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Wording change to footnote

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Andreas Tsouchlos 2023-03-12 20:26:23 +01:00
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latex/thesis/chapters/decoding_techniques.tex
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@ -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. 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) $, The first relaxation, onto the codeword polytope $\text{poly}\left( \mathcal{C} \right) $,
is shown in figure \ref{fig:dec:poly:exact}; 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 $\text{poly}\left( \mathcal{C} \right) $ is further relaxed onto the relaxed codeword polytope
$\overline{Q}$, shown in figure \ref{fig:dec:poly:relaxed}. $\overline{Q}$, shown in figure \ref{fig:dec:poly:relaxed}.
Figure \ref{fig:dec:poly:local} shows how $\overline{Q}$ is formed by intersecting the 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 In order to derive the objective function, the authors begin with the
\ac{MAP} decoding rule, expressed as a continuous maximization problem% \ac{MAP} decoding rule, expressed as a continuous maximization problem%
\footnote{The expansion of the domain to be continuous doesn't constitute a \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 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 $\boldsymbol{x}$ over $\boldsymbol{x}$
:% :%
% %