Fininshed first version of admm part and comparison

latex/presentations/final/presentation.tex

@@ -287,7 +287,8 @@
     \input{sections/theoretical_background.tex}
     \input{sections/decoding_algorithms.tex}
     \input{sections/examination_results.tex}
-    \input{sections/forthcoming_examination.tex}
+    %\input{sections/forthcoming_examination.tex}
+    \input{sections/comparison.tex}
     \input{sections/question_slide.tex}
 
     \begin{frame}[allowframebreaks]

latex/presentations/final/res/admm/avg_error_20433484.csv

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latex/presentations/final/res/admm/avg_error_20433484_metadata.json

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+{
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+    "name": "avg_error_20433484",
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+    "epsilon_dual": 1e-05,
+    "num_iterations": 100000,
+    "end_time": "2023-04-17 16:32:11.491868"
+}

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latex/presentations/final/res/admm/mu_rho_kavg_20433484_metadata.json

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latex/presentations/final/res/admm/mu_rho_kavg_40833844_metadata.json

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latex/presentations/final/res/admm/mu_rho_kavg_bch_31_26_metadata.json

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latex/presentations/final/res/admm/mu_rho_kavg_pegreg252x504_metadata.json

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latex/presentations/final/res/admm/rho_kavg_20433484.csv

@@ -0,0 +1,56 @@
+SNR,rho,BER,FER,DFR,num_iterations,k_avg
+1.0,0.1,0.04463235294117647,0.759,0.0,1000.0,200.0
+1.0,0.30000000000000004,0.06830392156862745,0.753,0.0,1000.0,188.94
+1.0,0.5000000000000001,0.07210294117647059,0.759,0.0,1000.0,179.549
+1.0,0.7000000000000001,0.07382843137254902,0.763,0.0,1000.0,175.321
+1.0,0.9000000000000001,0.07072058823529412,0.735,0.0,1000.0,171.153
+1.0,1.1000000000000003,0.0709264705882353,0.735,0.0,1000.0,168.135
+1.0,1.3000000000000003,0.0708921568627451,0.73,0.0,1000.0,165.505
+1.0,1.5000000000000004,0.07045098039215686,0.723,0.0,1000.0,162.8
+1.0,1.7000000000000004,0.07087745098039215,0.705,0.0,1000.0,156.641
+1.0,1.9000000000000004,0.07061274509803922,0.698,0.0,1000.0,153.433
+1.0,2.1000000000000005,0.07405882352941176,0.766,0.0,1000.0,161.052
+2.0,0.1,0.012377450980392156,0.332,0.0,1000.0,199.983
+2.0,0.30000000000000004,0.015029411764705883,0.258,0.0,1000.0,146.621
+2.0,0.5000000000000001,0.015848039215686276,0.249,0.0,1000.0,114.805
+2.0,0.7000000000000001,0.016019607843137256,0.243,0.0,1000.0,100.66
+2.0,0.9000000000000001,0.016186274509803922,0.241,0.0,1000.0,92.04
+2.0,1.1000000000000003,0.016009803921568627,0.228,0.0,1000.0,81.757
+2.0,1.3000000000000003,0.016137254901960784,0.228,0.0,1000.0,77.021
+2.0,1.5000000000000004,0.01598529411764706,0.226,0.0,1000.0,72.716
+2.0,1.7000000000000004,0.015911764705882354,0.223,0.0,1000.0,68.504
+2.0,1.9000000000000004,0.016088235294117646,0.211,0.0,1000.0,63.335
+2.0,2.1000000000000005,0.0186078431372549,0.277,0.0,1000.0,72.449
+3.0,0.1,0.0016470588235294118,0.059,0.0,1000.0,199.363
+3.0,0.30000000000000004,0.0013970588235294118,0.032,0.0,1000.0,92.689
+3.0,0.5000000000000001,0.0011029411764705882,0.019,0.0,1000.0,56.047
+3.0,0.7000000000000001,0.0009950980392156863,0.018,0.0,1000.0,40.743
+3.0,0.9000000000000001,0.0009509803921568628,0.016,0.0,1000.0,32.032
+3.0,1.1000000000000003,0.0015147058823529412,0.028,0.0,1000.0,28.373
+3.0,1.3000000000000003,0.0014166666666666668,0.027,0.0,1000.0,25.418
+3.0,1.5000000000000004,0.0014019607843137256,0.027,0.0,1000.0,22.899
+3.0,1.7000000000000004,0.0009068627450980392,0.015,0.0,1000.0,18.696
+3.0,1.9000000000000004,0.0009019607843137254,0.015,0.0,1000.0,16.99
+3.0,2.1000000000000005,0.0012990196078431372,0.03,0.0,1000.0,19.976
+4.0,0.1,0.00012745098039215687,0.005,0.0,1000.0,196.387
+4.0,0.30000000000000004,5.392156862745098e-05,0.001,0.0,1000.0,68.299
+4.0,0.5000000000000001,5.392156862745098e-05,0.001,0.0,1000.0,37.665
+4.0,0.7000000000000001,0.0,0.0,0.0,1000.0,25.98
+4.0,0.9000000000000001,5.392156862745098e-05,0.001,0.0,1000.0,19.312
+4.0,1.1000000000000003,0.0,0.0,0.0,1000.0,13.57
+4.0,1.3000000000000003,0.0,0.0,0.0,1000.0,11.838
+4.0,1.5000000000000004,0.0,0.0,0.0,1000.0,10.413
+4.0,1.7000000000000004,0.0,0.0,0.0,1000.0,9.371
+4.0,1.9000000000000004,0.0,0.0,0.0,1000.0,8.69
+4.0,2.1000000000000005,4.411764705882353e-05,0.001,0.0,1000.0,9.315
+5.0,0.1,0.0,0.0,0.0,1000.0,188.087
+5.0,0.30000000000000004,0.0,0.0,0.0,1000.0,58.059
+5.0,0.5000000000000001,0.0,0.0,0.0,1000.0,31.377
+5.0,0.7000000000000001,0.0,0.0,0.0,1000.0,21.032
+5.0,0.9000000000000001,0.0,0.0,0.0,1000.0,14.904
+5.0,1.1000000000000003,0.0,0.0,0.0,1000.0,10.095
+5.0,1.3000000000000003,0.0,0.0,0.0,1000.0,8.869
+5.0,1.5000000000000004,0.0,0.0,0.0,1000.0,7.89
+5.0,1.7000000000000004,0.0,0.0,0.0,1000.0,7.085
+5.0,1.9000000000000004,0.0,0.0,0.0,1000.0,6.48
+5.0,2.1000000000000005,0.0,0.0,0.0,1000.0,6.616

