 2023 19:31:02 +0200 Subject: [PATCH] Renamed theoretical comparison section --- latex/thesis/chapters/analysis_of_results.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/latex/thesis/chapters/analysis_of_results.tex b/latex/thesis/chapters/analysis_of_results.tex index 4622937..ae2ab62 100644 --- a/latex/thesis/chapters/analysis_of_results.tex +++ b/latex/thesis/chapters/analysis_of_results.tex @@ -30,8 +30,8 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Comparison of the Proximal Decoding and LP Decoding using ADMM algorithms}% -\label{sec:Comparison of the Proximal Decoding and LP Decoding using ADMM algorithms} +\section{Theoretical Comparison of Proximal Decoding and LP Decoding using ADMM}% +\label{sec:Theoretical Comparison of Proximal Decoding and LP Decoding using ADMM} In this section, some similarities between the proximal decoding algorithm and \ac{LP} decoding using \ac{ADMM} are be pointed out. @@ -123,8 +123,8 @@ codeword was sent and one associated to the constraints the codeword is subjected to. Their major difference is that the two parts of the objective minimized with proximal decoding are both functions of the same variable -$\tilde{\boldsymbol{x}}$, whereas with \ac{ADMM} the two parts depend on -different variables: $\tilde{\boldsymbol{c}}$ and $\boldsymbol{z}$. +$\tilde{\boldsymbol{x}}$, whereas with \ac{ADMM} the two parts are functions +of different variables: $\tilde{\boldsymbol{c}}$ and $\boldsymbol{z}$. This difference means that while with proximal decoding the alternating minimization of the two parts of the objective function inevitably leads to oscillatory behaviour (as explained in section (TODO)), this is not the