Moved all code names from footnotes to item

latex/presentations/final/presentation.tex

@@ -38,7 +38,7 @@
             doi=false,url=false,isbn=false]{biblatex}
 \addbibresource{presentation.bib}
 
-
+\input{common.tex}
 
 \pgfplotsset{
     /pgfplots/colormap/mako/.style={

latex/presentations/final/sections/comparison.tex

@@ -11,6 +11,10 @@
 \begin{frame}[t]
     \frametitle{Comparison: Convergence Behavior}
 
+    \begin{itemize}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
+    \end{itemize}
+
     \begin{figure}[H]
         \centering
         
@@ -53,9 +57,6 @@
                 \addlegendentry{$E_b / N_0 = \SI{8}{dB}$}
                 \end{axis}
             \end{tikzpicture}
-            
-            \caption{Average error for $\SI{500000}{}$ decodings,
-                $\omega = 0.05, \gamma = 0.05, K=200$\footnotemark}
         \end{subfigure}%
         \begin{subfigure}[t]{0.5\textwidth}
             \centering
@@ -98,24 +99,24 @@
                     \addlegendentry{$E_b / N_0 = \SI{4}{dB}$}
                 \end{axis}
             \end{tikzpicture}
-        
-            \caption{Average error for $\SI{100000}{}$ decodings\protect\footnotemark{}}
         \end{subfigure}%
-        
     \end{figure}
 
-        
+    \begin{itemize}
-    \footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
+        \item Minimum number of iterations independant of SNR
-        \cite[Code: 204.33.484]{mackay_enc}}
+    \end{itemize}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
     \frametitle{Comparison: Time Complexity}
 
+    \vspace*{-5mm}
+
     \begin{itemize}
-        \item Both algorithms are $\mathcal{O}\left( n \right)$ on average
+        \item The points shown are from the following codes: BCH $\left( 31, 11 \right)$;
-        \item LP decoding implementation significantly faster
+            BCH $\left( 31, 26 \right)$; \\
+            \cite[\text{96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
     \end{itemize}
 
     \begin{figure}[H]
@@ -148,16 +149,13 @@
         \end{tikzpicture}
     \end{figure}
 
-    \footnote{The points shown were calculated by evaluating the metadata
+    \begin{itemize}
-                  of BER simulation results for the following codes:
+        \item Both algorithms are $\mathcal{O}\left( n \right)$ on average
-                  BCH $\left( 31, 11 \right)$;
+        \item LP decoding implementation significantly faster
-                  BCH $\left( 31, 26 \right)$;
+    \end{itemize}
-                  \cite[\text{96.3.965; 204.33.484;
-                        204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
-              }
-
 \end{frame}
 
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
     \frametitle{Proximal Decoding: Improvement using \\``ML-in-the-List''}
@@ -165,11 +163,7 @@
     \vspace{-0.5cm}
 
     \begin{itemize}
-        \item Comparison of proximal \& improved (correction of $N = \SI{12}{\bit}$)
+        \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
-            decoding simulation%
-            \footnote{(3,6) regular LDPC code with $n=204, k=102$
-                \cite[Code: 204.33.484]{mackay_enc}}
-            results
     \end{itemize}
 
     \begin{figure}[H]
@@ -253,15 +247,12 @@
                 \addlegendentry{ML}
                 
                 \addlegendimage{RedOrange, mark=triangle, densely dashed, line width=1pt}
-                \addlegendentry{Improved}
+                \addlegendentry{Improved ($N$=12)}
                 
                 \addlegendimage{RoyalPurple, mark=*, line width=1pt}
                 \addlegendentry{BP}
             \end{axis}
         \end{tikzpicture}
-    
-        \caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, N=12$}
-        \label{fig:simulation_results_hybrid}
     \end{figure}
 \end{frame}
 

latex/presentations/final/sections/lp_dec_using_admm.tex

@@ -825,6 +825,13 @@
 \begin{frame}[t]
     \frametitle{LP Decoding using ADMM}
 
+    \begin{itemize}
+        \item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
+            \cite[\text{Margulis2640.1320.3}]{mackay_enc}
+%            ; $K=200, \mu = 3.3, \rho=1.9,
+%                \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
+    \end{itemize}
+
     \begin{figure}[H]
         \centering
 