latex/presentations/final/res/admm/rho_kavg_20433484_metadata.json

@@ -0,0 +1,10 @@
+{
+    "duration": 35.0865019390003,
+    "name": "rho_kavg_20433484",
+    "platform": "Linux-6.2.10-arch1-1-x86_64-with-glibc2.37",
+    "K": 200,
+    "epsilon_pri": 1e-05,
+    "epsilon_dual": 1e-05,
+    "max_frame_errors": 100000,
+    "end_time": "2023-04-18 00:26:20.424530"
+}

latex/presentations/final/res/generic/fer_bp_mackay_margulis.csv

@@ -0,0 +1,9 @@
+,SNR,FER
+0,0.9868766404199476,0.7914135529980044
+1,1.288713910761155,0.2149640062907639
+2,1.435695538057743,0.1346395694171198
+3,1.5826771653543306,0.0261816550874433
+4,1.8687664041994752,0.0010584575370171914
+5,2.144356955380577,1.2426236719115031e-05
+6,2.280839895013123,1.618074630152863e-06
+7,2.406824146981627,7.255504808245653e-07

latex/presentations/final/res/generic/fer_ml_20433484.csv

@@ -0,0 +1,10 @@
+SNR,FER,num_errors,num_iterations
+1.00,1.193e-01,100,838
+1.50,4.002e-02,100,2499
+2.00,6.572e-03,100,15216
+2.50,6.019e-04,100,166127
+3.00,7.677e-05,100,1302564
+3.50,1.562e-05,100,6401819
+4.00,4.406e-06,100,22694922
+4.50,1.103e-06,100,90621994
+5.00,2.800e-07,28,100000000

latex/presentations/final/res/generic/fer_ml_9633965.csv

@@ -0,0 +1,12 @@
+SNR,FER,num_errors,num_iterations
+1.00,1.724e-01,100,580
+1.50,6.752e-02,100,1481
+2.00,2.565e-02,100,3898
+2.50,9.100e-03,100,10989
+3.00,2.386e-03,100,41914
+3.50,6.214e-04,100,160939
+4.00,1.797e-04,100,556583
+4.50,4.750e-05,100,2105114
+5.00,1.802e-05,100,5549579
+5.50,4.103e-06,100,24374790
+6.00,9.400e-07,94,100000000

latex/presentations/final/res/generic/fer_ml_bch_31_26.csv

@@ -0,0 +1,9 @@
+SNR,FER,num_errors,num_iterations
+0.00,7.353e-01,100,136
+1.00,4.566e-01,100,219
+2.00,2.695e-01,100,371
+3.00,9.990e-02,100,1001
+4.00,3.271e-02,100,3057
+5.00,5.692e-03,100,17568
+6.00,5.506e-04,100,181625
+7.00,4.400e-05,44,1000000

