5 changed files with 186 additions and 111 deletions
--- a/README.md
+++ b/README.md
@ -14,7 +14,7 @@ $ make

 1. Build docker image
   ```bash
-   $ docker build -f Dockerfile . -t cel-presentation
+   $ docker build -f dockerfiles/Dockerfile.alpine . -t cel-presentation
   ```
 1. Build examples
   ```bash
--- a/presentation.tex
+++ b/presentation.tex
@ -12,7 +12,6 @@

 \usepackage{listings}
 \usepackage{subcaption}
-\usepackage{bbm}


 %
--- a/sections/appendix.tex
+++ b/sections/appendix.tex
@ -51,7 +51,7 @@
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
-                    \citereference{Mac24, 96.33.965}}
+                    \citereference{Mac23, 96.33.965}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -90,7 +90,7 @@
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
-                    \citereference{Mac24, 204.33.484}}
+                    \citereference{Mac23, 204.33.484}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -121,7 +121,7 @@
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
-                    \citereference{Mac24, 408.33.844}}
+                    \citereference{Mac23, 408.33.844}}
            \end{subfigure}%

            \vspace*{-2mm}
@ -190,7 +190,7 @@
                \vspace*{-2mm}
            
                \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
-                    \citereference{Mac24, 204.55.187}}
+                    \citereference{Mac23, 204.55.187}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -221,7 +221,7 @@
                \vspace*{-2mm}
                
                \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
-                    \citereference{Mac24, PEGReg252x504}}
+                    \citereference{Mac23, PEGReg252x504}}
            \end{subfigure}%
        \end{figure}
    \end{minipage}%
@ -237,8 +237,7 @@
                             xmin=10, xmax=50,
                             ymin=0, ymax=0.4,
                             legend columns=1,
-                             legend style={draw=white!15!black},
-                             legend cell align={left}]
+                             legend style={draw=white!15!black}]
                    \addlegendimage{scol2, line width=1pt, solid}
                    \addlegendentry{Proximal}

@ -257,8 +256,8 @@

    \vspace*{-1mm}

-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}


@ -346,7 +345,7 @@ return $\hat{\boldsymbol{c}}$

    \begin{itemize}
        \item Codes: BCH $\left( 31, 11 \right)$; BCH $\left( 31, 26 \right)$;
-            \citereference{Mac24, 96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}
+            \citereference{Mac23, 96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}
        \item Measured performance: $\sim\SI{10000}{}$ frames/s
            on Intel Core i7-7700HQ @ 2.80GHz; $n=204$
        \item Both algorithms are $\mathcal{O}\left( n \right)$ on average
@ -390,8 +389,8 @@ return $\hat{\boldsymbol{c}}$
    \smallskip
    \smallskip

-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}


@ -402,7 +401,7 @@ return $\hat{\boldsymbol{c}}$
    \vspace*{-6mm}

    \begin{itemize}
-        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
        \item Minimum number of iterations independent of SNR
    \end{itemize}

@ -497,8 +496,8 @@ return $\hat{\boldsymbol{c}}$
        \end{subfigure}%
    \end{figure}

-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}


@ -552,7 +551,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
-                    \citereference{Mac24, 96.3.965}}
+                    \citereference{Mac23, 96.3.965}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -590,7 +589,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
-                    \citereference{Mac24, 204.33.484}}
+                    \citereference{Mac23, 204.33.484}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -628,7 +627,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
-                    \citereference{Mac24, 408.33.844}}
+                    \citereference{Mac23, 408.33.844}}
            \end{subfigure}%

            \vspace*{-2mm}
@ -706,7 +705,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
            
                \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
-                    \citereference{Mac24, 204.55.187}}
+                    \citereference{Mac23, 204.55.187}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -744,7 +743,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
                
                \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
-                    \citereference{Mac24, PEGReg252x504}}
+                    \citereference{Mac23, PEGReg252x504}}
            \end{subfigure}%
        \end{figure}
    \end{minipage}%
@ -775,8 +774,8 @@ return $\hat{\boldsymbol{c}}$
    
    \vspace*{-1mm}
    
