Finish version ready for Probevortrag

presentation.tex

@@ -2,11 +2,13 @@
 
 \usepackage{tikz}
 \usepackage{tikz-3dplot}
-\usetikzlibrary{spy, external}
+\usetikzlibrary{spy, external, intersections}
 \tikzexternalize[prefix=build/]
 
 \usepackage{pgfplots}
 \pgfplotsset{compat=newest}
+\usepgfplotslibrary{fillbetween}
+
 
 \usepackage{listings}
 \usepackage{subcaption}
@@ -23,6 +25,15 @@
 \pgfplotsset{colorscheme/cel}
 \input{common.tex}
 
+\newcommand{\lineintext}[1]{%
+    \begin{tikzpicture}
+        \draw[#1] (0,0) -- (1.5em,0);
+
+        % Dummy node taking up the space of a letter to fix spacing
+        \node[outer sep=0, inner sep=0] () at (0.75em,0) {\phantom{a}};
+    \end{tikzpicture}%
+}
+
 
 %
 %

res/new_stuff/2d_ber_fer_dfr_20433484_abs.csv

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res/new_stuff/2d_ber_fer_dfr_20433484_abs_001.csv

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res/new_stuff/2d_ber_fer_dfr_20433484_abs_001_metadata.json

@@ -0,0 +1,9 @@
+{
+    "duration": 396.52261003799504,
+    "name": "2d_BER_FER_DFR_20433484_variance_001",
+    "platform": "Linux-6.4.12-arch1-1-x86_64-with-glibc2.38",
+    "omega": 0.01,
+    "K": 200,
+    "min_var_k": 100,
+    "end_time": "2023-09-07 00:29:56.518459"
+}

res/new_stuff/2d_ber_fer_dfr_20433484_abs_gamma_omega.csv

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res/new_stuff/2d_ber_fer_dfr_20433484_proximal_gamma_omega_metadata.json

@@ -0,0 +1,8 @@
+{
+    "duration": 72.15232186199864,
+    "name": "2d_BER_FER_DFR_20433484_proximal_gamma_omega",
+    "platform": "Linux-6.4.12-arch1-1-x86_64-with-glibc2.38",
+    "SNR": 4,
+    "K": 200,
+    "end_time": "2023-09-07 07:31:00.576800"
+}

res/new_stuff/2d_ber_fer_dfr_20433484_proximal_metadata.json

@@ -0,0 +1,8 @@
+{
+    "duration": 89.19017649098532,
+    "name": "2d_BER_FER_DFR_20433484_proximal",
+    "platform": "Linux-6.4.12-arch1-1-x86_64-with-glibc2.38",
+    "omega": 0.05,
+    "K": 200,
+    "end_time": "2023-09-06 23:51:45.444947"
+}

res/new_stuff/2d_ber_fer_dfr_20433484_variance.csv

@@ -0,0 +1,43 @@
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res/new_stuff/2d_ber_fer_dfr_20433484_variance_metadata.json

@@ -0,0 +1,9 @@
+{
+    "duration": 224.4556210610317,
+    "name": "2d_BER_FER_DFR_20433484_variance",
+    "platform": "Linux-6.4.12-arch1-1-x86_64-with-glibc2.38",
+    "omega": 0.05,
+    "K": 200,
+    "min_var_k": 100,
+    "end_time": "2023-09-06 23:49:53.037586"
+}

res/new_stuff/bad_ml_hamming_diff.csv

@@ -0,0 +1,11 @@
+SNR,diff_mean_BER,diff_mean_FER
+1.0,-0.045780885957614745,0.0013141444230320154
+1.5,-0.04149489718868045,-0.005270498396507506
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+5.5,-4.181360636118232e-05,1.8278991292149972e-05