latex/presentations/final/sections/comparison.tex

@@ -0,0 +1,458 @@
+\section{Comparison}%
+\label{sec:Comparison}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Comparison of Simulation Results}%
+\label{sub:Comparison of Simulation Results}
+
+\begin{frame}[t]
+    \frametitle{Decoding Performance}
+   
+    \vspace*{-5mm}
+
+    \begin{figure}[H]
+        \centering
+    
+        \begin{tikzpicture}
+            \begin{axis}[
+                grid=both,
+                xlabel={$E_b / N_0 \left( \text{dB} \right) $}, ylabel={FER},
+                ymode=log,
+                ymax=1.5, ymin=5e-5,
+                legend columns = 3,
+                legend style={at={(0.5,-0.5)},anchor=south},
+                width=0.45\textwidth,
+                height=0.3375\textwidth,
+            ]
+        
+                \addplot[RedOrange, line width=1pt, mark=*, solid]
+                    table [x=SNR, y=FER, col sep=comma,
+                           discard if not={gamma}{0.05},
+                           discard if gt={SNR}{5.5}]
+                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
+                \addlegendentry{Proximal decoding}
+                \addplot[NavyBlue, line width=1pt, mark=triangle, densely dashed]
+                    table [x=SNR, y=FER, col sep=comma,
+                           discard if not={mu}{3.0},
+                           discard if gt={SNR}{4.0}]
+                        {res/admm/ber_2d_20433484.csv};
+                \addlegendentry{LP Decoding}
+                \addplot[PineGreen, line width=1pt, mark=triangle, solid]
+                    table [col sep=comma, x=SNR, y=FER,
+                           discard if gt={SNR}{3.0}]
+                        {res/generic/fer_ml_20433484.csv};
+                \addlegendentry{ML}
+            \end{axis}
+        \end{tikzpicture}
+
+        \caption{Comparison of FER of proximal decoding and LP decoding using ADMM%
+            \protect\footnotemark{}}
+    \end{figure}%
+
+    \footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
+        \cite[Code: 204.33.484]{mackay_enc}}
+\end{frame}
+
+\begin{frame}[t]
+    \frametitle{Decoding Performance}
+    
+    \captionsetup[subfigure]{font=footnotesize}
+
+    \hspace*{-0.4cm}
+    \begin{minipage}[c]{0.9\textwidth}
+        \centering
+    
+        \begin{figure}[H]
+            \vspace*{-0.5cm}
+            \centering
+        
+            \begin{subfigure}[t]{0.33\textwidth}
+                \centering
+            
+                \begin{tikzpicture}[scale=0.4]
+                    \begin{axis}[
+                        grid=both,
+                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
+                        ymode=log,
+                        ymax=1.5, ymin=8e-5,
+    %                    width=1.1\textwidth,
+    %                    height=0.825\textwidth,
+                    ]
+
+                        \addplot[RedOrange, line width=1pt, mark=*, solid]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
+                                {res/proximal/2d_ber_fer_dfr_963965.csv};
+                        \addplot[NavyBlue, line width=1pt, mark=triangle, densely dashed]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
+                                %{res/hybrid/2d_ber_fer_dfr_963965.csv};
+                                {res/admm/ber_2d_963965.csv};
+%                        \addplot[PineGreen, line width=1pt, mark=triangle]
+%                            table [col sep=comma, x=SNR, y=FER,]
+%                                {res/generic/fer_ml_9633965.csv};
+                    \end{axis}
+                \end{tikzpicture}
+
+                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
+                    \cite[\text{96.3.965}]{mackay_enc}}
+            \end{subfigure}%
+            \begin{subfigure}[t]{0.33\textwidth}
+                \centering
+            
+                \begin{tikzpicture}[scale=0.4]
+                    \begin{axis}[
+                        grid=both,
+                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
+                        ymode=log,
+                        ymax=1.5, ymin=8e-5,
+    %                    width=1.1\textwidth,
+    %                    height=0.825\textwidth,
+                    ]
+                
+                        \addplot[RedOrange, line width=1pt, mark=*, solid]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
+                                {res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
+                        \addplot[NavyBlue, line width=1pt, mark=triangle, densely dashed]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
+                                {res/admm/ber_2d_bch_31_26.csv};
+    %                    \addplot[PineGreen, line width=1pt, mark=triangle*]
+    %                        table [x=SNR, y=FER, col sep=comma,
+    %                               discard if gt={SNR}{5.5},
+    %                               discard if lt={SNR}{1},
+    %                               ]
+    %                            {res/generic/fer_ml_bch_31_26.csv};
+                    \end{axis}
+                \end{tikzpicture}
+            
+                \caption{BCH code with $n=31, k=26$}
+            \end{subfigure}%
+            \begin{subfigure}[t]{0.33\textwidth}
+                \centering
+            
+                \begin{tikzpicture}[scale=0.4]
+                    \begin{axis}[
+                        grid=both,
+                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
+                        ymode=log,
+                        ymax=1.5, ymin=8e-5,
