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Renamed theoretical comparison section

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Andreas Tsouchlos 2023-04-01 19:31:02 +02:00
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latex/thesis/chapters/analysis_of_results.tex
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@ -30,8 +30,8 @@
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\section{Comparison of the Proximal Decoding and LP Decoding using ADMM algorithms}% \section{Theoretical Comparison of Proximal Decoding and LP Decoding using ADMM}%
\label{sec:Comparison of the Proximal Decoding and LP Decoding using ADMM algorithms} \label{sec:Theoretical Comparison of Proximal Decoding and LP Decoding using ADMM}
In this section, some similarities between the proximal decoding algorithm In this section, some similarities between the proximal decoding algorithm
and \ac{LP} decoding using \ac{ADMM} are be pointed out. 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. subjected to.
Their major difference is that the two parts of the objective minimized with Their major difference is that the two parts of the objective minimized with
proximal decoding are both functions of the same variable proximal decoding are both functions of the same variable
$\tilde{\boldsymbol{x}}$, whereas with \ac{ADMM} the two parts depend on $\tilde{\boldsymbol{x}}$, whereas with \ac{ADMM} the two parts are functions
different variables: $\tilde{\boldsymbol{c}}$ and $\boldsymbol{z}$. of different variables: $\tilde{\boldsymbol{c}}$ and $\boldsymbol{z}$.
This difference means that while with proximal decoding the alternating This difference means that while with proximal decoding the alternating
minimization of the two parts of the objective function inevitably leads to minimization of the two parts of the objective function inevitably leads to
oscillatory behaviour (as explained in section (TODO)), this is not the oscillatory behaviour (as explained in section (TODO)), this is not the