-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}


@ -787,7 +786,7 @@ return $\hat{\boldsymbol{c}}$
 	\vspace*{-5mm}

 	\begin{itemize}
-		\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
+		\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
 		\item No clear optimum value
 	\end{itemize}

@ -872,8 +871,8 @@ return $\hat{\boldsymbol{c}}$

 	\bigskip

-	\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-		June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+	\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+		Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -919,7 +918,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
-                    \citereference{Mac24, 96.3.965}}
+                    \citereference{Mac23, 96.3.965}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -950,7 +949,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
-                    \citereference{Mac24, 204.33.484}}
+                    \citereference{Mac23, 204.33.484}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -981,7 +980,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
            
                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
-                    \citereference{Mac24, 408.33.844}}
+                    \citereference{Mac23, 408.33.844}}
            \end{subfigure}%

            \vspace*{-2mm}
@ -1045,7 +1044,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
            
                \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
-                    \citereference{Mac24, 204.55.187}}
+                    \citereference{Mac23, 204.55.187}}
            \end{subfigure}%
            \begin{subfigure}[t]{0.33\textwidth}
                \centering
@ -1076,7 +1075,7 @@ return $\hat{\boldsymbol{c}}$
                \vspace*{-2mm}
                
                \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
-                    \citereference{Mac24, PEGReg252x504}}
+                    \citereference{Mac23, PEGReg252x504}}
            \end{subfigure}%
        \end{figure}
    \end{minipage}%
@ -1108,7 +1107,7 @@ return $\hat{\boldsymbol{c}}$
    
    \vspace*{-1mm}
    
-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}

--- a/sections/lp_dec_using_admm.tex
+++ b/sections/lp_dec_using_admm.tex
@ -556,7 +556,7 @@
 				\text{poly}\left( \mathcal{C} \right) & \
 			\end{align*}

-			\caption{Lifted integer constraint}
+			\caption{Motivation}
 		\end{subfigure}%
 		\hfill%
 		\begin{subfigure}[t]{0.3\textwidth}
@ -783,7 +783,10 @@
 	\vspace*{-6mm}

 	\begin{itemize}
-        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
+		\item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
+		      \citereference{Mac23, Margulis2640.1320.3}
+		\item Comparison of simulation with results from Barman et al.
+		      \citereference{$\text{Bar}^+\text{13}$}
 	\end{itemize}

 	\bigskip
@ -802,37 +805,124 @@
 					legend pos=outer north east,
 					legend cell align={left},
 				]
-
-                \addplot[scol1, line width=1pt]
-                    table [x=SNR, y=FER, col sep=comma,
-                           discard if not={mu}{3.0},
-                           discard if gt={SNR}{5.5}]
-                        {res/admm/ber_2d_20433484.csv};
-                \addlegendentry{ADMM}
-                \addplot [KITorange, line width=1pt]
-                    table [x=SNR, y=FER, col sep=comma,
-                           discard if gt={SNR}{5.5}]
-                        {res/generic/bp_20433484.csv};
-
-                \addlegendentry{BP}
-                \addplot[black, line width=1pt]
-                    table [col sep=comma, x=SNR, y=FER,
-                           discard if gt={SNR}{5.5}]
-                        {res/generic/fer_ml_20433484.csv};
-                \addlegendentry{ML \citereference{HEL+19}}
+				\addplot[scol0, line width=1pt]
+				table [col sep=comma, x=SNR, y=FER,]
+					{res/admm/ber_margulis264013203.csv};
+				\addlegendentry{ADMM}
+				\addplot[scol1, line width=1pt]
+				table [col sep=comma, x=SNR, y=FER, discard if gt={SNR}{2.2},]
+					{res/generic/fer_bp_mackay_margulis.csv};
+				\addlegendentry{BP \citereference{$\text{Bar}^+\text{13}$}}
 			\end{axis}
 		\end{tikzpicture}
 	\end{figure}%

-	\bigskip
-	\bigskip
+	\smallskip

 	\addreferences
-	{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-		June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
-    {Hel+19}{Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft,
-        Stefan Ruzika, and Norbert Wehn. \emph{Database of Channel Codes and 
-        ML Simulation Results}. June 2024. URL: \url{www.rptu.de/channel-codes}}
+	{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+		Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+	{$\text{Bar}^+\text{13}$}{Siddharth Barman et al.:
+		\emph{Decomposition Methods for Large Scale LP Decoding}.