+    %                    width=1.1\textwidth,
+    %                    height=0.825\textwidth,
+                    ]
+                
+                        \addplot[RedOrange, line width=1pt, mark=*, solid]
+                            table [x=SNR, y=FER, col sep=comma,
+                                   discard if not={gamma}{0.05},
+                                   discard if gt={SNR}{5.5}]
+                                {res/proximal/2d_ber_fer_dfr_20433484.csv};
+                        \addplot[NavyBlue, line width=1pt, mark=triangle, densely dashed]
+                            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};
+    %                    \addplot[PineGreen, line width=1pt, mark=triangle, solid]
+    %                        table [col sep=comma, x=SNR, y=FER,
+    %                               discard if gt={SNR}{5.5}]
+    %                            {res/generic/fer_ml_20433484.csv};
+                    \end{axis}
+                \end{tikzpicture}
+            
+                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
+                    \cite[\text{204.33.484}]{mackay_enc}}
+            \end{subfigure}%
+
+            \begin{subfigure}[t]{0.33\textwidth}
+                \centering
+            
+                \begin{tikzpicture}[scale=0.4]
+                    \begin{axis}[
+                        grid=both,
+                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
+                        ymode=log,
+                        ymax=1.5, ymin=8e-5,
+    %                    width=1.1\textwidth,
+    %                    height=0.825\textwidth,
+                    ]
+                
+                        \addplot[RedOrange, line width=1pt, mark=*, solid]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
+                                {res/proximal/2d_ber_fer_dfr_20455187.csv};
+                        \addplot[NavyBlue, line width=1pt, mark=triangle, densely dashed]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
+                                {res/admm/ber_2d_20455187.csv};
+                    \end{axis}
+                \end{tikzpicture}
+            
+                \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
+                    \cite[\text{204.55.187}]{mackay_enc}}
+            \end{subfigure}%
+            \begin{subfigure}[t]{0.33\textwidth}
+                \centering
+            
+                \begin{tikzpicture}[scale=0.4]
+                    \begin{axis}[
+                        grid=both,
+                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
+                        ymode=log,
+                        ymax=1.5, ymin=8e-5,
+    %                    width=1.1\textwidth,
+    %                    height=0.825\textwidth,
+                    ]
+                
+                        \addplot[RedOrange, line width=1pt, mark=*, solid]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
+                                {res/proximal/2d_ber_fer_dfr_40833844.csv};
+                        \addplot[NavyBlue, line width=1pt, mark=triangle, densely dashed]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
+                                {res/admm/ber_2d_40833844.csv};
+                    \end{axis}
+                \end{tikzpicture}
+            
+                \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
+                    \cite[\text{204.33.484}]{mackay_enc}}
+            \end{subfigure}%
+            \begin{subfigure}[t]{0.33\textwidth}
+                \centering
+            
+                \begin{tikzpicture}[scale=0.4]
+                    \begin{axis}[
+                        grid=both,
+                        xlabel={$E_b / N_0$ (dB)}, ylabel={FER},
+                        ymode=log,
+                        ymax=1.5, ymin=8e-5,
+    %                    width=1.1\textwidth,
+    %                    height=0.825\textwidth,
+                    ]
+                
+                        \addplot[RedOrange, line width=1pt, mark=*, solid]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
+                                {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
+                        \addplot[NavyBlue, line width=1pt, mark=triangle, densely dashed]
+                            table [x=SNR, y=FER, col sep=comma, discard if not={mu}{3.0}]
+                                {res/admm/ber_2d_pegreg252x504.csv};
+                    \end{axis}
+                \end{tikzpicture}
+            
+                \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
+                    \cite[\text{PEGReg252x504}]{mackay_enc}}
+            \end{subfigure}%
+        \end{figure}
+    \end{minipage}%
+    \begin{minipage}[c]{0.1\textwidth}
+        \centering
+    
+        \begin{figure}
+            \centering
+            \vspace*{-1.2cm}
+            \hspace*{-0.5cm}
+            \begin{tikzpicture}[scale=0.7]
+                \begin{axis}[hide axis,
+                             xmin=10, xmax=50,
+                             ymin=0, ymax=0.4,
+                             legend columns=1,
+                             legend style={draw=white!15!black}]
+                    \addlegendimage{RedOrange, line width=1pt, mark=*, solid}
+                    \addlegendentry{Proximal decoding}
+                   
+                    \addlegendimage{NavyBlue, line width=1pt, mark=triangle, densely dashed}
+                    \addlegendentry{LP decoding}
+                    
+%                    \addlegendimage{PineGreen, line width=1pt, mark=triangle*, solid}
+%                    \addlegendentry{ML}