res/new_stuff/diff.py

@@ -0,0 +1,35 @@
+import numpy as np
+import pandas as pd
+
+
+def main():
+    df_prox = pd.read_csv('2d_ber_fer_dfr_20433484_proximal_gamma_omega.csv')
+    df_abs  = pd.read_csv('2d_ber_fer_dfr_20433484_abs_gamma_omega.csv')
+
+    df_diff = df_abs
+    df_diff["BER"] /= df_prox["BER"]
+    df_diff["FER"] /= df_prox["FER"]
+    df_diff["DFR"] /= df_prox["DFR"]
+
+#    df_prox["BER"] = np.log10(df_prox["BER"])
+#    df_abs["BER"] = np.log10(df_abs["BER"])
+#    df_prox["FER"] = np.log10(df_prox["FER"])
+#    df_abs["FER"] = np.log10(df_abs["FER"])
+#    df_prox["DFR"] = np.log10(df_prox["DFR"])
+#    df_abs["DFR"] = np.log10(df_abs["DFR"])
+#
+#    df_diff = df_prox
+#    df_diff["BER"] -= df_abs["BER"]
+#    df_diff["FER"] -= df_abs["FER"]
+#    df_diff["DFR"] -= df_abs["DFR"]
+
+    print(df_prox)
+    print(df_abs)
+    print(df_diff)
+
+    df_diff.to_csv("2d_ber_fer_dfr_20433484_diff_gamma_omega.csv", index=False)
+
+
+if __name__=="__main__":
+    main()
+

res/new_stuff/hamming_hamming_diff.csv

@@ -0,0 +1,11 @@
+SNR,diff_mean_BER,diff_mean_FER
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+4.0,0.0,0.0
+4.5,0.0,0.0
+5.0,0.0,0.0
+5.5,0.0,0.0

res/new_stuff/improved_bad_ml.csv

@@ -0,0 +1,11 @@
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res/new_stuff/improved_bad_ml_new.csv

@@ -0,0 +1,11 @@
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res/new_stuff/improved_fer_lower_bound.csv

@@ -0,0 +1,11 @@
+SNR,max_BER,min_BER,max_FER,min_FER,max_DFR,min_DFR
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res/new_stuff/improved_hamming.csv

@@ -0,0 +1,11 @@
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res/new_stuff/improved_hamming_ccsds.csv

@@ -0,0 +1,11 @@
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res/new_stuff/improved_ml.csv

@@ -0,0 +1,11 @@
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res/new_stuff/improved_random.csv

@@ -0,0 +1,11 @@
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res/new_stuff/list_size_true.csv

@@ -0,0 +1,12 @@
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res/new_stuff/ml_hamming_diff.csv

@@ -0,0 +1,11 @@
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res/new_stuff/num_of_words_in_list.csv

@@ -0,0 +1,11 @@
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res/new_stuff/p_error.csv

@@ -0,0 +1,205 @@
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res/new_stuff/proximal.csv

@@ -0,0 +1,11 @@
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res/new_stuff/proximal_200_100.csv

@@ -0,0 +1,11 @@
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res/new_stuff/proximal_200_20.csv

@@ -0,0 +1,11 @@
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res/new_stuff/proximal_500_100.csv

@@ -0,0 +1,11 @@
+SNR,max_BER,min_BER,max_FER,min_FER,max_DFR,min_DFR
+1.0,0.0967279975423745,0.09586733453541323,0.9748574687996949,0.9690313142942228,0.4936325575362276,0.49213127689827485
+1.5,0.07029857177155663,0.06845100003931676,0.9068425019711887,0.8947320184627768,0.4755149067735847,0.4721674297698563
+2.0,0.04804317346379875,0.04709183281178785,0.7871778518940883,0.7766502583695983,0.44044162674077847,0.43713105993466506
+2.5,0.027709565869569984,0.026672114196320464,0.6014434275746023,0.581448743866255,0.37548052837165663,0.3676049130875138
+3.0,0.014315514664187241,0.013852931601733023,0.3965280394085692,0.38758218541872336,0.283883364856731,0.2792685153463242
+3.5,0.006817250677759145,0.006534640674454555,0.23190050127653403,0.22492872700760055,0.1882205285585424,0.1835654703516895
+4.0,0.0027212933162363093,0.002615443829498171,0.11377548102488251,0.1099201556685694,0.10214514171188241,0.09902611936683836
+4.5,0.0010395844282843432,0.0009810446164112603,0.04911723276337511,0.04696903886888379,0.04680931803653589,0.04485074656370891
+5.0,0.0003545301542793413,0.000337380722961854,0.018721986763043805,0.01784413958556475,0.018374174383187312,0.017528307350093367
+5.5,0.00011838975673058871,0.00011302167577051726,0.0067781616987241606,0.006470490693462912,0.006732455166041253,0.006428827629331017

