Finished corrections

latex/presentations/final/sections/comparison.tex

@@ -15,7 +15,7 @@
 
     \begin{itemize}
         \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
-        \item Minimum number of iterations independant of SNR
+        \item Minimum number of iterations independent of SNR
     \end{itemize}
 
     \bigskip
@@ -137,24 +137,27 @@
         \begin{tikzpicture}
             \begin{axis}[
                 grid=both,
-                xlabel={$n$}, ylabel={time per frame (s)},
+                xlabel={$n$}, ylabel={time per frame (ms)},
                 legend style={at={(0.05,0.6)},anchor=south west},
                 legend cell align={left},
                 width=0.43\textwidth,
                 height=0.32\textwidth,
             ]
                 \addplot[RedOrange, only marks, mark=square*]
-                    table [col sep=comma, x=n, y=spf]
+                    table [col sep=comma, x=n, y=spf,
+                           y expr=\thisrow{spf} * 1000]
                         {res/proximal/fps_vs_n.csv};
                 \addlegendentry{proximal}
 
                 \addplot[Gray, only marks, mark=*]
-                    table [col sep=comma, x=n, y=spf]
+                    table [col sep=comma, x=n, y=spf,
+                           y expr=\thisrow{spf} * 1000]
                         {res/hybrid/fps_vs_n.csv};
-                \addlegendentry{improved ($\SI{12}{\bit}$)}
+                \addlegendentry{improved ($N=12$)}
 
                 \addplot[NavyBlue, only marks, mark=triangle*]
-                    table [col sep=comma, x=n, y=spf]
+                    table [col sep=comma, x=n, y=spf,
+                           y expr=\thisrow{spf} * 1000]
                         {res/admm/fps_vs_n.csv};
                 \addlegendentry{ADMM}
             \end{axis}    
@@ -617,7 +620,7 @@ while stopping critierion unfulfilled do
         \textbf{prox}_{\gamma h}\left( \boldsymbol{r} \right)} $|\Suppressnumber|
 |\Reactivatenumber|
 end while
-return $\boldsymbol{s}$
+return $\hat{\boldsymbol{c}}$
         \end{algorithm}
     \end{subfigure}\hfill%
     \begin{subfigure}[b]{0.5\textwidth}
@@ -652,7 +655,7 @@ while stopping criterion unfulfilled do
     $\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j
         + \tilde{\boldsymbol{c}} - \boldsymbol{z}_j, \hspace{14.5mm}\forall j\in\mathcal{J}$
 end while
-return $\tilde{\boldsymbol{c}}$
+return $\hat{\boldsymbol{c}}$
         \end{algorithm}
     \end{subfigure}%
 \end{figure}%
@@ -663,7 +666,7 @@ return $\tilde{\boldsymbol{c}}$
 \begin{frame}[t, fragile]
     \frametitle{Comparison: Algorithm Structure}
    
-    \vspace*{-1cm}
+    \vspace*{-0.6cm}
 
     \begin{figure}[h]
         \centering
@@ -674,12 +677,12 @@ return $\tilde{\boldsymbol{c}}$
             \begin{algorithm}[caption={}, label={},]
 Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$
 while stopping critierion unfulfilled do
-    for j in $\mathcal{J}$ do
+    for $j$ in $\mathcal{J}$ do
         $p_j \leftarrow \prod_{i\in N_c\left( j \right) } r_i $
         $\textcolor{KITblue}{M_{j\to i} \leftarrow p_j^2 - p_j}$|\Suppressnumber|
 |\vspace{0.7mm}\Reactivatenumber|
     end for
-    for i in $\mathcal{I}$ do
+    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) }
@@ -687,7 +690,7 @@ while stopping critierion unfulfilled do
         $r_i \leftarrow r_i + \omega \left( s_i - y_i \right)$
     end for
 end while
-return $\boldsymbol{s}$
+return $\hat{\boldsymbol{c}}$
             \end{algorithm}
         \end{subfigure}%
         \hfill
@@ -697,7 +700,7 @@ return $\boldsymbol{s}$
             \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
+    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}}
@@ -705,14 +708,14 @@ while stopping criterion unfulfilled do
         $\textcolor{KITblue}{M_{j\to i} \leftarrow \left( z_j \right)_i - \left( u_j \right)_i,
             \hspace{3mm} \forall i \in N_c\left( j \right)}$
     end for
-    for i in $\mathcal{I}$ do
+    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
-return $\tilde{\boldsymbol{c}}$
+return $\hat{\boldsymbol{c}}$
             \end{algorithm}
         \end{subfigure}%
     \end{figure}%