+                \end{axis}
+            \end{tikzpicture}
+        \end{figure}
+    \end{minipage}
+
+\end{frame}
+
+\begin{frame}[t]
+    \frametitle{Time Complexity}
+   
+    \vspace*{-8mm}
+
+    \begin{itemize}
+        \item Both algorithms are $\mathcal{O}\left( n \right)$ on average
+        \item LP decoding implementation significantly faster
+    \end{itemize}
+
+    \begin{figure}[h]
+        \centering
+
+        \begin{tikzpicture}
+            \begin{axis}[grid=both,
+                         xlabel={$n$}, ylabel={Time per frame (s)},
+                         width=0.45\textwidth,
+                         height=0.3375\textwidth,
+                         legend style={at={(0.03,0.96)},anchor=north west},
+                         %legend pos=outer north east,
+                         legend cell align={left},]
+
+                \addplot[RedOrange, only marks, mark=*]
+                    table [col sep=comma, x=n, y=spf]
+                        {res/proximal/fps_vs_n.csv};
+                \addlegendentry{Proximal decoding}
+                \addplot[RoyalPurple, only marks, mark=triangle*]
+                    table [col sep=comma, x=n, y=spf]
+                        {res/admm/fps_vs_n.csv};
+                \addlegendentry{LP decoding}
+            \end{axis}
+        \end{tikzpicture}
+    
+        \vspace*{-2mm}
+
+        \caption{Timing requirements of the proximal decoding and LP decoding imlementations%
+            \protect\footnotemark{}}
+    \end{figure}%
+    
+    \footnotetext{The points shown were calculated by evaluating the metadata
+                  of BER simulation results for the following codes:
+                  BCH $\left( 31, 11 \right)$;
+                  BCH $\left( 31, 26 \right)$;
+                  \cite[\text{96.3.965; 204.33.484;
+                        204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
+              }
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Theoretical Comparison}%
+\label{sub:Theoretical Comparison}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t, fragile]
+    \frametitle{Comparison of Proximal Decoding and\\LP Decoding using ADMM}
+
+    \vspace*{-1cm}
+
+    \begin{figure}[h]
+    \centering
+   
+    \begin{subfigure}[b]{0.47\textwidth}
+        \centering
+   
+        \begin{align*}
+            \text{minimize}\hspace{2mm}   & \textcolor{KITblue}{\underbrace{L\left(
+                    \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right)}_{\text{Likelihood}}}
+                    + \textcolor{KITred}{\underbrace{\gamma h\left( \tilde{\boldsymbol{x}}
+                        \right)} _{\text{Constraints}}} \\
+            \text{subject to}\hspace{2mm} &\tilde{\boldsymbol{x}} \in \mathbb{R}^n
+        \end{align*}
+       
+        \vspace*{-5mm}
+
+        \begin{algorithm}[caption={}, label={},
+            basicstyle=\fontsize{10}{18}\selectfont
+            ]
+Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$
+while stopping critierion unfulfilled do
+    $\textcolor{KITblue}{\boldsymbol{r} \leftarrow \boldsymbol{r}
+        + \omega \nabla L\left( \boldsymbol{y} \mid \boldsymbol{s} \right)} $
+    $\textcolor{KITred}{\boldsymbol{s} \leftarrow
+        \textbf{prox}_{\gamma h}\left( \boldsymbol{r} \right)} $|\Suppressnumber|
+|\Reactivatenumber|
+end while
+return $\boldsymbol{s}$
+        \end{algorithm}
+    \end{subfigure}\hfill%
+    \begin{subfigure}[b]{0.5\textwidth}
+        \centering
+        
+        \begin{align*}
+            \text{minimize}\hspace{5mm} &
+                \textcolor{KITblue}{\underbrace{\boldsymbol{\gamma}^\text{T}
+                    \tilde{\boldsymbol{c}}}_{\text{Likelihood}}}
+                + \textcolor{KITred}{\underbrace{\sum\nolimits_{j\in\mathcal{J}}
+                    g_j\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+                    \right)}_{\text{Constraints}}} \\
+            \text{subject to}\hspace{5mm} &
+                \tilde{\boldsymbol{c}} \in \mathbb{R}^n
+        \end{align*}
+        
+        \vspace*{-5mm}
+    
+        \begin{algorithm}[caption={}, label={},
+            basicstyle=\fontsize{10}{18}\selectfont
+            ]
+Initialize $\tilde{\boldsymbol{c}}, \boldsymbol{z}, \boldsymbol{u}, \boldsymbol{\gamma}, \rho$
+while stopping criterion unfulfilled do
+    $\textcolor{KITblue}{\tilde{\boldsymbol{c}} \leftarrow \argmin_{\tilde{\boldsymbol{c}}}
+        \left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
+        + \frac{\rho}{2}\sum_{j\in\mathcal{J}} \left\Vert
+            \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j
+            + \boldsymbol{u}_j \right\Vert \right)}$
+    $\textcolor{KITred}{\boldsymbol{z}_j \leftarrow \textbf{prox}_{g_j}
+        \left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+        + \boldsymbol{u}_j \right), \hspace{5mm}\forall j\in\mathcal{J}}$
+    $\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j
+        + \tilde{\boldsymbol{c}} - \boldsymbol{z}_j, \hspace{14.5mm}\forall j\in\mathcal{J}$
+end while
+return $\tilde{\boldsymbol{c}}$
+        \end{algorithm}
+    \end{subfigure}%
+\end{figure}%
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t, fragile]
+    \frametitle{Comparison of Proximal Decoding and\\LP Decoding using ADMM}
+   
+    \vspace*{-1cm}
+
+    \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
+return $\boldsymbol{s}$
+            \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
+return $\tilde{\boldsymbol{c}}$
+            \end{algorithm}
+        \end{subfigure}%
+    \end{figure}%
+\end{frame}
+
+\begin{frame}[t]
+    \frametitle{Conclusion}
+   
+\end{frame}

