Added message passing slide

latex/presentations/final/sections/decoding_algorithms.tex

@@ -837,6 +837,70 @@ return $\boldsymbol{\hat{c}}$
     \end{itemize}
 \end{frame}
 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t, fragile]
+    \frametitle{Comparison of Proximal Decoding and \\LP Decoding using ADMM}
+   
+    \vspace*{-0.75cm}
+
+    \begin{itemize}
+        \item Both algorithms can be understood as message passing algorithms
+    \end{itemize}
+    
+    \vspace*{-0.25cm}
+
+    \begin{figure}[h]
+        \centering
+
+        \begin{subfigure}{0.48\textwidth}
+            \centering
+            
+            \begin{algorithm}[caption={}, label={},]
+Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$
+while stopping critierion unfulfilled do
+    for j in $\mathcal{J}$ do
+        $p_j \leftarrow \prod_{i\in N_c\left( j \right) } r_i $
+        $\textcolor{KITblue}{M_{j\to} \leftarrow p_j^2 - p_j}$|\Suppressnumber|
+|\vspace{0.7mm}\Reactivatenumber|
+    end for
+    for i in $\mathcal{I}$ do
+        $s_i \leftarrow s_i + \gamma \left[ 4\left( s_i^2 - 1 \right)s_i
+            \phantom{\frac{4}{s_i}}\right.$|\Suppressnumber|
+                     |\Reactivatenumber|$\left.+ \frac{4}{s_i}\sum_{j\in N_v\left( i \right) }
+                        M_{j\to} \right] $
+        $r_i \leftarrow r_i + \omega \left( s_i - y_i \right)$
+    end for
+end while
+            \end{algorithm}
+        \end{subfigure}%
+        \hfill
+        \begin{subfigure}{0.48\textwidth}
+            \centering
+            
+            \begin{algorithm}[caption={}, label={},]
+Initialize $\tilde{\boldsymbol{c}}, \boldsymbol{z}, \boldsymbol{u}, \boldsymbol{\gamma}, \rho$
+while stopping criterion unfulfilled do
+    for j in $\mathcal{J}$ do
+        $\boldsymbol{z}_j \leftarrow \Pi_{P_{d_j}}\left(
+            \boldsymbol{T}_j\tilde{\boldsymbol{c}} + \boldsymbol{u}_j\right)$
+        $\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j + \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+            - \boldsymbol{z}_j$
+        $\textcolor{KITblue}{M_{j\to i} \leftarrow \left( z_j \right)_i - \left( u_j \right)_i,
+            \hspace{3mm} \forall i \in N_c\left( j \right)}$
+    end for
+    for i in $\mathcal{I}$ do
+        $\tilde{c}_i \leftarrow \frac{1}{d_i}
+            \left(\sum_{j\in N_v\left( i \right) } M_{j\to i}
+                - \frac{\gamma_i}{\mu} \right)$|\Suppressnumber|
+|\vspace{7mm}\Reactivatenumber|
+    end for
+end while
+            \end{algorithm}
+        \end{subfigure}%
+    \end{figure}%
+\end{frame}
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %\begin{frame}[t]
 %    \frametitle{LP Relaxation}