+		IEEE Transactions on Information Theory 59.12 (2013), pp. 7870–7886.}
 	\stopreferences
 \end{frame}

+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\begin{frame}[t]
+%    \frametitle{LP Decoding using ADMM: Choice of Penalty\\
+%        Parameters}
+%   
+%    \vspace*{-5mm}
+%
+%    \begin{itemize}
+%        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
+%        \item For lower decoding time, choose low $\mu$ and high $\rho$
+%    \end{itemize}
+%
+%    \bigskip
+%
+%    \begin{figure}[H]
+%        \centering
+%
+%        \begin{subfigure}[c]{0.48\textwidth}
+%            \centering
+%        
+%            \begin{tikzpicture}
+%                \begin{axis}[
+%                    grid=both,
+%                    xlabel={$\mu$}, ylabel={Average \# of iterations},
+%                    width=0.8\textwidth,
+%                    height=0.6\textwidth,
+%                ]
+%                    \addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
+%                        table [col sep=comma, x=mu, y=k_avg,
+%                               discard if not={SNR}{2.0},]
+%                            {res/admm/mu_kavg_20433484.csv};
+%                    \addplot[NavyBlue, line width=1pt, densely dashed, mark=*]
+%                        table [col sep=comma, x=mu, y=k_avg,
+%                            discard if not={SNR}{3.0},]
+%                            {res/admm/mu_kavg_20433484.csv};
+%                    \addplot[RedOrange, line width=1pt, densely dashed, mark=*]
+%                        table [col sep=comma, x=mu, y=k_avg,
+%                               discard if not={SNR}{4.0},]
+%                            {res/admm/mu_kavg_20433484.csv};
+%                \end{axis}
+%            \end{tikzpicture}
+%        \end{subfigure}%
+%        \begin{subfigure}[c]{0.48\textwidth}
+%            \centering
+%        
+%            \begin{tikzpicture}
+%                \begin{axis}[
+%                    grid=both,
+%                    xlabel={$\rho$}, ylabel={Average \# of iterations},
+%                    width=0.8\textwidth,
+%                    height=0.6\textwidth,
+%                ]
+%                    \addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
+%                        table [col sep=comma, x=rho, y=k_avg,
+%                               discard if not={SNR}{2.0},]
+%                            {res/admm/rho_kavg_20433484.csv};
+%                    \addplot[NavyBlue, line width=1pt, densely dashed, mark=*]
+%                        table [col sep=comma, x=rho, y=k_avg,
+%                               discard if not={SNR}{3.0},]
+%                            {res/admm/rho_kavg_20433484.csv};
+%                    \addplot[RedOrange, line width=1pt, densely dashed, mark=*]
+%                        table [col sep=comma, x=rho, y=k_avg,
+%                               discard if not={SNR}{4.0},]
+%                            {res/admm/rho_kavg_20433484.csv};
+%                \end{axis}
+%            \end{tikzpicture}
+%        \end{subfigure}%
+%        
+%        \begin{subfigure}[t]{\textwidth}
+%            \centering
+%
+%            \begin{tikzpicture}
+%                \begin{axis}[hide axis,
+%                             xmin=10, xmax=50,
+%                             ymin=0, ymax=0.4,
+%                             legend columns=3,
+%                             legend style={draw=white!15!black,legend cell align=left}]
+%
+%                    \addlegendimage{ForestGreen, line width=1pt, densely dashed, mark=*}
+%                    \addlegendentry{$E_b / N_0 = \SI{2}{dB}$}
+%                    \addlegendimage{RedOrange, line width=1pt, densely dashed, mark=*}
+%                    \addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
+%                    \addlegendimage{NavyBlue, line width=1pt, densely dashed, mark=*}
+%                    \addlegendentry{$E_b / N_0 = \SI{4}{dB}$}
+%                \end{axis}
+%            \end{tikzpicture}
+%        \end{subfigure}
+%    \end{figure}%
+%    
+%    \smallskip
+%    \smallskip
+%    \smallskip
+%
+%    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+%        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+%\end{frame}
+%
--- a/sections/proximal_decoding.tex
+++ b/sections/proximal_decoding.tex
@ -32,7 +32,7 @@
                        \sum_{\boldsymbol{c} \in \mathcal{C} }
                        \delta\left( \tilde{\boldsymbol{x}} - \left( -1 \right)^{\boldsymbol{c}}
                            \right) 
-                    \approx \frac{1}{Z} \mathrm{e}^{-\gamma h\left( \tilde{\boldsymbol{x}} \right) }
+                    \approx \frac{1}{Z} e^{-\gamma h\left( \tilde{\boldsymbol{x}} \right) }
            \end{align*}
        \item Code constraint polynomial:
            \begin{minipage}[c]{0.56\textwidth}
@ -126,7 +126,7 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$
 for $K$ iterations do
    $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $
    $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
-    $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$
+    $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