latex/presentations/final/sections/decoding_algorithms.tex

@@ -123,8 +123,8 @@ return $\boldsymbol{\hat{c}}$
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{LP Decoding}%
-\label{sub:LP Decoding}
+\subsection{LP Decoding using ADMM}%
+\label{sub:LP Decoding using ADMM}
 
 \begin{frame}[t]
     \frametitle{LP Decoding \cite{feldman_paper}}
@@ -757,10 +757,6 @@ return $\boldsymbol{\hat{c}}$
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{LP Decoding using ADMM}%
-\label{sub:LP Decoding using ADMM}
-
-
 \begin{frame}[t]
     \frametitle{LP Decoding using ADMM}
 
@@ -838,144 +834,6 @@ return $\boldsymbol{\hat{c}}$
 \end{frame}
 
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t, fragile]
-    \frametitle{Comparison of Proximal Decoding and\\LP Decoding using ADMM}
-
-    \vspace*{-1cm}
-
-    \begin{figure}[h]
-    \centering
-   
-    \begin{subfigure}[b]{0.47\textwidth}
-        \centering
-   
-        \begin{align*}
-            \text{minimize}\hspace{2mm}   & \textcolor{KITblue}{\underbrace{L\left(
-                    \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right)}_{\text{Likelihood}}}
-                    + \textcolor{KITred}{\underbrace{\gamma h\left( \tilde{\boldsymbol{x}}
-                        \right)} _{\text{Constraints}}} \\
-            \text{subject to}\hspace{2mm} &\tilde{\boldsymbol{x}} \in \mathbb{R}^n
-        \end{align*}
-       
-        \vspace*{-5mm}
-
-        \begin{algorithm}[caption={}, label={},
-            basicstyle=\fontsize{10}{18}\selectfont
-            ]
-Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$
-while stopping critierion unfulfilled do
-    $\textcolor{KITblue}{\boldsymbol{r} \leftarrow \boldsymbol{r}
-        + \omega \nabla L\left( \boldsymbol{y} \mid \boldsymbol{s} \right)} $
-    $\textcolor{KITred}{\boldsymbol{s} \leftarrow
-        \textbf{prox}_{\gamma h}\left( \boldsymbol{r} \right)} $|\Suppressnumber|
-|\Reactivatenumber|
-end while
-return $\boldsymbol{s}$
-        \end{algorithm}
-    \end{subfigure}\hfill%
-    \begin{subfigure}[b]{0.5\textwidth}
-        \centering
-        
-        \begin{align*}
-            \text{minimize}\hspace{5mm} &
-                \textcolor{KITblue}{\underbrace{\boldsymbol{\gamma}^\text{T}
-                    \tilde{\boldsymbol{c}}}_{\text{Likelihood}}}
-                + \textcolor{KITred}{\underbrace{\sum\nolimits_{j\in\mathcal{J}}
-                    g_j\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
-                    \right)}_{\text{Constraints}}} \\
-            \text{subject to}\hspace{5mm} &
-                \tilde{\boldsymbol{c}} \in \mathbb{R}^n
-        \end{align*}
-        
-        \vspace*{-5mm}
-    
-        \begin{algorithm}[caption={}, label={},
-            basicstyle=\fontsize{10}{18}\selectfont
-            ]
-Initialize $\tilde{\boldsymbol{c}}, \boldsymbol{z}, \boldsymbol{u}, \boldsymbol{\gamma}, \rho$
-while stopping criterion unfulfilled do
-    $\textcolor{KITblue}{\tilde{\boldsymbol{c}} \leftarrow \argmin_{\tilde{\boldsymbol{c}}}
-        \left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
-        + \frac{\rho}{2}\sum_{j\in\mathcal{J}} \left\Vert
-            \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j
-            + \boldsymbol{u}_j \right\Vert \right)}$
-    $\textcolor{KITred}{\boldsymbol{z}_j \leftarrow \textbf{prox}_{g_j}
-        \left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
-        + \boldsymbol{u}_j \right), \hspace{5mm}\forall j\in\mathcal{J}}$
-    $\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j
-        + \tilde{\boldsymbol{c}} - \boldsymbol{z}_j, \hspace{14.5mm}\forall j\in\mathcal{J}$
-end while
-return $\tilde{\boldsymbol{c}}$
-        \end{algorithm}
-    \end{subfigure}%
-\end{figure}%
-
-\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}

latex/presentations/final/sections/examination_results.tex

@@ -1570,23 +1570,345 @@ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_l\text{ with lowest }d
 
