From d36cd83cf6c4412871d5e67e5c4b83cbcb8ffee3 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Mon, 20 Feb 2023 09:21:20 +0100 Subject: [PATCH] Last few changes before submitting for correction --- latex/thesis/chapters/decoding_techniques.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex index 5811f68..177630f 100644 --- a/latex/thesis/chapters/decoding_techniques.tex +++ b/latex/thesis/chapters/decoding_techniques.tex @@ -40,7 +40,7 @@ $f$ must be minimized under certain constraints:% \text{subject to}\hspace{2mm} &\boldsymbol{c} \in D ,\end{align*}% % -where $D$ is the domain of values attainable for $c$ and represents the +where $D$ is the domain of values attainable for $\boldsymbol{c}$ and represents the constraints. In contrast to the established message-passing decoding algorithms, @@ -214,8 +214,8 @@ decoding is the following:% \text{subject to }\hspace{2mm} &\boldsymbol{c} \in \mathcal{C} .\end{align*}% % -\todo{$\boldsymbol{c}$ or some other variable name? e.g. $\boldsymbol{c}^{*}$. -Especially for the continuous variable in LP decoding} +%\todo{$\boldsymbol{c}$ or some other variable name? e.g. $\boldsymbol{c}^{*}$. +%Especially for the continuous variable in LP decoding} As solving integer linear programs is generally NP-hard, this decoding problem has to be approximated by one with looser constraints. @@ -633,7 +633,7 @@ determined by the channel model. The prior \ac{PDF} $f_{\boldsymbol{X}}\left( \boldsymbol{x} \right)$ is also known as the equal probability assumption is made on $\mathcal{C}\left( \boldsymbol{H} \right)$. -However, because in this case the considered domain is continuous, +However, because the considered domain is continuous, the prior \ac{PDF} cannot be ignored as a constant during the minimization as is often done, and has a rather unwieldy representation:% % @@ -643,7 +643,7 @@ as is often done, and has a rather unwieldy representation:% \sum_{c \in \mathcal{C}\left( \boldsymbol{H} \right) } \delta\left( \boldsymbol{x} - \left( -1 \right) ^{\boldsymbol{c}}\right) \label{eq:prox:prior_pdf} -\end{align}% +.\end{align}% % In order to rewrite the prior \ac{PDF} $f_{\boldsymbol{X}}\left( \boldsymbol{x} \right)$,