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Added message passing slide

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Andreas Tsouchlos 2023-04-13 02:21:57 +02:00
parent 696e31ed24
commit 922c60fe7f
2 changed files with 138 additions and 14 deletions
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88
latex/presentations/final/presentation.tex
View File

@ -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:
% 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
\captionsetup{labelformat=algocaption,labelsep=colon}
\lstset{
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
% a language as Rubens explains in his comment above.
keywords={,for, while, end, do, nd, or, return, if,}
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)
captionpos=b,
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}{}

64
latex/presentations/final/sections/decoding_algorithms.tex
View File

@ -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}