@@ -850,23 +857,24 @@
                 \addlegendentry{BP (Barman et al.)}
             \end{axis}
         \end{tikzpicture}
+    \end{figure}
 
-        \caption{Comparison of datapoints from Barman et al. with own simulation results%
+    \begin{itemize}
-            \protect\footnotemark{}}
+        \item Comparison of simulation with results from Barman et al. \cite{original_admm} 
-        \label{fig:admm:results}
+    \end{itemize}
-    \end{figure}%
-    %
-    \footnotetext{``Margulis'' LDPC code with $n = 2640$, $k = 1320$
-        \cite[\text{Margulis2640.1320.3}]{mackay_enc}; $K=200, \mu = 3.3, \rho=1.9,
-            \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
-    }%
-    %
 
 \end{frame}
 
 \begin{frame}[t]
     \frametitle{LP Decoding using ADMM}
 
+    \begin{itemize}
+        \item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
+            \cite[\text{Margulis2640.1320.3}]{mackay_enc}
+%            ; $K=200, \mu = 3.3, \rho=1.9,
+%                \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
+    \end{itemize}
+
     \begin{figure}[H]
         \centering
 
@@ -896,18 +904,11 @@
                 \addlegendentry{BP (Barman et al.)}
             \end{axis}
         \end{tikzpicture}
-        
-        \caption{Comparison of datapoints from Barman et al. with own simulation results%
-            \protect\footnotemark{}}
-        \label{fig:admm:results}
     \end{figure}%
-    %
-    \footnotetext{``Margulis'' LDPC code with $n = 2640$, $k = 1320$
-        \cite[\text{Margulis2640.1320.3}]{mackay_enc}; $K=200, \mu = 3.3, \rho=1.9,
-            \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
-    }%
-    %
 
+    \begin{itemize}
+        \item Comparison of simulation with results from Barman et al. \cite{original_admm} 
+    \end{itemize}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -915,6 +916,10 @@
     \frametitle{LP Decoding using ADMM: Choice of Penalty\\
         Parameters}
 
+    \begin{itemize}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
+    \end{itemize}
+
     \begin{figure}[H]
         \centering
 
@@ -990,13 +995,11 @@
                 \end{axis}
             \end{tikzpicture}
         \end{subfigure}
-
-        \caption{Relation between $\mu$ and $\rho$ and decoding performance%
-            \protect\footnotemark{}}
     \end{figure}%
 
-    \footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
+    \begin{itemize}
-        \cite[Code: 204.33.484]{mackay_enc}}
+        \item Similar to $\gamma$ with proximal decoding: no clear optimum
+    \end{itemize}
 
 \end{frame}
 
@@ -1005,6 +1008,10 @@
     \frametitle{LP Decoding using ADMM: Choice of Penalty\\
         Parameters}
     
+    \begin{itemize}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
+    \end{itemize}
+
     \begin{figure}[H]
         \centering
 
@@ -1078,12 +1085,10 @@
                 \end{axis}
             \end{tikzpicture}
         \end{subfigure}
-
-        \caption{Relation between $\mu$ and $\rho$ and speed of convergence%
-            \protect\footnotemark{}}
     \end{figure}%
 
