Added message passing slide

latex/presentations/final/presentation.tex

@@ -180,32 +180,92 @@
 }
 
 
-\DeclareCaptionLabelFormat{algocaption}{Algorithm} % defines a new caption label as Algorithm x.y
 
-\lstnewenvironment{algorithm}[1][] %defines the algorithm listing environment
+%
+% Generic algorithm environment allowing for pseudocode and mathematical expressions
+% Source: https://tex.stackexchange.com/a/218450 (taken from source and modified)
+%
+ 
+% defines algorithm counter for chapter-level
+\newcounter{genericAlgorithmCounter}
+\let\OldSection\section
+\renewcommand{\section}{\setcounter{genericAlgorithmCounter}{1}\OldSection}
+%defines appearance of the algorithm counter
+\renewcommand{\thegenericAlgorithmCounter}{\thechapter .\arabic{genericAlgorithmCounter}}
+% defines a new caption label as Algorithm x.y
+\DeclareCaptionLabelFormat{algocaption}{Algorithm \thegenericAlgorithmCounter} 
+
+\lstnewenvironment{algorithm}[1][] 
 {
-    \captionsetup{labelformat=algocaption,labelsep=colon} % defines the caption setup for:
+    \captionsetup{labelformat=algocaption,labelsep=colon}
-                                                          % it ises label format as the declared
+    \lstset{
-                                                          % caption label above and makes label
-                                                          % and caption text to be separated
-                                                          % by a ':'
-    \lstset{ %this is the stype
         mathescape=true,
-        frame=tB,
+        escapeinside=||,
+        frame=TB,
         numbers=left,
         numberstyle=\tiny,
         basicstyle=\normalfont,
         columns=fullflexible,
         keywordstyle=\color{black}\bfseries,
-        keywords={a, for, end, do, return, if, b} % add the keywords you want, or load
+        keywords={,for, while, end, do, nd, or, return, if,}
-                                      % a language as Rubens explains in his comment above.
         numbers=left,
         xleftmargin=.04\textwidth,
-        #1 % this is to add specific settings to an usage of this
+        captionpos=b,
-           % environment (for instnce, the caption and referable label)
+        belowskip=1.5em,
+        aboveskip=1.5em,
+        #1 % This is to add custom settings
     }
 }
-{}
+{\addtocounter{genericAlgorithmCounter}{1}}
+
+%
+% Allows for pausing and resuming the numbering in an lstlisting environment
+% Taken from https://tex.stackexchange.com/q/215697
+%
+
+\let\origthelstnumber\thelstnumber
+\makeatletter
+\newcommand*\Suppressnumber{%
+  \lst@AddToHook{OnNewLine}{%
+    \let\thelstnumber\relax%
+     \advance\c@lstnumber-\@ne\relax%
+    }%
+}
+\newcommand*\Reactivatenumber{%
+  \lst@AddToHook{OnNewLine}{%
+   \let\thelstnumber\origthelstnumber%
+   \advance\c@lstnumber\@ne\relax}%
+}
+\makeatother
+
+
+
+%\DeclareCaptionLabelFormat{algocaption}{Algorithm} % defines a new caption label as Algorithm x.y
+%
+%\lstnewenvironment{algorithm}[1][] %defines the algorithm listing environment
+%{
+%    \captionsetup{labelformat=algocaption,labelsep=colon} % defines the caption setup for:
+%                                                          % it ises label format as the declared
+%                                                          % caption label above and makes label
+%                                                          % and caption text to be separated
+%                                                          % by a ':'
+%    \lstset{ %this is the stype
+%        mathescape=true,
+%        frame=tB,
+%        numbers=left,
+%        numberstyle=\tiny,
+%        basicstyle=\normalfont,
+%        columns=fullflexible,
+%        keywordstyle=\color{black}\bfseries,
+%        keywords={a, for, end, do, return, if, b} % add the keywords you want, or load
+%                                      % a language as Rubens explains in his comment above.
+%        numbers=left,
+%        xleftmargin=.04\textwidth,
+%        #1 % this is to add specific settings to an usage of this
+%           % environment (for instnce, the caption and referable label)
+%    }
+%}
+%{}
 
 \setbeamertemplate{frametitle continuation}{}
 

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}