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Added comparison between proximal and hybrid decoding

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Andreas Tsouchlos 2023-01-23 20:42:54 +01:00
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latex/presentations/midterm/sections/examination_results.tex
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@ -347,6 +347,67 @@ Output $\boldsymbol{\tilde{x}}_n$ with lowest $d\left( \boldsymbol{ \tilde{x}}_n
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t, fragile]
\frametitle{Proximal Decoding: Improvement using ``ML-on-List''}
\setcounter{footnote}{0}
\begin{itemize}
\item Improvement of proximal decoding by adding an ``ML-on-list'' step after iterating
\end{itemize}
\begin{minipage}[t]{.48\textwidth}
\centering
\begin{figure}
\centering
\begin{algorithm}[caption={}, label={},
basicstyle=\fontsize{7.5}{9.5}\selectfont
]
$\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$
for $k=0$ to $K-1$ do
$\boldsymbol{r}^{\left( k+1 \right)} = \boldsymbol{s}^{(k)} - \omega \nabla L \left( \boldsymbol{s}^{(k)}; \boldsymbol{y} \right) $
Compute $\nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right)$
$\boldsymbol{s}^{\left( k+1 \right)} = \boldsymbol{r}^{(k+1)} - \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) $
$\boldsymbol{\hat{x}} = \text{sign}\left( \boldsymbol{s}^{\left( k+1 \right) } \right) $
If $\boldsymbol{\hat{x}}$ passes the parity check condition, break the loop.
end for
Output $\boldsymbol{\hat{x}}$
\end{algorithm}
\caption{Proximal decoding algorithm}
\end{figure}
\end{minipage}%
\hfill\begin{minipage}[t]{.48\textwidth}
\centering
\begin{figure}
\centering
\begin{algorithm}[caption={}, label={},
basicstyle=\fontsize{7.5}{9.5}\selectfont
]
$\boldsymbol{s}^{\left( 0 \right)} = \boldsymbol{0}$
for $k=0$ to $K-1$ do
$\boldsymbol{r}^{\left( k+1 \right)} = \boldsymbol{s}^{(k)} - \omega \nabla L \left( \boldsymbol{s}^{(k)}; \boldsymbol{y} \right) $
Compute $\nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right)$
$\boldsymbol{s}^{\left( k+1 \right)} = \boldsymbol{r}^{(k+1)} - \gamma \nabla h\left( \boldsymbol{r}^{\left( k+1 \right) } \right) $
$\boldsymbol{\hat{x}} = \text{sign}\left( \boldsymbol{s}^{\left( k+1 \right) } \right) $
$\textcolor{KITblue}{\text{If }\boldsymbol{\hat{x}}\text{ passes the parity check condition, output }\boldsymbol{\hat{x}}}$
end for
$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$
$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{x}}_n\text{ of }\boldsymbol{\hat{x}}\text{ with the }N\text{ bits modified.}}$
$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right) \forall n \in \left[ 1 : N-1 \right]}$
$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{x}}_n\text{ with lowest }d_H\left( \boldsymbol{ \tilde{x}}_n, \boldsymbol{\hat{x}} \right)}$
\end{algorithm}
\caption{Hybrid proximal \& ML decoding algorithm}
\end{figure}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{ADMM: Examination Results}%
\label{sub:Ex ADMM}