    if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do
        return $\boldsymbol{\hat{c}}$
    end if
@ -146,7 +146,7 @@ return $\boldsymbol{\hat{c}}$
    \vspace*{-7mm}

    \begin{itemize} 
-        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
        \item Comparison of simulation with results of Wadayama et al. \citereference{WT22}
    \end{itemize}

@ -156,7 +156,7 @@ return $\boldsymbol{\hat{c}}$
        \begin{tikzpicture}
            \begin{axis}[
                grid=both, grid style={line width=.1pt},
-                xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
+                xlabel={$E_b / N_0$ (dB)}, ylabel={BER},
                ymode=log,
                legend pos=outer north east,
                width=0.45\textwidth,
@ -165,7 +165,6 @@ return $\boldsymbol{\hat{c}}$
                xtick={1, 2, ..., 5},
                xmin=0.9, xmax=5.6,
                legend columns=1,
-                legend cell align={left},
            ]

            \addplot [scol0, line width=1pt]
@ -200,15 +199,11 @@ return $\boldsymbol{\hat{c}}$

    \bigskip

-
-	\addreferences
-    {\text{Mac24}}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}}
-    {\text{WT22}}{Tadashi Wadayama; Satoshi Takabe: \emph{Proximal Decoding for LDPC
+    \addreference{WT22}{Tadashi Wadayama; Satoshi Takabe: \emph{Proximal Decoding for LDPC
        Codes}. IEICE Transactions on Fundamentals of Electronics, Communications and Computer
        Sciences advpub (2022), 2022TAP0002.}
-	\stopreferences
-
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}}
 \end{frame}


@ -436,7 +431,7 @@ return $\boldsymbol{\hat{c}}$

    \begin{itemize}
        \item (3,6) regular LDPC code with $n=204$,\\
-            $k=102$ \citereference{Mac24, 204.33.484}
+            $k=102$ \citereference{Mac23, 204.33.484}
    \end{itemize}
    
    \vspace*{-2mm}
@ -452,7 +447,7 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$
 for $K$ iterations do
    $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $
    $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
-    $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$
+    $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
    if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do
        return $\boldsymbol{\hat{c}}$
    end if
@ -463,8 +458,8 @@ return $\boldsymbol{\hat{c}}$

        \vspace*{-4mm}
        \hspace*{-4mm}
-        \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-            June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+        \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+            Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
    \end{minipage}%
    \begin{minipage}{.6\textwidth}
        \centering
@ -578,7 +573,6 @@ return $\boldsymbol{\hat{c}}$
                    scale only axis,
                    xtick={0, 50, ..., 200},
                    xticklabels={0, 25, ..., 100},
-                    legend cell align={left},
                ]
                    \addplot [scol0, mark=none, line width=1]
                        table [col sep=comma, x=k, y=comb_r_s_1]
@ -603,7 +597,6 @@ return $\boldsymbol{\hat{c}}$
                    scale only axis,
                    xtick={0, 50, ..., 200},
                    xticklabels={0, 25, ..., 100},
-                    legend cell align={left},
                ]
                    \addplot [scol0, mark=none, line width=1]
                        table [col sep=comma, x=k, y=comb_r_s_2]
@ -628,7 +621,6 @@ return $\boldsymbol{\hat{c}}$
                    scale only axis,
                    xtick={0, 50, ..., 200},
                    xticklabels={0, 25, ..., 100},
-                    legend cell align={left},
                ]
                    \addplot [scol0, mark=none, line width=1]
                        table [col sep=comma, x=k, y=comb_r_s_3]
@ -659,7 +651,6 @@ return $\boldsymbol{\hat{c}}$
                    scale only axis,
                    xtick={0, 50, ..., 200},
                    xticklabels={0, 25, ..., 100},
-                    legend cell align={left},
                ]
                    \addplot [scol0, mark=none, line width=1]
                        table [col sep=comma, x=k, y=comb_r_s_0]
@ -693,7 +684,6 @@ return $\boldsymbol{\hat{c}}$
                    scale only axis,
                    xtick={0, 50, ..., 200},
                    xticklabels={0, 25, ..., 100},
-                    legend cell align={left},
                ]
                    \addplot [scol0, mark=none, line width=1]
                        table [col sep=comma, x=k, y=comb_r_s_4]
@ -718,7 +708,6 @@ return $\boldsymbol{\hat{c}}$
                    scale only axis,
                    xtick={0, 50, ..., 200},
                    xticklabels={0, 25, ..., 100},
-                    legend cell align={left},
                ]
                    \addplot [scol0, mark=none, line width=1]
                        table [col sep=comma, x=k, y=comb_r_s_5]
@ -743,7 +732,6 @@ return $\boldsymbol{\hat{c}}$
                    scale only axis,
                    xtick={0, 50, ..., 200},
                    xticklabels={0, 25, ..., 100},