res/new_stuff/proximal_paper.csv

@@ -0,0 +1,12 @@
+SNR,gamma_0_15,gamma_0_05,gamma_0_01,BP
+1,0.3669767287,0.0983527875,0.09440942764,0.06443019397
+1.5,0.3669767287,0.07297050292,0.07602178383,0.03398665526
+2,0.3669767287,0.04854153852,0.05563899358,0.01257341759
+2.5,0.3669767287,0.03099619799,0.03962553082,0.003089064275
+3,0.3669767287,0.01635036356,0.02635975022,0.001038700586
+3.5,0.3669767287,0.007422688173,0.01572148666,0.0001272453028
+4,0.3669767287,0.002980400475,0.008639663866,0
+4.5,0.3669767287,0.001044021313,0.004434697304,0
+5,0.3669767287,0.0003969287889,0.002126155473,0
+5.5,0.3908851459,0.00008863357225,0.0007759378638,0
+

res/new_stuff/random_hamming_diff.csv

@@ -0,0 +1,11 @@
+SNR,diff_mean_BER,diff_mean_FER
+1.0,-0.027995098147335543,0.0015606383333586216
+1.5,-0.0270468426402614,-0.006893166814146312
+2.0,-0.0203256709730747,0.004761461684660517
+2.5,-0.014980085981453797,0.0007196634507337096
+3.0,-0.008602231720793902,-0.00046449077454818744
+3.5,-0.0040075484705680495,-0.00037790428674833176
+4.0,-0.0015038151529272498,-0.000375620014995956
+4.5,-0.00044892253506065007,0.00011400650989430022
+5.0,-0.00012193266348805802,-9.57266937044992e-06
+5.5,-2.8287910556313992e-05,2.0586606327299955e-05

sections/proximal_decoding.tex

@@ -754,7 +754,7 @@ return $\boldsymbol{\hat{c}}$
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-    \frametitle{Proximal Decoding: Visualization of Gradients}
+    \frametitle{Proximal Decoding: Oscillation of Estimate}
 
     \vspace*{-5mm}
 
@@ -836,10 +836,10 @@ return $\boldsymbol{\hat{c}}$
 \end{frame}
 
 
-% TODO: Change second figure
+% TODO: Maybe add newly simulated second figure
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-    \frametitle{Proximal Decoding: Improvement}
+    \frametitle{Proximal Decoding: Oscillation of Estimate}
    
     \vspace*{-3mm}
 
@@ -847,7 +847,7 @@ return $\boldsymbol{\hat{c}}$
         \item Single decoding using a (3,6) regular LDPC code with $n=204, k=102$
             \citereference{Mac23, 204.33.484}
         \item For larger $n$, the gradient itself starts to oscillate
-        \item Dynamic range of oscillation highly correlated with probability of bit error
+        \item Amplitude of oscillation highly correlated with probability of bit error
     \end{itemize}
 
     \bigskip
@@ -885,23 +885,20 @@ return $\boldsymbol{\hat{c}}$
         \end{subfigure}%
         \begin{subfigure}[t]{0.5\textwidth}
             \centering
-
             \begin{tikzpicture}
                 \begin{axis}[
-                    point meta min = -1,
-                    point meta max = 1,
                     grid=both,
-                    xlabel={$Var\left( \nabla h\left( \tilde{\boldsymbol{x}} \right)  \right) $},
-                    ylabel={Bit error (bool)},
-                    ytick={0, 1},
+                    ylabel=$P(\hat{c}_{i'} \ne c_{i'})$,
+                    xlabel=$i'$,
+                    ymode=log,
+                    ymin=8e-9,ymax=1e-5,
+                    xmin=0,xmax=200,
                     width=0.85\textwidth,
                     height=0.4\textwidth,
                     scale only axis,
-%                    colormap/viridis,
                 ]
-                    \addplot [KITorange, only marks,]
-                        table [col sep=comma, x=grad_h_vars, y=bit_error]
-                            {res/proximal/extreme_components_20433484_variance.csv};
+                     \addplot+ [scol0, mark=none, line width=1]
+                        table [col sep=comma, y=p_error]{res/new_stuff/p_error.csv};
                 \end{axis}
             \end{tikzpicture}
         \end{subfigure}
@@ -1028,7 +1025,7 @@ return $\boldsymbol{\hat{c}}$
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t, fragile]
-    \frametitle{Proximal Decoding: Improvement}
+    \frametitle{Improved Algorithm}
 
