diff --git a/presentation.tex b/presentation.tex index b4b16fa..a738570 100644 --- a/presentation.tex +++ b/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}% +} + % % diff --git a/res/new_stuff/2d_ber_fer_dfr_20433484_abs.csv b/res/new_stuff/2d_ber_fer_dfr_20433484_abs.csv new file mode 100644 index 0000000..968f864 --- /dev/null +++ b/res/new_stuff/2d_ber_fer_dfr_20433484_abs.csv @@ -0,0 +1,43 @@ 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No newline at end of file diff --git a/res/new_stuff/2d_ber_fer_dfr_20433484_proximal_metadata.json b/res/new_stuff/2d_ber_fer_dfr_20433484_proximal_metadata.json new file mode 100644 index 0000000..4522dff --- /dev/null +++ b/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" +} \ No newline at end of file diff --git a/res/new_stuff/2d_ber_fer_dfr_20433484_variance.csv b/res/new_stuff/2d_ber_fer_dfr_20433484_variance.csv new file mode 100644 index 0000000..3af7d56 --- /dev/null +++ b/res/new_stuff/2d_ber_fer_dfr_20433484_variance.csv @@ -0,0 +1,43 @@ +SNR,gamma,BER,FER,DFR,num_iterations +1.0,0.01,0.09294215198517218,1.0,0.5,201.0 +1.0,0.05,0.09266287160025301,0.9262672811059908,0.48086124401913877,217.0 +1.0,0.15,0.36579358111403765,1.0,0.5,201.0 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+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" +} \ No newline at end of file diff --git a/res/new_stuff/bad_ml_hamming_diff.csv b/res/new_stuff/bad_ml_hamming_diff.csv new file mode 100644 index 0000000..41ff548 --- /dev/null +++ b/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 +2.0,-0.03243618943714469,-0.0012258427020246376 +2.5,-0.02237818757956165,0.002915304993033274 +3.0,-0.01283617032801615,-0.003688769065607722 +3.5,-0.005836966154339851,0.0010568915640299659 +4.0,-0.0021547663311747,-0.0004678620824345031 +4.5,-0.0006497523519598499,4.186123790774973e-05 +5.0,-0.00017733295873135802,-3.056069052344984e-05 +5.5,-4.181360636118232e-05,1.8278991292149972e-05 diff --git a/res/new_stuff/diff.py b/res/new_stuff/diff.py new file mode 100644 index 0000000..b4145a5 --- /dev/null +++ b/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() + diff --git a/res/new_stuff/hamming_hamming_diff.csv b/res/new_stuff/hamming_hamming_diff.csv new file mode 100644 index 0000000..52aa6ba --- /dev/null +++ b/res/new_stuff/hamming_hamming_diff.csv @@ -0,0 +1,11 @@ +SNR,diff_mean_BER,diff_mean_FER +1.0,0.0,0.0 +1.5,0.0,0.0 +2.0,0.0,0.0 +2.5,0.0,0.0 +3.0,0.0,0.0 +3.5,0.0,0.0 +4.0,0.0,0.0 +4.5,0.0,0.0 +5.0,0.0,0.0 +5.5,0.0,0.0 diff --git a/res/new_stuff/improved_bad_ml.csv b/res/new_stuff/improved_bad_ml.csv new file mode 100644 index 0000000..68f818a --- /dev/null +++ b/res/new_stuff/improved_bad_ml.csv @@ -0,0 +1,11 @@ +SNR,max_BER,min_BER,max_FER,min_FER,max_DFR,min_DFR +1.0,0.11344502491529662,0.11189694433342695,0.9567602123037345,0.9471789630564101,0.48894089966196463,0.48642855635334714 +1.5,0.08625805655159474,0.08371329627654384,0.8769509576302362,0.8607833541871258,0.46717714495462787,0.4625567722572366 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+5.5,3.689954353583904e-05,3.516684717990945e-05,0.0009887728249293678,0.000942289213614766,0.000987515128311518,0.0009410696881952495 diff --git a/res/new_stuff/improved_bad_ml_new.csv b/res/new_stuff/improved_bad_ml_new.csv new file mode 100644 index 0000000..ced094d --- /dev/null +++ b/res/new_stuff/improved_bad_ml_new.csv @@ -0,0 +1,11 @@ +SNR,max_BER,min_BER,max_FER,min_FER,max_DFR,min_DFR +1.0,0.11297983305660485,0.11121901640881311,0.9609017934698552,0.9465393950143015,0.490007421108949,0.4862508977975749 +1.5,0.0855076256816604,0.08337991365385758,0.8875618250980833,0.8672820306267567,0.47017557950475963,0.46441239464681205 +2.0,0.059234011509049285,0.055763979548991614,0.725880785050065,0.6986309324389088,0.42045387351685054,0.4112095365351079 +2.5,0.03415061311677852,0.03172036348419042,0.5044528272085026,0.48058741463072935,0.3351973983904628,0.3244521495459487 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index 0000000..a96c108 --- /dev/null +++ b/res/new_stuff/proximal_200_100.csv @@ -0,0 +1,11 @@ +SNR,max_BER,min_BER,max_FER,min_FER,max_DFR,min_DFR +1.0,0.09964286217485964,0.09582249346058545,0.9725381349951536,0.9640258171679859,0.4930304609324223,0.4908361765346084 +1.5,0.07197146769620098,0.0701195446038856,0.910935998999496,0.8943018120379623,0.4766631099657174,0.4720748069760164 +2.0,0.048552855225546025,0.046190088442304746,0.7926168165048454,0.7733503502336271,0.4420703426595684,0.4360863229310879 +2.5,0.027826819835489344,0.026356584247061252,0.6077610035944617,0.5882901255965679,0.37795156352470227,0.37031990007934446 +3.0,0.01459033139580947,0.013645629831897939,0.40042462413711627,0.3796663633373543,0.2857965780846893,0.27508490560705756 +3.5,0.006962374063094883,0.006322742910517653,0.23607377480722788,0.21781910215671454,0.19080755984977135,0.17877501484421018 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+1.5,0.07072797090790005,0.07011846769641904,0.9022846523257748,0.8865009277781524,0.474290973138446,0.46989213082239795 +2.0,0.05028555960166944,0.04855057661676573,0.8058164038133984,0.7851107484253399,0.445712113138357,0.43924245308108667 +2.5,0.02992752353968238,0.02923125191809236,0.6391667287194593,0.6145808714738445,0.3898064086294432,0.3805769346444314 +3.0,0.015045697511919831,0.014134604667699545,0.4149702178851355,0.3890196892239613,0.2932345139535679,0.27975274634948044 +3.5,0.006204957681637722,0.0060148333454333415,0.2040706556443539,0.19864885643511188,0.16947143385158092,0.16571611096140665 +4.0,0.002653481147431547,0.0024636707718166204,0.10546000935145333,0.10133589058924386,0.09539081385839278,0.09200245574034994 +4.5,0.0010546903936343199,0.0009890117824900922,0.04961363099120288,0.0463967424705272,0.04725712431011586,0.04433835148618934 +5.0,0.0003237195277398876,0.0003065538141430916,0.017720484000797586,0.016883233527465895,0.017411101156577163,0.01660282641701705 +5.5,0.00010634282915333439,0.00010000280920538312,0.006078439186276759,0.005772831733766474,0.0060416339578304255,0.005739650019889511 diff --git a/res/new_stuff/proximal_500_100.csv b/res/new_stuff/proximal_500_100.csv new file mode 100644 index 0000000..782a1f8 --- /dev/null +++ b/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 diff --git a/res/new_stuff/proximal_paper.csv b/res/new_stuff/proximal_paper.csv new file mode 100644 index 0000000..43ea011 --- /dev/null +++ b/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 + diff --git a/res/new_stuff/random_hamming_diff.csv b/res/new_stuff/random_hamming_diff.csv new file mode 100644 index 0000000..21a51c5 --- /dev/null +++ b/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 diff --git a/sections/proximal_decoding.tex b/sections/proximal_decoding.tex index 751efd2..ff75eaa 100644 --- a/sections/proximal_decoding.tex +++ b/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} -