From a9b1e882b6000678e0c82cce39c883f9501085cb Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Wed, 12 Apr 2023 23:18:43 +0200 Subject: [PATCH] Fixed spelling errors --- latex/thesis/chapters/comparison.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/latex/thesis/chapters/comparison.tex b/latex/thesis/chapters/comparison.tex index d6181e5..7aaa70b 100644 --- a/latex/thesis/chapters/comparison.tex +++ b/latex/thesis/chapters/comparison.tex @@ -3,7 +3,7 @@ In this chapter, proximal decoding and \ac{LP} Decoding using \ac{ADMM} are compared. First the two algorithms are compared on a theoretical basis. -Subsequently, their respective simulation results are examined and their +Subsequently, their respective simulation results are examined, and their differences are interpreted on the basis of their theoretical structure. %some similarities between the proximal decoding algorithm @@ -119,13 +119,13 @@ return $\tilde{\boldsymbol{c}}$ \end{figure}% % -Their major differece is that while with proximal decoding the constraints +Their major difference is that while with proximal decoding the constraints are regarded in a global context, considering all parity checks at the same time, with \ac{ADMM} each parity check is considered separately and in a more local context (line 4 in both algorithms). 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 +oscillatory behavior (as explained in section \ref{subsec:prox:conv_properties}), this is not the case with \ac{ADMM}, which partly explains the disparate decoding performance of the two methods. Furthermore, while with proximal decoding the step considering the constraints @@ -137,7 +137,7 @@ The contrasting treatment of the constraints (global and approximate with proximal decoding as opposed to local and exact with \ac{LP} decoding using \ac{ADMM}) also leads to different prospects when the decoding process gets stuck in a local minimum. -With proximal decoding this occurrs due to the approximate nature of the +With proximal decoding this occurs due to the approximate nature of the calculation, whereas with \ac{LP} decoding it occurs due to the approximate formulation of the constraints - independent of the optimization method itself. @@ -241,7 +241,7 @@ computed for each check node (line 6 in figure \ref{fig:comp:message_passing:admm}), whereas with proximal decoding, the same message is transmitted to all \acp{VN} (line 5 of figure \ref{fig:comp:message_passing:proximal}). -This means that while both algorithms have an averege time complexity of +This means that while both algorithms have an average time complexity of $\mathcal{O}\left( n \right)$, more arithmetic operations are required for the \ac{ADMM} case.