diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex
index f74f6d4..dfafca7 100644
--- a/latex/thesis/chapters/decoding_techniques.tex
+++ b/latex/thesis/chapters/decoding_techniques.tex
@@ -30,25 +30,24 @@ the \ac{ML} decoding problem:%
         f_{\boldsymbol{Y} \mid \boldsymbol{C}} \left( \boldsymbol{y} \mid \boldsymbol{c} \right) 
 .\end{align*}%
 %
-\todo{Note about these generally being the same thing, when the a priori probability
-is uniformly distributed}%
-\todo{Here the two problems are written in terms of $\hat{\boldsymbol{c}}$; below MAP
-decoding is applied in terms of $\hat{\boldsymbol{x}}$. Is that a problem?}%
 The goal is to arrive at a formulation, where a certain objective function
 $f$ has to be minimized under certain constraints:%
 %
 \begin{align*}
-    \text{minimize } f\left( \boldsymbol{x} \right)\\
-    \text{subject to \ldots}
-.\end{align*}
+    \text{minimize } f\left( \boldsymbol{c} \right)\\
+    \text{subject to $\boldsymbol{c} \in D$}
+,\end{align*}%
+%
+where $D$ is the domain of values attainable for $c$ and represents the
+constraints.
 
 In contrast to the established message-passing decoding algorithms,
 the viewpoint then changes from observing the decoding process in its
 tanner graph representation (as shown in figure \ref{fig:dec:tanner})
-to a spacial representation, where the codewords are some of the edges
-of a hypercube and the goal is to find that point $\boldsymbol{x}$,
-\todo{$\boldsymbol{x}$? Or some other variable?}
-which minimizes the objective function $f$ (as shown in figure \ref{fig:dec:spacial}).
+to a spacial representation (figure \ref{fig:dec:spacial}),
+where the codewords are some of the edges of a hypercube.
+The goal is to find that point $\boldsymbol{c}$,
+which minimizes the objective function $f$.
 
 %
 % Figure showing decoding space
@@ -143,11 +142,11 @@ which minimizes the objective function $f$ (as shown in figure \ref{fig:dec:spac
             \node[color=KITblue, right=0cm of c110]    {$\left( 1, 1, 0 \right) $};
             \node[color=KITblue, above=0cm of c011]    {$\left( 0, 1, 1 \right) $};
 
-            % x
+            % c
 
             \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] {$\boldsymbol{x}$};
+                  draw, circle, inner sep=0pt, minimum size=4pt] (c) at (0.9, 0.7, 1) {};
+            \node[color=KITgreen, right=0cm of c] {$\boldsymbol{c}$};
         \end{tikzpicture}
 
         \caption{Spacial representation of a single parity-check code}
@@ -164,7 +163,6 @@ which minimizes the objective function $f$ (as shown in figure \ref{fig:dec:spac
 \label{sec:dec:LP Decoding}
 
 \Ac{LP} decoding is a subject area introduced by Feldman et al.
-\todo{Space before citation?}
 \cite{feldman_paper}. They reframe the decoding problem as an
 \textit{integer linear program} and subsequently present two relaxations into
 \textit{linear programs}, one representing a formulation of exact \ac{LP}
@@ -179,7 +177,8 @@ making the \ac{ML} and \ac{MAP} decoding problems equivalent.}%
 %
 \begin{align}
     \hat{\boldsymbol{c}} = \argmax_{\boldsymbol{c} \in \mathcal{C}}
-        f_{\boldsymbol{Y} \mid \boldsymbol{C}} \left( \boldsymbol{y} \mid \boldsymbol{c} \right)%
+        f_{\boldsymbol{Y} \mid \boldsymbol{C}}
+            \left( \boldsymbol{y} \mid \boldsymbol{c} \right)%
     \label{eq:lp:ml}
 .\end{align}%
 %