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Moved all code names from footnotes to item

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Andreas Tsouchlos 2023-04-18 20:19:18 +02:00
parent b367115824
commit 700401fac3
5 changed files with 94 additions and 119 deletions
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2
latex/presentations/final/presentation.tex
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@ -38,7 +38,7 @@
doi=false,url=false,isbn=false]{biblatex} doi=false,url=false,isbn=false]{biblatex}
\addbibresource{presentation.bib} \addbibresource{presentation.bib}
\input{common.tex}
\pgfplotsset{ \pgfplotsset{
/pgfplots/colormap/mako/.style={ /pgfplots/colormap/mako/.style={

51
latex/presentations/final/sections/comparison.tex
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@ -11,6 +11,10 @@
\begin{frame}[t] \begin{frame}[t]
\frametitle{Comparison: Convergence Behavior} \frametitle{Comparison: Convergence Behavior}
\begin{itemize}
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -53,9 +57,6 @@
\addlegendentry{$E_b / N_0 = \SI{8}{dB}$} \addlegendentry{$E_b / N_0 = \SI{8}{dB}$}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Average error for $\SI{500000}{}$ decodings,
$\omega = 0.05, \gamma = 0.05, K=200$\footnotemark}
\end{subfigure}% \end{subfigure}%
\begin{subfigure}[t]{0.5\textwidth} \begin{subfigure}[t]{0.5\textwidth}
\centering \centering
@ -98,24 +99,24 @@
\addlegendentry{$E_b / N_0 = \SI{4}{dB}$} \addlegendentry{$E_b / N_0 = \SI{4}{dB}$}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Average error for $\SI{100000}{}$ decodings\protect\footnotemark{}}
\end{subfigure}% \end{subfigure}%
\end{figure} \end{figure}
\begin{itemize}
\footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$ \item Minimum number of iterations independant of SNR
\cite[Code: 204.33.484]{mackay_enc}} \end{itemize}
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t] \begin{frame}[t]
\frametitle{Comparison: Time Complexity} \frametitle{Comparison: Time Complexity}
\vspace*{-5mm}
\begin{itemize} \begin{itemize}
\item Both algorithms are $\mathcal{O}\left( n \right)$ on average \item The points shown are from the following codes: BCH $\left( 31, 11 \right)$;
\item LP decoding implementation significantly faster BCH $\left( 31, 26 \right)$; \\
\cite[\text{96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
\end{itemize} \end{itemize}
\begin{figure}[H] \begin{figure}[H]
@ -148,16 +149,13 @@
\end{tikzpicture} \end{tikzpicture}
\end{figure} \end{figure}
\footnote{The points shown were calculated by evaluating the metadata \begin{itemize}
of BER simulation results for the following codes: \item Both algorithms are $\mathcal{O}\left( n \right)$ on average
BCH $\left( 31, 11 \right)$; \item LP decoding implementation significantly faster
BCH $\left( 31, 26 \right)$; \end{itemize}
\cite[\text{96.3.965; 204.33.484;
204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
}
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t] \begin{frame}[t]
\frametitle{Proximal Decoding: Improvement using \\``ML-in-the-List''} \frametitle{Proximal Decoding: Improvement using \\``ML-in-the-List''}
@ -165,11 +163,7 @@
\vspace{-0.5cm} \vspace{-0.5cm}
\begin{itemize} \begin{itemize}
\item Comparison of proximal \& improved (correction of $N = \SI{12}{\bit}$) \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
decoding simulation%
\footnote{(3,6) regular LDPC code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
results
\end{itemize} \end{itemize}
\begin{figure}[H] \begin{figure}[H]
@ -253,15 +247,12 @@
\addlegendentry{ML} \addlegendentry{ML}
\addlegendimage{RedOrange, mark=triangle, densely dashed, line width=1pt} \addlegendimage{RedOrange, mark=triangle, densely dashed, line width=1pt}
\addlegendentry{Improved} \addlegendentry{Improved ($N$=12)}
\addlegendimage{RoyalPurple, mark=*, line width=1pt} \addlegendimage{RoyalPurple, mark=*, line width=1pt}
\addlegendentry{BP} \addlegendentry{BP}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, N=12$}
\label{fig:simulation_results_hybrid}
\end{figure} \end{figure}
\end{frame} \end{frame}

