From e3cd531767fa5215df58e9d880c264c39d09fde5 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Mon, 20 Feb 2023 08:14:34 +0100 Subject: [PATCH] Added faces do codeword polytopes --- latex/thesis/chapters/decoding_techniques.tex | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex index 3250fdc..a0b320f 100644 --- a/latex/thesis/chapters/decoding_techniques.tex +++ b/latex/thesis/chapters/decoding_techniques.tex @@ -412,7 +412,7 @@ The resulting formulation of the relaxed optimization problem is the following:% \node[codeword] (c110) at (p110) {}; \node[codeword] (c011) at (p011) {}; - % Polytope Edges + % Polytope Edges & Faces \draw[line width=1pt, color=KITblue] (c000) -- (c101); \draw[line width=1pt, color=KITblue] (c000) -- (c110); @@ -422,6 +422,10 @@ The resulting formulation of the relaxed optimization problem is the following:% \draw[line width=1pt, color=KITblue] (c101) -- (c011); \draw[line width=1pt, color=KITblue] (c011) -- (c110); + + \fill[KITblue, opacity=0.15] (p000) -- (p101) -- (p011) -- cycle; + \fill[KITblue, opacity=0.15] (p000) -- (p110) -- (p101) -- cycle; + \fill[KITblue, opacity=0.15] (p110) -- (p011) -- (p101) -- cycle; % Polytope Annotations @@ -472,13 +476,15 @@ The resulting formulation of the relaxed optimization problem is the following:% \node[codeword] (c100) at (p100) {}; \node[codeword] (c111) at (p111) {}; - % Polytope Edges + % Polytope Edges & Faces \draw[line width=1pt, color=KITblue] (c000) -- (c011); \draw[line width=1pt, color=KITblue] (c000) -- (c100); \draw[line width=1pt, color=KITblue] (c100) -- (c111); \draw[line width=1pt, color=KITblue] (c111) -- (c011); + \fill[KITblue, opacity=0.2] (p000) -- (p100) -- (p111) -- (p011) -- cycle; + % Polytope Annotations \node[color=KITblue, below=0cm of c000] {$\left( 0, 0, 0 \right) $}; @@ -553,12 +559,14 @@ The resulting formulation of the relaxed optimization problem is the following:% \node[codeword] (c011) at (p011) {}; \node[pseudocodeword] (cpseudo) at (2, 1, 1) {}; - % Polytope Edges + % Polytope Edges & Faces \draw[line width=1pt, color=KITblue] (c000) -- (c011); \draw[line width=1pt, color=KITred] (cpseudo) -- (c000); \draw[line width=1pt, color=KITred] (cpseudo) -- (c011); + \fill[KITred, opacity=0.2] (p000) -- (p011) -- (2,1,1) -- cycle; + % Polytope Annotations \node[color=KITblue, below=0cm of c000] {$\left( 0, 0, 0 \right) $};