-                    legend cell align={left},
                ]
                    \addplot [scol0, mark=none, line width=1]
                        table [col sep=comma, x=k, y=comb_r_s_6]
@ -857,7 +845,7 @@ return $\boldsymbol{\hat{c}}$

    \begin{itemize}
        \item Single decoding using a (3,6) regular LDPC code with $n=204, k=102$
-            \citereference{Mac24, 204.33.484}
+            \citereference{Mac23, 204.33.484}
        \item For larger $n$, the gradient itself starts to oscillate
        \item Amplitude of oscillation highly correlated to probability of bit error
    \end{itemize}
@ -879,7 +867,6 @@ return $\boldsymbol{\hat{c}}$
                    scale only axis,
                    xtick={0, 100, ..., 400},
                    xticklabels={0, 50, ..., 200},
-                    legend cell align={left},
                ]
                    \addplot [scol0, mark=none, line width=1]
                        table [col sep=comma, x=k, y=comb_r_s_0]
@ -919,8 +906,8 @@ return $\boldsymbol{\hat{c}}$

    \bigskip
        
-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}


@ -1060,7 +1047,7 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$
 for $K$ iterations do
    $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $
    $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
-    $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$
+    $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
    if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do
        return $\boldsymbol{\hat{c}}$
    end if
@ -1083,13 +1070,13 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$
 for $K$ iterations do
    $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $
    $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
-    $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$
+    $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
    if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$
        return $\boldsymbol{\hat{c}}$
    end if
 end for
 $\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits}}$
-$\textcolor{KITblue}{L' := \left\{ \text{Variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with }N\text{ bits modified} \right\}}$
+$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with }N\text{ bits modified}}$
 $\textcolor{KITblue}{\text{Compute }\boldsymbol{y}^\text{T}\boldsymbol{ \hat{c}}_l \text{ for all codewords } \boldsymbol{\hat{c}}_l}$
 $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }\boldsymbol{y}^\text{T}\boldsymbol{ \hat{c}}_l \text{, prioritizing valid codewords}}$
            \end{algorithm}
@ -1104,7 +1091,7 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }
    \vspace{-0.6cm}

    \begin{itemize}
-        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
        \item Up to $\sim \SI{1}{dB}$ improvement
    \end{itemize}

@ -1208,8 +1195,8 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }

    \bigskip

-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -1219,7 +1206,7 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }
    \vspace*{-5mm}

    \begin{itemize}
-        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
        \item Chosen parameters: $\gamma = 0.05$
    \end{itemize}

@ -1268,8 +1255,8 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }
        \end{tikzpicture}
    \end{figure}%

-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}


@ -1280,7 +1267,7 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }
    \vspace*{-5mm}

    \begin{itemize}
-        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
        \item Chosen parameters: $N=8, \gamma = 0.05$
    \end{itemize}

@ -1416,26 +1403,26 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }
            \centering

            \begin{tabular}{c c c c c c}
-                $E_b/N_0$ (dB) & \shortstack{List size\\ mean} \\
+                $E_b/N_0$ & \shortstack{List size\\ mean} & \shortstack{List size\\ var.} \\
                \hline
-                1.0 & 1.0 \\
-                1.5 & 1.0 \\
-                2.0 & 1.0 \\
-                2.5 & 1.0 \\
-                3.0 & 1.0 \\
-                3.5 & 1.0 \\
-                4.0 & 1.0 \\
-                4.5 & 1.0 \\
-                5.0 & 1.0 \\
-                5.5 & 1.0
+                1.0 & 1.0            & 0.0 \\
+                1.5 & 1.0            & 0.0 \\
+                2.0 & 1.0            & 0.0 \\
+                2.5 & 1.0            & 0.0 \\
+                3.0 & 1.0            & 0.0 \\
+                3.5 & 1.0            & 0.0 \\
+                4.0 & 1.0            & 0.0 \\
+                4.5 & 1.0            & 0.0 \\
+                5.0 & 1.0            & 0.0 \\
+                5.5 & 1.0            & 0.0
            \end{tabular}

            \caption{List size statistics for successful decodings (no frame error).}
        \end{subfigure}
    \end{figure}

-    \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
-        June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
+    \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
+        Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}