diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex
index 68a5e7b..3211b0d 100644
--- a/latex/thesis/chapters/decoding_techniques.tex
+++ b/latex/thesis/chapters/decoding_techniques.tex
@@ -237,7 +237,7 @@ However, since the number of constraints needed to characterize the codeword
 polytope is exponential in the code length, this formulation is relaxed futher.
 By observing that each check-node defines its own local single parity-check
 code, and thus its own \textit{local codeword polytope},
-the \textit{relaxed codeword polytope} $Q$ is defined as the intersection of all
+the \textit{relaxed codeword polytope} $\overline{Q}$ is defined as the intersection of all
 local codeword polytopes.
 This consideration leads to the following constraints:%
 %
@@ -245,7 +245,7 @@ This consideration leads to the following constraints:%
     \ldots
 .\end{align*}
 
-In figure \ref{fig:dec:poly} the two relaxations are compared based on an
+In figure \ref{fig:dec:poly}, the two relaxations are compared based on an
 example code.
 Figure \ref{fig:dec:poly:exact} shows the codeword polytope
 $\text{poly}\left( \mathcal{C} \right) $, i.e. the constraints for the
@@ -253,7 +253,7 @@ equivalent linear program to exact \ac{ML} decoding - only valid codewords are
 feasible solutions.
 Figures \ref{fig:dec:poly:local1} and \ref{fig:dec:poly:local2} show the local
 codeword polytopes of each check node.
-Their intersection, the relaxed codeword polytope $Q$, is shown in figure
+Their intersection, the relaxed codeword polytope $\overline{Q}$, is shown in figure
 \ref{fig:dec:poly:relaxed}.
 
 %
@@ -537,7 +537,7 @@ Their intersection, the relaxed codeword polytope $Q$, is shown in figure
                     {$\left( 1, \frac{1}{2}, \frac{1}{2} \right) $};
             \end{tikzpicture}
         
-            \caption{Relaxed codeword polytope $Q$}
+            \caption{Relaxed codeword polytope $\overline{Q}$}
             \label{fig:dec:poly:relaxed}
         \end{subfigure}
     \end{subfigure}
@@ -548,12 +548,12 @@ Their intersection, the relaxed codeword polytope $Q$, is shown in figure
 \end{figure}
 
 \noindent%
-It can be seen, that the relaxed codeword polytope $Q$ introduces fractional
-vertices;
+It can be seen, that the relaxed codeword polytope $\overline{Q}$ introduces
+vertices with fractional values;
 these represent erroneous non-codeword solutions to the linear program and
 correspond to the so-called \textit{pseudocodewords} introduced in
 \cite{feldman_paper}.
-However, since for \ac{LDPC} codes $Q$ scales linearly with $n$ instead of
+However, since for \ac{LDPC} codes $\overline{Q}$ scales linearly with $n$ instead of
 exponentially, it is a lot more tractable for practical applications.
 
 The resulting formulation of the relaxed optimization problem