Wording change to footnote

latex/thesis/chapters/decoding_techniques.tex

@@ -298,7 +298,7 @@ and has only two possible codewords:
 Figure \ref{fig:dec:poly:exact_ilp} shows the domain of exact \ac{ML} decoding.
 The first relaxation, onto the codeword polytope $\text{poly}\left( \mathcal{C} \right) $,
 is shown in figure \ref{fig:dec:poly:exact};
-this constitues the constraints for the equivalent linear program to exact \ac{ML} decoding.
+this expresses the constraints for the equivalent linear program to exact \ac{ML} decoding.
 $\text{poly}\left( \mathcal{C} \right) $ is further relaxed onto the relaxed codeword polytope
 $\overline{Q}$, shown in figure \ref{fig:dec:poly:relaxed}.
 Figure \ref{fig:dec:poly:local} shows how $\overline{Q}$ is formed by intersecting the
@@ -708,9 +708,9 @@ non-convex optimization formulation of the \ac{MAP} decoding problem.
 In order to derive the objective function, the authors begin with the
 \ac{MAP} decoding rule, expressed as a continuous maximization problem%
 \footnote{The expansion of the domain to be continuous doesn't constitute a
-material difference.
+material difference in the meaning of the rule.
 The only change is that what previously were \acp{PMF} now have to be expressed
-in terms of \acp{PDF}}
+in terms of \acp{PDF}.}
 over $\boldsymbol{x}$
 :%
 %