diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex
index fcb279c..241bc79 100644
--- a/latex/thesis/chapters/decoding_techniques.tex
+++ b/latex/thesis/chapters/decoding_techniques.tex
@@ -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}%