     \vspace*{-0.5cm}
 
@@ -1080,8 +1077,8 @@ for $K$ iterations do
 end for
 $\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits}}$
 $\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with }N\text{ bits modified}}$
-$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \hat{c}}_l, \boldsymbol{\hat{c}} \right) \text{ for all valid codewords } \boldsymbol{\hat{c}}_l}$
-$\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d_H\left( \boldsymbol{ \hat{c}}_l, \boldsymbol{\hat{c}} \right)}$
+$\textcolor{KITblue}{\text{Compute }\boldsymbol{y}^\text{T}\boldsymbol{ \hat{c}}_l \text{ for all codewords } \boldsymbol{\hat{c}}_l}$
+$\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }\boldsymbol{y}^\text{T}\boldsymbol{ \hat{c}}_l \text{, prioritizing valid codewords}}$
             \end{algorithm}
         \end{figure}
     \end{minipage} 
@@ -1089,7 +1086,7 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-    \frametitle{Proximal Decoding: Improvement}
+    \frametitle{Improved Algorithm}
    
     \vspace{-0.6cm}
 
@@ -1202,441 +1199,230 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d
         Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
 \end{frame}
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+    \frametitle{Improved Algorithm: Effect of parameter $N$}
+
+    \vspace*{-5mm}
+
+    \begin{itemize}
+        \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
+        \item Chosen parameters: $\gamma = 0.05$
+    \end{itemize}
+
+    \smallskip
+
+    \begin{figure}[H]
+        \centering
+
+        \begin{tikzpicture}
+
+            \begin{axis}[ymode=log,
+                         xlabel={$E_b / N_0$ (dB)},
+                         ylabel={FER},
+                         legend pos=outer north east,
+                         width=0.45\textwidth,
+                         height=0.3375\textwidth,
+                         legend cell align={left}, grid,
+                         ]
+                    
+            \addplot[scol3, line width=1pt]
+            table [col sep=comma, discard if not={gamma}{0.05},
+                x = SNR, y=FER] {res/new_stuff/2d_ber_fer_dfr_20433484_abs_N_4.csv};
+                \addlegendentry{$N=4$}
+                
+            \addplot[KITorange, line width=1pt]
+            table [col sep=comma, discard if not={gamma}{0.05},
+                x = SNR, y=FER] {res/new_stuff/2d_ber_fer_dfr_20433484_abs_N_6.csv};
+                \addlegendentry{$N=6$}
+                
+            \addplot[scol2, line width=1pt]
+            table [col sep=comma, discard if not={gamma}{0.05},
+                x = SNR, y=FER] {res/new_stuff/2d_ber_fer_dfr_20433484_abs_N_8.csv};
+                \addlegendentry{$N=8$}
+                
+            \addplot[scol1, line width=1pt]
+            table [col sep=comma, discard if not={gamma}{0.05},
+                x = SNR, y=FER] {res/new_stuff/2d_ber_fer_dfr_20433484_abs_N_10.csv};
+                \addlegendentry{$N=10$}
+            
+            \addplot[scol0, line width=1pt]
+            table [col sep=comma, discard if not={gamma}{0.05},
+                x = SNR, y=FER] {res/new_stuff/2d_ber_fer_dfr_20433484_abs.csv};
+                \addlegendentry{$N=12$}
+
+            \end{axis}
+        \end{tikzpicture}
+    \end{figure}%
+
+    \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}
+
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\begin{frame}[t]
-%    \frametitle{Proximal Decoding: Improvement using \\``ML-in-the-List''}
-%   
-%    \vspace{-0.5cm}
-%
-%    \begin{itemize}
-%        \item Comparison of proximal \& improved (correction of $N = \SI{12}{\bit}$)
-%            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]
-%        \centering
-%    
-%        \begin{tikzpicture}
-%            \begin{axis}[
-%                grid=both,
-%                xlabel={$E_b / N_0$}, ylabel={BER},
-%                ymode=log,
-%                legend columns=2,
-%                legend style={at={(0.5,-0.45)},anchor=south},
-%                ymax=1.5, ymin=3e-8,
-%                width=0.33\textwidth,
-%                height=0.28\textwidth,
-%            ]
-%                \addplot[ForestGreen, mark=*, solid]
-%                    table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[Emerald, mark=triangle, densely dashed]
-%                    table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%                
-%                \addplot[NavyBlue, mark=*, solid]
-%                    table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                    table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%
-%                \addplot[RedOrange, mark=*, solid]
-%                    table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[red, mark=triangle, densely dashed]
-%                    table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%            \end{axis}
-%        \end{tikzpicture}
-%        \begin{tikzpicture}