-    \footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
+    \begin{itemize}
-        \cite[Code: 204.33.484]{mackay_enc}}
+        \item For lower decoding time, choose low $\mu$ and high $\rho$
+    \end{itemize}
 \end{frame}
 

latex/presentations/final/sections/proximal_decoding.tex

@@ -129,12 +129,9 @@ return $\boldsymbol{\hat{c}}$
 
 \begin{frame}[t]
     \frametitle{Proximal Decoding: Bit Error Rate and Performance}
-    \vspace*{-0.5cm}
+
     \begin{itemize} 
-        \item Comparison of simulation%
+        \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
-            \footnote{(3,6) regular LDPC code with $n=204, k=102$
-            \cite[\text{204.33.484}]{mackay_enc}}
-            with results of Wadayama et al. \cite{proximal_paper}
     \end{itemize}
 
     \begin{figure}[H]
@@ -190,11 +187,12 @@ return $\boldsymbol{\hat{c}}$
 
             \end{axis}
         \end{tikzpicture}
-        
-        \caption{Simulation results for $\omega = 0.05, K=100$}
-        \label{fig:sim_results_prox}
     \end{figure}
 
+    \begin{itemize}
+        \item Comparison of simulation with results of Wadayama et al. \cite{proximal_paper}
+    \end{itemize}
+
 %    \vspace*{-0.5cm}
 %    \begin{itemize}
 %        \item $\mathcal{O}\left(n  \right) $ time complexity - same as BP;
@@ -211,10 +209,7 @@ return $\boldsymbol{\hat{c}}$
     \frametitle{Proximal Decoding: Choice of $\gamma$}
     
     \begin{itemize}
-        \item Simulation%
+        \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
-            \footnote{(3,6) regular LDPC code with $n=204, k=102$
-            \cite[\text{204.33.484}]{mackay_enc}}
-            results for different values of $\gamma$
     \end{itemize}
 
     \begin{figure}[H]
@@ -282,15 +277,11 @@ return $\boldsymbol{\hat{c}}$
                 \end{axis}
             \end{tikzpicture}
         \end{subfigure}
-
-        \caption{BER for $\omega = 0.05, K=100$}
-        \label{fig:ber_3d}
     \end{figure}
 
     \begin{itemize}
         \item Not great benefit in finding the optimal value for $\gamma$
     \end{itemize}
-    \vspace{3mm}
 \end{frame}
 
 
@@ -514,12 +505,12 @@ return $\boldsymbol{\hat{c}}$
     \frametitle{Proximal Decoding: Frame Error Rate}
 
     \begin{itemize}
-        \item Analysis of simulated%
+        \item (3,6) regular LDPC code with $n=204$,\\
-            \footnote{(3,6) regular LDPC code with $n=204, k=102$
+            $k=102$ \cite[\text{204.33.484}]{mackay_enc}
-            \cite[\text{204.33.484}]{mackay_enc}}
-            BER and FER
     \end{itemize}
     
+    \vspace*{-5mm}
+
     \begin{minipage}{.4\textwidth}
         \centering
 
@@ -538,10 +529,6 @@ for $K$ iterations do
 end for
 return $\boldsymbol{\hat{c}}$
             \end{algorithm}
-
-            \vspace*{-5mm}
-
-            \caption{Proximal decoding algorithm \cite{proximal_paper}}
         \end{figure}
     \end{minipage}%
     \begin{minipage}{.6\textwidth}
@@ -622,9 +609,6 @@ return $\boldsymbol{\hat{c}}$
                 \addlegendentry{$\gamma = 0.05$}
                 \end{axis}
             \end{tikzpicture}
-        
-            \caption{Simulation results for $\omega = 0.05, K=100$}
-            \label{fig:simulation_results_ber_fer_dfr}
         \end{figure}
     \end{minipage} 
 \end{frame}
@@ -634,10 +618,10 @@ return $\boldsymbol{\hat{c}}$
 \begin{frame}[t]
     \frametitle{Proximal Decoding: Oscillation of Estimate}
 
