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Added hypercube figure

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Andreas Tsouchlos 2023-02-13 15:01:15 +01:00
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latex/thesis/chapters/decoding_techniques.tex
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@ -6,10 +6,66 @@
\section{Decoding using Optimization Methods}%
\label{sec:dec:Decoding using Optimization Methods}
%
% TODOs
%
\begin{itemize}
\item General methodology
\end{itemize}
%
% Figure showing decoding space
%
\begin{figure}[H]
\centering
\tikzstyle{codeword} = [color=KITblue, fill=KITblue,
draw, circle, inner sep=0pt, minimum size=4pt]
\tdplotsetmaincoords{60}{245}
\begin{tikzpicture}[scale=1, transform shape, tdplot_main_coords]
% Cube
\draw[dashed] (0, 0, 0) -- (2, 0, 0);
\draw[dashed] (2, 0, 0) -- (2, 0, 2);
\draw[] (2, 0, 2) -- (0, 0, 2);
\draw[] (0, 0, 2) -- (0, 0, 0);
\draw[] (0, 2, 0) -- (2, 2, 0);
\draw[] (2, 2, 0) -- (2, 2, 2);
\draw[] (2, 2, 2) -- (0, 2, 2);
\draw[] (0, 2, 2) -- (0, 2, 0);
\draw[] (0, 0, 0) -- (0, 2, 0);
\draw[dashed] (2, 0, 0) -- (2, 2, 0);
\draw[] (2, 0, 2) -- (2, 2, 2);
\draw[] (0, 0, 2) -- (0, 2, 2);
% Polytope Annotations
\node[codeword] (c000) at (0, 0, 0) {};% {$\left( 0, 0, 0 \right) $};
\node[codeword] (c101) at (2, 0, 2) {};% {$\left( 1, 0, 1 \right) $};
\node[codeword] (c110) at (2, 2, 0) {};% {$\left( 1, 1, 0 \right) $};
\node[codeword] (c011) at (0, 2, 2) {};% {$\left( 0, 1, 1 \right) $};
\node[color=KITblue, right=0cm of c000] {$\left( 0, 0, 0 \right) $};
\node[color=KITblue, above=0cm of c101] {$\left( 1, 0, 1 \right) $};
\node[color=KITblue, left=0cm of c110] {$\left( 1, 1, 0 \right) $};
\node[color=KITblue, left=-0.1cm of c011] {$\left( 0, 1, 1 \right) $};
% f
\node[color=KITgreen, fill=KITgreen,
draw, circle, inner sep=0pt, minimum size=4pt] (f) at (0.9, 0.7, 1) {};
\node[color=KITgreen, right=0cm of f] {$\boldsymbol{f}$};
\end{tikzpicture}
\caption{Hypercube ($n=3$) and valid codewords for a single parity-check code}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{LP Decoding using ADMM}%