-%            \begin{axis}[
-%                grid=both,
-%                xlabel={$E_b / N_0$}, ylabel={FER},
-%                ymode=log,
-%                legend columns=2,
-%                legend style={at={(0.5,-0.45)},anchor=south},
-%                ymax=1.5, ymin=3e-8,
-%                width=0.33\textwidth,
-%                height=0.28\textwidth,
-%            ]
-%
-%                \addplot[ForestGreen, mark=*, solid]
-%                    table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[Emerald, mark=triangle, densely dashed]
-%                    table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%                
-%                \addplot[NavyBlue, mark=*, solid]
-%                    table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                    table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%
-%                \addplot[RedOrange, mark=*, solid]
-%                    table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[red, mark=triangle, densely dashed]
-%                    table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%            \end{axis}
-%        \end{tikzpicture}
-%        \begin{tikzpicture}
-%            \begin{axis}[
-%                grid=both,
-%                xlabel={$E_b / N_0$}, ylabel={Decoding Failure Rate},
-%                ymode=log,
-%                legend columns=2,
-%                legend style={at={(0.5,-0.45)},anchor=south},
-%                ymax=1.5, ymin=3e-8,
-%                width=0.33\textwidth,
-%                height=0.28\textwidth,
-%            ]
-%                
-%                \addplot[ForestGreen, mark=*, solid]
-%                    table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[Emerald, mark=triangle, densely dashed]
-%                    table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%                
-%                \addplot[NavyBlue, mark=*, solid]
-%                    table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                    table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%
-%                \addplot[RedOrange, mark=*, solid]
-%                    table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
-%                        {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                \addplot[red, mark=triangle, densely dashed]
-%                    table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
-%                        {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%            \end{axis}
-%        \end{tikzpicture}
-%        \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, mark=*, solid}
-%                \addlegendentry{proximal, $\gamma = 0.15$}
-%               
-%                \addlegendimage{NavyBlue, mark=*, solid}
-%                \addlegendentry{proximal, $\gamma = 0.01$}
-%                
-%                \addlegendimage{RedOrange, mark=*, solid}
-%                \addlegendentry{proximal, $\gamma = 0.05$}
-%                
-%                \addlegendimage{Emerald, mark=triangle, densely dashed}
-%                \addlegendentry{improved, $\gamma = 0.15$}
-%                
-%                \addlegendimage{RoyalPurple, mark=triangle, densely dashed}
-%                \addlegendentry{improved, $\gamma = 0.01$}
-%                
-%                \addlegendimage{red, mark=triangle, densely dashed}
-%                \addlegendentry{improved, $\gamma = 0.05$}
-%            \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}
+\begin{frame}[fragile]
+    \frametitle{Improved Algorithm: List Choice Policy}
+
+    \vspace*{-5mm}
+
+    \begin{itemize}
+        \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}
+
+    \vspace*{-5mm}
+
+    \begin{figure}
+        \centering
+        \begin{subfigure}[c]{0.66\textwidth}
+            \centering
+
+            \begin{tikzpicture}
+                \begin{axis}[
+                    grid=both, grid style={line width=.1pt},
+                    xlabel={$E_b / N_0$ (dB)},
+                    ylabel={BER (\lineintext{}), FER (\lineintext{dashed})},
+                    ymode=log,
+                    legend cell align={left},
+                    legend pos={outer north east},
+                    width=0.68\textwidth,
+                    height=0.51\textwidth,
+                    ymax=1.2, ymin=0.8e-4,
+                    xtick={1, 2, ..., 5},
+                    xmin=0.9, xmax=5.6,
+                    legend columns=1,
+                ]
+
+                    %
+                    % Proximal
+                    %
+
+                    \addplot[name path=maxBER1, mark=none, scol0]
+                    table[col sep=comma, x=SNR, y=max_BER]
+                        {res/new_stuff/proximal.csv};
+                    \addplot[name path=minBER1, mark=none, scol0, forget plot]
+                    table[col sep=comma, x=SNR, y=min_BER]
+                        {res/new_stuff/proximal.csv};
