an.tsouchlos/ba-thesis
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases 1 Wiki Activity

Fixed spelling errors

Browse Source
This commit is contained in:
Andreas Tsouchlos 2023-04-12 23:18:43 +02:00
parent 0ac256ded8
commit a9b1e882b6
1 changed files with 5 additions and 5 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

10
latex/thesis/chapters/comparison.tex
View File

@ -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.