 \end{frame}
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\begin{frame}[t]
+%    \frametitle{Conclusion}
+%   
+%    \begin{itemize}
+%        \item Analysis of proximal decoding for AWGN channels:
+%            \begin{itemize}
+%                \item Error correcting performance (BER, FER, decoding failures)
+%                \item Computational performance ($\mathcal{O}\left( n \right) $ time complexity,
+%                                                 fast implementation possible)
+%                \item Number of iterations independent of SNR
+%            \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}
+%    \end{itemize}
+%\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{LP Decoding using ADMM}%
+\label{sub:LP Decoding using ADMM}
+
+\begin{frame}[t]
+    \frametitle{LP Decoding using ADMM}
+
+    \begin{figure}[H]
+        \centering
+
+        \begin{tikzpicture}
+            \begin{axis}[
+                grid=both,
+                xlabel={$E_b / N_0 \left( \text{dB} \right) $}, ylabel={FER},
+                ymode=log,
+                width=0.45\textwidth,
+                height=0.325\textwidth,
+                %legend style={at={(0.03,0.04)},anchor=south west},
+                legend pos=outer north east,
+            ]
+                \addplot[RedOrange, line width=1pt]
+                    table [col sep=comma, x=SNR, y=FER,
+                           discard if gt={SNR}{2.2},
+                           ]
+                        {res/admm/fer_paper_margulis.csv};
+                \addlegendentry{ADMM (Barman et al.)}
+                \addplot[NavyBlue, only marks, mark=o, line width=1pt]
+                    table [col sep=comma, x=SNR, y=FER,]
+                        {res/admm/ber_margulis264013203.csv};
+                \addlegendentry{ADMM (Own results)}
+                \addplot[RoyalPurple, line width=1pt, densely dashed]
+                    table [col sep=comma, x=SNR, y=FER, discard if gt={SNR}{2.2},]
+                        {res/generic/fer_bp_mackay_margulis.csv};
+                \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}; $K=200, \mu = 3.3, \rho=1.9,
+            \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
+    }%
+    %
+
+\end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-    \frametitle{Conclusion}
-   
-    \begin{itemize}
-        \item Analysis of proximal decoding for AWGN channels:
-            \begin{itemize}
-                \item Error correcting performance (BER, FER, decoding failures)
-                \item Computational performance ($\mathcal{O}\left( n \right) $ time complexity,
-                                                 fast implementation possible)
-                \item Number of iterations independent of SNR
-            \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}
-    \end{itemize}
+    \frametitle{LP Decoding using ADMM: Choice of Penalty\\
+        Parameters}
+
+    \begin{figure}[H]
+        \centering
+
+        \begin{subfigure}[c]{0.48\textwidth}
+            \centering
+        
+            \begin{tikzpicture}
+                \begin{axis}[
+                    grid=both,
+                    xlabel={$\mu$}, ylabel={FER},
+                    ymode=log,
+                    width=0.9\textwidth,
+                    height=0.675\textwidth,
+                ]
+                    \addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
+                        table [col sep=comma, x=mu, y=FER,
+                               discard if not={SNR}{2.0},]
+                            {res/admm/ber_2d_20433484.csv};
+                    \addplot[RedOrange, line width=1pt, densely dashed, mark=*]
+                        table [col sep=comma, x=mu, y=FER,
+                               discard if not={SNR}{3.0},]
+                            {res/admm/ber_2d_20433484.csv};
+                    \addplot[NavyBlue, line width=1pt, densely dashed, mark=*]
+                        table [col sep=comma, x=mu, y=FER,
+                               discard if not={SNR}{4.0},]
+                            {res/admm/ber_2d_20433484.csv};
+                \end{axis}
+            \end{tikzpicture}
+        \end{subfigure}%
+        \begin{subfigure}[c]{0.48\textwidth}
+            \centering
+        
+            \begin{tikzpicture}
+                \begin{axis}[
+                    grid=both,
+                    xlabel={$\rho$}, ylabel={FER},
+                    ymode=log,
+                    width=0.9\textwidth,
+                    height=0.675\textwidth,
+                ]
+                    \addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
+                        table [col sep=comma, x=rho, y=FER,
+                               discard if not={SNR}{2.0},]
+                            {res/admm/ber_2d_20433484_rho.csv};
+                    \addplot[RedOrange, line width=1pt, densely dashed, mark=*]
+                        table [col sep=comma, x=rho, y=FER,
+                               discard if not={SNR}{3.0},]
+                            {res/admm/ber_2d_20433484_rho.csv};
+                    \addplot[NavyBlue, line width=1pt, densely dashed, mark=*]
+                        table [col sep=comma, x=rho, y=FER,
+                               discard if not={SNR}{4.0},]