+
+                    \addplot[scol0!50, forget plot] fill between[of=minBER1 and maxBER1];
+
+                    \addplot[name path=maxFER1, mark=none, scol0, densely dashed, forget plot]
+                    table[col sep=comma, x=SNR, y=max_FER]
+                        {res/new_stuff/proximal.csv};
+                    \addplot[name path=minFER1, mark=none, scol0, densely dashed, forget plot]
+                    table[col sep=comma, x=SNR, y=min_FER]
+                        {res/new_stuff/proximal.csv};
+
+                    \addplot[scol0!50, forget plot] fill between[of=minFER1 and maxFER1];
+
+                    \addlegendentry{Proximal}
+
+                    %
+                    % Improved Random
+                    %
+
+                    \addplot[name path=maxBER2, mark=none, scol1]
+                    table[col sep=comma, x=SNR, y=max_BER]
+                        {res/new_stuff/improved_random.csv};
+                    \addplot[name path=minBER2, mark=none, scol1, forget plot]
+                    table[col sep=comma, x=SNR, y=min_BER]
+                        {res/new_stuff/improved_random.csv};
+
+                    \addplot[scol1!50, forget plot] fill between[of=minBER2 and maxBER2];
+
+                    \addplot[name path=maxFER2, mark=none, scol1, densely dashed, forget plot]
+                    table[col sep=comma, x=SNR, y=max_FER]
+                        {res/new_stuff/improved_random.csv};
+                    \addplot[name path=minFER2, mark=none, scol1, densely dashed, forget plot]
+                    table[col sep=comma, x=SNR, y=min_FER]
+                        {res/new_stuff/improved_random.csv};
+
+                    %                \addplot[only marks, scol0, forget plot]
+                    %                    table[col sep=comma, x=SNR, y=min_DFR]
+                    %                        {res/new_stuff/improved_random.csv};
+
+                    \addplot[scol1!50, forget plot] fill between[of=minFER2 and maxFER2];
+
+                    \addlegendentry{Improved: Random}
+
+                    %
+                    % Improved ML
+                    %
+
+                    \addplot[name path=maxBER4, mark=none, scol2]
+                    table[col sep=comma, x=SNR, y=max_BER]
+                        {res/new_stuff/improved_ml.csv};
+                    \addplot[name path=minBER4, mark=none, scol2, forget plot]
+                    table[col sep=comma, x=SNR, y=min_BER]
+                        {res/new_stuff/improved_ml.csv};
+
+                    \addplot[scol2!50, forget plot] fill between[of=minBER4 and maxBER4];
+
+                    \addplot[name path=maxFER4, mark=none, scol2, densely dashed, forget plot]
+                    table[col sep=comma, x=SNR, y=max_FER]
+                        {res/new_stuff/improved_ml.csv};
+                    \addplot[name path=minFER4, mark=none, scol2, densely dashed, forget plot]
+                    table[col sep=comma, x=SNR, y=min_FER]
+                        {res/new_stuff/improved_ml.csv};
+
+                    \addplot[scol2!50, forget plot] fill between[of=minFER4 and maxFER4];
+
+                    \addlegendentry{Improved: ML}
+
+                    %
+                    % Improved Hamming
+                    %
+
+                    \addplot[name path=maxBER3, mark=none, KITorange]
+                    table[col sep=comma, x=SNR, y=max_BER]
+                        {res/new_stuff/improved_hamming.csv};
+                    \addplot[name path=minBER3, mark=none, KITorange, forget plot]
+                    table[col sep=comma, x=SNR, y=min_BER]
+                        {res/new_stuff/improved_hamming.csv};
+
+                    \addplot[KITorange!50, forget plot] fill between[of=minBER3 and maxBER3];
+
+                    \addplot[name path=maxFER3, mark=none, KITorange, densely dashed, forget plot]
+                    table[col sep=comma, x=SNR, y=max_FER]
+                        {res/new_stuff/improved_hamming.csv};
+                    \addplot[name path=minFER3, mark=none, KITorange, densely dashed, forget plot]
+                    table[col sep=comma, x=SNR, y=min_FER]
+                        {res/new_stuff/improved_hamming.csv};
+
+                    \addplot[KITorange!50, forget plot] fill between[of=minFER3 and maxFER3];
+
+                    \addlegendentry{Improved: Hamming}
+                \end{axis}
+            \end{tikzpicture}
+
+            %\caption{Comparison of FER and BER of the improved algorithm for
+            %    different list choice policies.}
+        \end{subfigure}%
+        \begin{subfigure}[c]{0.33\textwidth}
+            \centering
+
+            \begin{tabular}{c c c c c c}
+                $E_b/N_0$ & \shortstack{list size\\ mean} & \shortstack{list size\\ var.} \\
+                \hline
+                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{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}
 
