From 5ca2410a8fe1f9dd3957f96e20b4417b39ecf149 Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Tue, 18 Apr 2023 01:08:18 +0200
Subject: [PATCH] Added conclusion slide and fixed mu rho debacle

---
 .../presentations/final/sections/comparison.tex | 17 +++++++++++++++++
 .../final/sections/decoding_algorithms.tex      | 14 +++++++++-----
 2 files changed, 26 insertions(+), 5 deletions(-)

diff --git a/latex/presentations/final/sections/comparison.tex b/latex/presentations/final/sections/comparison.tex
index 82da42f..59c8fe7 100644
--- a/latex/presentations/final/sections/comparison.tex
+++ b/latex/presentations/final/sections/comparison.tex
@@ -455,4 +455,21 @@ return $\tilde{\boldsymbol{c}}$
 \begin{frame}[t]
     \frametitle{Conclusion}
    
+    \begin{itemize}
+        \item Analysis of the general behavior of the two decoding algorithms
+            \begin{itemize}
+                \item Parameter choice
+                \item Verification of theoretical considerations with simulation results
+            \end{itemize}
+        \item Suggestion for improvement of proximal decoding
+            \begin{itemize}
+                \item Addition of "ML-in-the-List" step
+                \item Up to $\sim \SI{1}{dB}$ gain under certain conditions
+            \end{itemize}
+        \item Comparison of the two decoding algorithms
+            \begin{itemize}
+                \item based on simulation results
+                \item based on their theoretical structure
+            \end{itemize}
+    \end{itemize}
 \end{frame}
diff --git a/latex/presentations/final/sections/decoding_algorithms.tex b/latex/presentations/final/sections/decoding_algorithms.tex
index c9b99f4..6e917a8 100644
--- a/latex/presentations/final/sections/decoding_algorithms.tex
+++ b/latex/presentations/final/sections/decoding_algorithms.tex
@@ -780,19 +780,19 @@ return $\boldsymbol{\hat{c}}$
             \begin{alignat*}{3}
                 \tilde{\boldsymbol{c}} &\leftarrow \argmin_{\tilde{\boldsymbol{c}}}
                     \left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
-                    + \frac{\rho}{2}\sum_{j\in\mathcal{J}} \left\Vert
+                    + \frac{\mu}{2}\sum_{j\in\mathcal{J}} \left\Vert
                         \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j
                         + \boldsymbol{u}_j \right\Vert \right) \\
                 \boldsymbol{z}_j &\leftarrow \argmin_{\boldsymbol{z}_j}
                     \left( g\left( \boldsymbol{z}_j \right)
-                    + \frac{\rho}{2} \left\Vert \boldsymbol{T}_j \tilde{\boldsymbol{c}}
+                    + \frac{\mu}{2} \left\Vert \boldsymbol{T}_j \tilde{\boldsymbol{c}}
                     - \boldsymbol{z}_j + \boldsymbol{u}_j \right\Vert \right),
                     \hspace{5mm} &&\forall j\in\mathcal{J} \\
                 \boldsymbol{u}_j &\leftarrow \boldsymbol{u}_j
                     + \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j,
                     \hspace{5mm} &&\forall j\in\mathcal{J}
 %                    \left( g\left( \boldsymbol{\boldsymbol{z}_j} \right)
-%                    + \frac{\rho}{2} \left\Vert \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+%                    + \frac{\mu}{2} \left\Vert \boldsymbol{T}_j\tilde{\boldsymbol{c}}
 %                    - \boldsymbol{z}_j + \boldsymbol{u}_j\right\Vert \right) 
             \end{alignat*}
     \end{itemize} 
@@ -802,7 +802,9 @@ return $\boldsymbol{\hat{c}}$
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
     \frametitle{LP Decoding using ADMM}
-    
+   
+    \vspace*{-7mm}
+
     \begin{itemize}
         \item Simplified rules%
             \footnote{$\left( \boldsymbol{z}_j \right)_i $ is a slight abuse of notation.
@@ -829,7 +831,9 @@ return $\boldsymbol{\hat{c}}$
             $\Pi_{\mathcal{P}_{d_j}}, \hspace{1mm} j\in\mathcal{J}$. Many
             different approaches exist, e.g., \cite{original_admm},
             \cite{efficient_lp_dec_admm}, \cite{lautern}.
-        \item The approach chosen here is the one described in \cite{lautern}
+        \item The approach chosen here is the one described in \cite{original_admm}
+        \item The convergence properties can be enhanced by performing an
+            \textit{over-relaxation}, introducing the parameter $\rho$
     \end{itemize}
 \end{frame}