From fa90a0417a0d109fe9cd9ed9048d4c1533bc079f Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Sun, 12 Mar 2023 20:26:23 +0100 Subject: [PATCH] Wording change to footnote --- latex/thesis/chapters/decoding_techniques.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex index 452e3f8..25d9820 100644 --- a/latex/thesis/chapters/decoding_techniques.tex +++ b/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 $\boldsymbol{x}$ :% %