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\begin{frame}[t]
-%    \frametitle{Proximal Decoding: Improvement}
-%   
-%    \begin{minipage}[c]{0.9\textwidth}
-%        \centering
-%        \begin{figure}[H]
-%            \vspace*{-0.6cm}
-%            \hspace*{-0.7cm}
-%            \centering
-%            \begin{subfigure}[c]{0.33\textwidth}
-%                \centering
-%
-%                \begin{tikzpicture}[scale=0.4]
-%                    \begin{axis}[
-%                        grid=both,
-%                        xlabel={$E_b / N_0$}, ylabel={FER},
-%                        ymode=log,
-%                        legend columns=1,
-%                        legend pos=outer north east,
-%                        %legend columns=2,
-%                        %legend style={at={(0.5,-0.45)},anchor=south},
-%                        ymax=1.5, ymin=8e-5,
-%                    ]
-%
-%                        \addplot[ForestGreen, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/proximal/2d_ber_fer_dfr_963965.csv};
-%                        \addplot[Emerald, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/hybrid/2d_ber_fer_dfr_963965.csv};
-%                        
-%                            \addplot[NavyBlue, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/proximal/2d_ber_fer_dfr_963965.csv};
-%                        \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/hybrid/2d_ber_fer_dfr_963965.csv};
-%
-%                        \addplot[RedOrange, 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[red, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
-%                                {res/hybrid/2d_ber_fer_dfr_963965.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}[c]{0.33\textwidth}
-%                \centering
-%                \begin{tikzpicture}[scale=0.4]
-%                    \begin{axis}[
-%                        grid=both,
-%                        xlabel={$E_b / N_0$}, ylabel={FER},
-%                        ymode=log,
-%                        legend columns=1,
-%                        legend pos=outer north east,
-%                        xmin=0.5, xmax=6, xtick={1, ..., 5},
-%                        ymax=1.5, ymin=8e-5,
-%                    ]
-%
-%                        \addplot[ForestGreen, mark=*, solid,]
-%                            table [x=SNR, y=FER, col sep=comma,
-%                                   discard if not={gamma}{0.15},
-%                                   discard if gt={SNR}{5.5},]
-%                                {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                        \addplot[Emerald, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma,
-%                                   discard if not={gamma}{0.15},
-%                                   discard if gt={SNR}{5.5},]
-%                                {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%                        
-%                            \addplot[NavyBlue, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma,
-%                                   discard if not={gamma}{0.01},
-%                                   discard if gt={SNR}{5.5},]
-%                                {res/proximal/2d_ber_fer_dfr_20433484.csv};
-%                        \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma,
-%                                   discard if not={gamma}{0.01},
-%                                   discard if gt={SNR}{5.5},]
-%                                {res/hybrid/2d_ber_fer_dfr_20433484.csv};
-%
-%                        \addplot[RedOrange, 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[red, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma,
-%                                   discard if not={gamma}{0.05},
-%                                   discard if gt={SNR}{5.5},]
-%                                {res/hybrid/2d_ber_fer_dfr_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}[c]{0.33\textwidth}
-%                \centering
-%                \begin{tikzpicture}[scale=0.4]
-%                    \begin{axis}[
-%                        grid=both,
-%                        xlabel={$E_b / N_0$}, ylabel={FER},
-%                        ymode=log,
-%                        legend columns=1,
-%                        legend pos=outer north east,
-%                        %legend columns=2,
-%                        %legend style={at={(0.5,-0.45)},anchor=south},
-%                        ymax=1.5, ymin=8e-5,
-%                    ]
-%
-%                        \addplot[ForestGreen, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/proximal/2d_ber_fer_dfr_40833844.csv};
-%                        \addplot[Emerald, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/hybrid/2d_ber_fer_dfr_40833844.csv};
-%                        
-%                            \addplot[NavyBlue, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/proximal/2d_ber_fer_dfr_40833844.csv};
-%                        \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/hybrid/2d_ber_fer_dfr_40833844.csv};
-%
-%                        \addplot[RedOrange, 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[red, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
-%                                {res/hybrid/2d_ber_fer_dfr_40833844.csv};
-%                    \end{axis}
-%                \end{tikzpicture}
-%            \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ \cite[\text{408.33.844}]{mackay_enc}}
-%            \end{subfigure}
-%            \hspace*{-0.7cm}
-%            \begin{subfigure}[c]{0.33\textwidth}
-%                \centering