latex/presentations/final/sections/conclusion.tex

@@ -1,5 +1,5 @@
 \section{Conclusion and Outlook}%
-\label{sec:Comparison}
+\label{sec:Conclusion}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -19,8 +19,18 @@
             \end{itemize}
         \item Comparison
             \begin{itemize}
-                \item based on simulation results
+                \item Based on simulation results
-                \item based on their theoretical structure
+                \item Based on their theoretical structure
+            \end{itemize}
+    \end{itemize}
+
+    \bigskip
+
+    \begin{itemize}
+        \item Future work
+            \begin{itemize}
+                \item Usage of adaptive LP decoding to lower runtime or approximate ML performance
+                \item Combination of proximal and LP decoding
             \end{itemize}
     \end{itemize}
 \end{frame}

latex/presentations/final/sections/lp_dec_using_admm.tex

@@ -688,14 +688,14 @@
         \item Iterative algorithm:
             \begin{alignat*}{3}
                 \tilde{\boldsymbol{c}} &\leftarrow \argmin_{\tilde{\boldsymbol{c}}}
-                    \left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
+                    \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
                     + \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{u}_j \right\Vert \\
                 \boldsymbol{z}_j &\leftarrow \argmin_{\boldsymbol{z}_j}
-                    \left( g\left( \boldsymbol{z}_j \right)
+                    g\left( \boldsymbol{z}_j \right)
                     + \frac{\mu}{2} \left\Vert \boldsymbol{T}_j \tilde{\boldsymbol{c}}
-                    - \boldsymbol{z}_j + \boldsymbol{u}_j \right\Vert \right),
+                    - \boldsymbol{z}_j + \boldsymbol{u}_j \right\Vert,
                     \hspace{5mm} &&\forall j\in\mathcal{J} \\
                 \boldsymbol{u}_j &\leftarrow \boldsymbol{u}_j
                     + \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j,
@@ -729,7 +729,7 @@
 %                \boldsymbol{z}_j \right)_i$.\\
 %            The same is true for $\left( \boldsymbol{u}_j \right)_i$}:
 
-            \vspace*{-3mm}
+            \vspace*{-4mm}
 
             \begin{alignat*}{3}
                 \tilde{c}_i &\leftarrow \frac{1}{\left| N_v\left( i \right) \right|} \left( 
@@ -759,7 +759,7 @@
     \end{itemize}
     
     \bigskip
-    \smallskip
+    \bigskip
 
     \addreferences
         {$\text{Bar}^+\text{13}$}{Siddharth Barman et al.:
@@ -890,6 +890,7 @@
                 height=0.325\textwidth,
                 %legend style={at={(0.03,0.04)},anchor=south west},
                 legend pos=outer north east,
+                legend cell align={left},
             ]
                 \addplot[Emerald, line width=1pt, mark=*]
                     table [col sep=comma, x=SNR, y=FER,

latex/presentations/final/sections/proximal_decoding.tex

@@ -226,7 +226,7 @@ return $\boldsymbol{\hat{c}}$
 
     \begin{itemize}
         \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
-        \item Not great benefit in finding the optimal value for $\gamma$
+        \item Observation: not great benefit in finding the optimal value for $\gamma$
     \end{itemize}
 
     \bigskip
@@ -936,7 +936,7 @@ return $\boldsymbol{\hat{c}}$
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-    \frametitle{Proximal Decoder: Oscillation of $\nabla h\left( \tilde{\boldsymbol{x}} \right) $}
+    \frametitle{Proximal Decoding: Improvement}
    
     \vspace*{-3mm}
 
@@ -1175,8 +1175,8 @@ for $K$ iterations do
         return $\boldsymbol{\hat{c}}$
     end if
 end for
-$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$
+$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits}}$
-$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified.}}$
+$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with }N\text{ bits modified}}$
 $\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \hat{c}}_l, \boldsymbol{\hat{c}} \right) \text{ for all valid codewords } \boldsymbol{\hat{c}}_l}$
 $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d_H\left( \boldsymbol{ \hat{c}}_l, \boldsymbol{\hat{c}} \right)}$
             \end{algorithm}