+                            {res/admm/ber_2d_20433484_rho.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}
+
+        \caption{Relation between $\mu$ and $\rho$ and decoding performance%
+            \protect\footnotemark{}}
+    \end{figure}%
+
+    \footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
+        \cite[Code: 204.33.484]{mackay_enc}}
+
 \end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t]
+    \frametitle{LP Decoding using ADMM: Choice of Penalty\\
+        Parameters}
+
+    \begin{figure}[H]
+        \centering
+
+        \begin{subfigure}[c]{0.48\textwidth}
+            \centering
+        
+            \begin{tikzpicture}
+                \begin{axis}[
+                    grid=both,
+                    xlabel={$\mu$}, ylabel={Average \# of iterations},
+                    width=0.9\textwidth,
+                    height=0.675\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[RedOrange, 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[NavyBlue, 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=0.9\textwidth,
+                    height=0.675\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[RedOrange, 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[NavyBlue, 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}
+
+        \caption{Relation between $\mu$ and $\rho$ and speed of convergence%
+            \protect\footnotemark{}}
+    \end{figure}%
+
+    \footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
+        \cite[Code: 204.33.484]{mackay_enc}}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t]
+    \frametitle{LP Decoding using ADMM: Average Error}
+
+    \begin{figure}[H]
+        \centering
+
+        \begin{tikzpicture}
+            \begin{axis}[
+                grid=both,
+                width=0.5\textwidth,
+                height=0.375\textwidth,
+                xlabel={Iteration}, ylabel={Average $\left\Vert \hat{\boldsymbol{c}}
+                    - \boldsymbol{c} \right\Vert$}
+            ]
+                \addplot[ForestGreen, line width=1pt]
+                    table [col sep=comma, x=k, y=err,
+                           discard if not={SNR}{1.0},
+                           discard if gt={k}{100}]
+                        {res/admm/avg_error_20433484.csv};
+                \addlegendentry{$E_b / N_0 = \SI{1}{dB}$}
+
+                \addplot[RedOrange, line width=1pt]
+                    table [col sep=comma, x=k, y=err,
+                           discard if not={SNR}{2.0},
+                           discard if gt={k}{100}]
+                        {res/admm/avg_error_20433484.csv};
+                \addlegendentry{$E_b / N_0 = \SI{2}{dB}$}
+
+                \addplot[NavyBlue, line width=1pt]
+                    table [col sep=comma, x=k, y=err,
+                           discard if not={SNR}{3.0},
+                           discard if gt={k}{100}]
+                        {res/admm/avg_error_20433484.csv};
+                \addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
+
+                \addplot[RoyalPurple, line width=1pt]
+                    table [col sep=comma, x=k, y=err,
+                           discard if not={SNR}{4.0},
+                           discard if gt={k}{100}]
+                        {res/admm/avg_error_20433484.csv};
+                \addlegendentry{$E_b / N_0 = \SI{4}{dB}$}
+            \end{axis}
+        \end{tikzpicture}
+
+        \caption{Average error for $\SI{100000}{}$ decodings\protect\footnotemark{}}
+    \end{figure}%
+
+    \footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
+        \cite[Code: 204.33.484]{mackay_enc}}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t]
+    \frametitle{LP Decoding using ADMM: Time Complexity}
+
+    \begin{figure}[h]
+        \centering
+
+        \begin{tikzpicture}
+            \begin{axis}[grid=both,
+                         xlabel={$n$}, ylabel={Time per frame (s)},
+                         width=0.45\textwidth,
+                         height=0.3375\textwidth,
+                         legend style={at={(0.03,0.96)},anchor=north west},
+                         %legend pos=outer north east,
+                         legend cell align={left},]
+
+%                \addplot[RedOrange, only marks, mark=*]
+%                    table [col sep=comma, x=n, y=spf]
+%                        {res/proximal/fps_vs_n.csv};
+%                \addlegendentry{Proximal decoding}
+                \addplot[RoyalPurple, only marks, mark=triangle*]
+                    table [col sep=comma, x=n, y=spf]
+                        {res/admm/fps_vs_n.csv};
+%                \addlegendentry{LP decoding using ADMM}
+            \end{axis}
+        \end{tikzpicture}
+
+        \caption{Timing requirements of the LP decoding imlementation%
+            \protect\footnotemark{}}
+    \end{figure}%
+
+    \footnotetext{The points shown were calculated by evaluating the metadata
+                  of BER simulation results for the following codes:
+                  BCH $\left( 31, 11 \right)$;
+                  BCH $\left( 31, 26 \right)$;
+                  \cite[\text{96.3.965; 204.33.484;
+                        204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
+              }
+
+\end{frame}
+