-%                \begin{tikzpicture}[scale=0.4]
-%                    \begin{axis}[
-%                        grid=both,
-%                        xlabel={$E_b / N_0$}, ylabel={FER},
-%                        ymode=log,
-%                        legend columns=1,
-%                        legend pos=outer north east,
-%                        %legend columns=2,
-%                        %legend style={at={(0.5,-0.45)},anchor=south},
-%                        ymax=1.5, ymin=8e-5,
-%                    ]
-%
-%                        \addplot[ForestGreen, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
-%                        \addplot[Emerald, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
-%                        
-%                            \addplot[NavyBlue, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
-%                        \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
-%
-%                        \addplot[RedOrange, 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[red, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
-%                                {res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
-%                    \end{axis}
-%                \end{tikzpicture}
-%                \caption{BCH code with $n=31, k=26$\\[\baselineskip]}
-%            \end{subfigure}%
-%            \begin{subfigure}[c]{0.33\textwidth}
-%                \centering
-%                \begin{tikzpicture}[scale=0.4]
-%                    \begin{axis}[
-%                        grid=both,
-%                        xlabel={$E_b / N_0$}, ylabel={FER},
-%                        ymode=log,
-%                        legend columns=1,
-%                        legend pos=outer north east,
-%                        %legend columns=2,
-%                        %legend style={at={(0.5,-0.45)},anchor=south},
-%                        ymax=1.5, ymin=8e-5,
-%                    ]
-%
-%                        \addplot[ForestGreen, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/proximal/2d_ber_fer_dfr_20455187.csv};
-%                        \addplot[Emerald, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/hybrid/2d_ber_fer_dfr_20455187.csv};
-%                        
-%                            \addplot[NavyBlue, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/proximal/2d_ber_fer_dfr_20455187.csv};
-%                        \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/hybrid/2d_ber_fer_dfr_20455187.csv};
-%
-%                        \addplot[RedOrange, 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[red, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
-%                                {res/hybrid/2d_ber_fer_dfr_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}[c]{0.33\textwidth}
-%                \centering
-%                \begin{tikzpicture}[scale=0.4]
-%                    \begin{axis}[
-%                        grid=both,
-%                        xlabel={$E_b / N_0$}, ylabel={FER},
-%                        ymode=log,
-%                        legend columns=1,
-%                        legend pos=outer north east,
-%                        ymax=1.5, ymin=8e-5,
-%                    ]
-%
-%                        \addplot[ForestGreen, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
-%                        \addplot[Emerald, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
-%                                {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv};
-%                        
-%                            \addplot[NavyBlue, mark=*, solid]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
-%                        \addplot[RoyalPurple, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
-%                                {res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv};
-%
-%                        \addplot[RedOrange, 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[red, mark=triangle, densely dashed]
-%                            table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
-%                                {res/hybrid/2d_ber_fer_dfr_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}
-%            \vspace*{-1.5cm}
-%            \hspace*{-0.7cm}
-%            \centering
-%            \begin{tikzpicture}[scale=0.7]
-%                \begin{axis}[hide axis,
-%                             xmin=10, xmax=50,
-%                             ymin=0, ymax=0.4,
-%                             legend style={draw=white!15!black,legend cell align=left}]
-%                    \addlegendimage{ForestGreen, mark=*, solid}
-%                    \addlegendentry{proximal, $\gamma = 0.15$}
-%                   
-%                    \addlegendimage{Emerald, mark=triangle, densely dashed}
-%                    \addlegendentry{improved, $\gamma = 0.15$}
-%                    
-%                    \addlegendimage{NavyBlue, mark=*, solid}
-%                    \addlegendentry{proximal, $\gamma = 0.01$}
-%                    
-%                    \addlegendimage{RoyalPurple, mark=triangle, densely dashed}
-%                    \addlegendentry{improved, $\gamma = 0.01$}
-%                    
-%                    \addlegendimage{RedOrange, mark=*, solid}
-%                    \addlegendentry{proximal, $\gamma = 0.05$}
-%                    
-%                    \addlegendimage{red, mark=triangle, densely dashed}
-%                    \addlegendentry{improved, $\gamma = 0.05$}
-%                \end{axis}
-%            \end{tikzpicture}
-%            
-%        \end{figure}
-%    \end{minipage}
-%\end{frame}
-