+    \vspace*{-5mm}
+
     \begin{itemize}
-        \item $\nabla L \left( \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right) $
+        \item Single decoding using the BCH$\left( 7,4 \right) $ code; $E_b / N_0 = \SI{5}{dB}$
-            and $\nabla h \left( \tilde{\boldsymbol{x}} \right) $ generally end up
-            in an equilibrium
     \end{itemize}
 
     \begin{figure}[H]
@@ -829,13 +813,13 @@ return $\boldsymbol{\hat{c}}$
                 \end{axis}
             \end{tikzpicture}
         \end{minipage}
-
-        \caption{Internal variables of proximal decoder
-                 as a function of the number of iterations ($n=7$)\footnotemark}
-
-        \footnotetext{A single decoding is shown, using the BCH$\left( 7,4 \right) $ code;
-                      $\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$}
     \end{figure}
+    
+    \begin{itemize}
+        \item $\nabla L \left( \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right) $
+            and $\nabla h \left( \tilde{\boldsymbol{x}} \right) $ generally end up
+            in an equilibrium
+    \end{itemize}
 \end{frame}
 
 
@@ -843,6 +827,8 @@ return $\boldsymbol{\hat{c}}$
 \begin{frame}[t]
     \frametitle{Proximal Decoding: Visualization of Gradients}
 
+    \vspace*{-5mm}
+
     \begin{figure}[H]
         \centering
 
@@ -928,9 +914,9 @@ return $\boldsymbol{\hat{c}}$
     \frametitle{Proximal Decoder: Oscillation of $\nabla h\left( \tilde{\boldsymbol{x}} \right) $}
    
     \begin{itemize}
-        \item For larger $n$, the gradient itself starts to oscillate
+        \item Single decoding using a (3,6) regular LDPC code with $n=204, k=102$
-        \item The dynamic range of the oscillation is highly correlated
+                \cite[\text{204.33.484}]{mackay_enc}
-              with the probability of a bit error
+%                ; $\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$
     \end{itemize}
 
     \begin{figure}
@@ -963,9 +949,6 @@ return $\boldsymbol{\hat{c}}$
                     \addlegendentry{$\left(\nabla h \right)_1$}
                 \end{axis}
             \end{tikzpicture}
-
-            \caption{Internal variables of proximal decoder as a function of the iteration
-                     ($n=204$)\footnotemark}
         \end{subfigure}%
         \begin{subfigure}[t]{0.5\textwidth}
             \centering
@@ -988,15 +971,13 @@ return $\boldsymbol{\hat{c}}$
                             {res/proximal/extreme_components_20433484_variance.csv};
                 \end{axis}
             \end{tikzpicture}
-
-            \caption{Correlation between bit error and dynamic range of oscillation}
         \end{subfigure}
     \end{figure}
     
-
+    \begin{itemize}
-    \footnotetext{A single decoding is shown, using a (3,6) regular LDPC code
+        \item For larger $n$, the gradient itself starts to oscillate
-                  with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc};
+        \item Dynamic range of oscillation highly correlated with probability of bit error
-                  $\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$}
+    \end{itemize}
 \end{frame}
 
 
@@ -1119,7 +1100,7 @@ return $\boldsymbol{\hat{c}}$
     \vspace*{-0.5cm}
 
     \begin{itemize}
-        \item Improvement of proximal decoding by adding an ``ML-in-the-List'' step after
+        \item Improvement of proximal decoding by addition of ``ML-in-the-List'' step after
             iterating
     \end{itemize}
 

latex/presentations/final/sections/theoretical_background.tex

@@ -9,13 +9,11 @@
 \begin{frame}[t]
     \frametitle{Motivation}
     \begin{itemize}
-        \item The general [ML] decoding problem for linear codes and the general problem
+        \item The general ML decoding problem is NP-complete \cite{ml_np_hard_proof}
-            of finding the weights of a linear code are both NP-complete \cite{ml_np_hard_proof}.
         \item The iterative message–passing algorithms preferred in practice do not guarantee
-            optimality and may fail to decode correctly when the graph contains cycles
+            optimality when the graph contains cycles \cite{ldpc_conv}
-            \cite{ldpc_conv}.
+        \item The standard message-passing algorithms are often difficult to
-        \item The standard message-passing algorithms used for decoding LDPC and turbo codes
+            analyze \cite{feldman_thesis}
-            are often difficult to analyze. \cite{feldman_thesis}
 
     \end{itemize}
 \end{frame}