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Added conclusion slide and fixed mu rho debacle

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Andreas Tsouchlos 2023-04-18 01:08:18 +02:00
parent a37dede8e6
commit 5ca2410a8f
2 changed files with 26 additions and 5 deletions
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17
latex/presentations/final/sections/comparison.tex
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@ -455,4 +455,21 @@ return $\tilde{\boldsymbol{c}}$
\begin{frame}[t]
\frametitle{Conclusion}
\begin{itemize}
\item Analysis of the general behavior of the two decoding algorithms
\begin{itemize}
\item Parameter choice
\item Verification of theoretical considerations with simulation results
\end{itemize}
\item Suggestion for improvement of proximal decoding
\begin{itemize}
\item Addition of "ML-in-the-List" step
\item Up to $\sim \SI{1}{dB}$ gain under certain conditions
\end{itemize}
\item Comparison of the two decoding algorithms
\begin{itemize}
\item based on simulation results
\item based on their theoretical structure
\end{itemize}
\end{itemize}
\end{frame}

14
latex/presentations/final/sections/decoding_algorithms.tex
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@ -780,19 +780,19 @@ return $\boldsymbol{\hat{c}}$
\begin{alignat*}{3}
\tilde{\boldsymbol{c}} &\leftarrow \argmin_{\tilde{\boldsymbol{c}}}
\left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
+ \frac{\rho}{2}\sum_{j\in\mathcal{J}} \left\Vert
+ \frac{\mu}{2}\sum_{j\in\mathcal{J}} \left\Vert
\boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j
+ \boldsymbol{u}_j \right\Vert \right) \\
\boldsymbol{z}_j &\leftarrow \argmin_{\boldsymbol{z}_j}
\left( g\left( \boldsymbol{z}_j \right)
+ \frac{\rho}{2} \left\Vert \boldsymbol{T}_j \tilde{\boldsymbol{c}}
+ \frac{\mu}{2} \left\Vert \boldsymbol{T}_j \tilde{\boldsymbol{c}}
- \boldsymbol{z}_j + \boldsymbol{u}_j \right\Vert \right),
\hspace{5mm} &&\forall j\in\mathcal{J} \\
\boldsymbol{u}_j &\leftarrow \boldsymbol{u}_j
+ \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j,
\hspace{5mm} &&\forall j\in\mathcal{J}
% \left( g\left( \boldsymbol{\boldsymbol{z}_j} \right)
% + \frac{\rho}{2} \left\Vert \boldsymbol{T}_j\tilde{\boldsymbol{c}}
% + \frac{\mu}{2} \left\Vert \boldsymbol{T}_j\tilde{\boldsymbol{c}}
% - \boldsymbol{z}_j + \boldsymbol{u}_j\right\Vert \right)
\end{alignat*}
\end{itemize}
@ -802,7 +802,9 @@ return $\boldsymbol{\hat{c}}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{LP Decoding using ADMM}
\vspace*{-7mm}
\begin{itemize}
\item Simplified rules%
\footnote{$\left( \boldsymbol{z}_j \right)_i $ is a slight abuse of notation.
@ -829,7 +831,9 @@ return $\boldsymbol{\hat{c}}$
$\Pi_{\mathcal{P}_{d_j}}, \hspace{1mm} j\in\mathcal{J}$. Many
different approaches exist, e.g., \cite{original_admm},
\cite{efficient_lp_dec_admm}, \cite{lautern}.
\item The approach chosen here is the one described in \cite{lautern}
\item The approach chosen here is the one described in \cite{original_admm}
\item The convergence properties can be enhanced by performing an
\textit{over-relaxation}, introducing the parameter $\rho$
\end{itemize}
\end{frame}