67
latex/presentations/final/sections/lp_dec_using_admm.tex
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@ -825,6 +825,13 @@
\begin{frame}[t] \begin{frame}[t]
\frametitle{LP Decoding using ADMM} \frametitle{LP Decoding using ADMM}
\begin{itemize}
\item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
\cite[\text{Margulis2640.1320.3}]{mackay_enc}
% ; $K=200, \mu = 3.3, \rho=1.9,
% \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
\end{itemize}
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -850,23 +857,24 @@
\addlegendentry{BP (Barman et al.)} \addlegendentry{BP (Barman et al.)}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\end{figure}
\caption{Comparison of datapoints from Barman et al. with own simulation results%
\protect\footnotemark{}} \begin{itemize}
\label{fig:admm:results} \item Comparison of simulation with results from Barman et al. \cite{original_admm}
\end{figure}% \end{itemize}
%
\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} \end{frame}
\begin{frame}[t] \begin{frame}[t]
\frametitle{LP Decoding using ADMM} \frametitle{LP Decoding using ADMM}
\begin{itemize}
\item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
\cite[\text{Margulis2640.1320.3}]{mackay_enc}
% ; $K=200, \mu = 3.3, \rho=1.9,
% \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
\end{itemize}
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -896,18 +904,11 @@
\addlegendentry{BP (Barman et al.)} \addlegendentry{BP (Barman et al.)}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Comparison of datapoints from Barman et al. with own simulation results%
\protect\footnotemark{}}
\label{fig:admm:results}
\end{figure}% \end{figure}%
%
\footnotetext{``Margulis'' LDPC code with $n = 2640$, $k = 1320$
\cite[\text{Margulis2640.1320.3}]{mackay_enc}; $K=200, \mu = 3.3, \rho=1.9,
\epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
}%
%
\begin{itemize}
\item Comparison of simulation with results from Barman et al. \cite{original_admm}
\end{itemize}
\end{frame} \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -915,6 +916,10 @@
\frametitle{LP Decoding using ADMM: Choice of Penalty\\ \frametitle{LP Decoding using ADMM: Choice of Penalty\\
Parameters} Parameters}
\begin{itemize}
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -990,13 +995,11 @@
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\end{subfigure} \end{subfigure}
\caption{Relation between $\mu$ and $\rho$ and decoding performance%
\protect\footnotemark{}}
\end{figure}% \end{figure}%
\footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$ \begin{itemize}
\cite[Code: 204.33.484]{mackay_enc}} \item Similar to $\gamma$ with proximal decoding: no clear optimum
\end{itemize}
\end{frame} \end{frame}
@ -1004,6 +1007,10 @@
\begin{frame}[t] \begin{frame}[t]
\frametitle{LP Decoding using ADMM: Choice of Penalty\\ \frametitle{LP Decoding using ADMM: Choice of Penalty\\
Parameters} Parameters}
\begin{itemize}
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -1078,12 +1085,10 @@
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\end{subfigure} \end{subfigure}
\caption{Relation between $\mu$ and $\rho$ and speed of convergence%
\protect\footnotemark{}}
\end{figure}% \end{figure}%
\footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$ \begin{itemize}
\cite[Code: 204.33.484]{mackay_enc}} \item For lower decoding time, choose low $\mu$ and high $\rho$
\end{itemize}
\end{frame} \end{frame}

83
latex/presentations/final/sections/proximal_decoding.tex
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@ -129,12 +129,9 @@ return $\boldsymbol{\hat{c}}$
\begin{frame}[t] \begin{frame}[t]
\frametitle{Proximal Decoding: Bit Error Rate and Performance} \frametitle{Proximal Decoding: Bit Error Rate and Performance}
\vspace*{-0.5cm}
\begin{itemize} \begin{itemize}
\item Comparison of simulation% \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\footnote{(3,6) regular LDPC code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}}
with results of Wadayama et al. \cite{proximal_paper}
\end{itemize} \end{itemize}
\begin{figure}[H] \begin{figure}[H]
@ -190,11 +187,12 @@ return $\boldsymbol{\hat{c}}$
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Simulation results for $\omega = 0.05, K=100$}
\label{fig:sim_results_prox}
\end{figure} \end{figure}
\begin{itemize}
\item Comparison of simulation with results of Wadayama et al. \cite{proximal_paper}
\end{itemize}
% \vspace*{-0.5cm} % \vspace*{-0.5cm}
% \begin{itemize} % \begin{itemize}
% \item $\mathcal{O}\left(n \right) $ time complexity - same as BP; % \item $\mathcal{O}\left(n \right) $ time complexity - same as BP;
@ -211,10 +209,7 @@ return $\boldsymbol{\hat{c}}$
\frametitle{Proximal Decoding: Choice of $\gamma$} \frametitle{Proximal Decoding: Choice of $\gamma$}
\begin{itemize} \begin{itemize}
\item Simulation% \item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\footnote{(3,6) regular LDPC code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}}
results for different values of $\gamma$
\end{itemize} \end{itemize}
\begin{figure}[H] \begin{figure}[H]
@ -282,15 +277,11 @@ return $\boldsymbol{\hat{c}}$
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\end{subfigure} \end{subfigure}
\caption{BER for $\omega = 0.05, K=100$}
\label{fig:ber_3d}
\end{figure} \end{figure}
\begin{itemize} \begin{itemize}
\item Not great benefit in finding the optimal value for $\gamma$ \item Not great benefit in finding the optimal value for $\gamma$
\end{itemize} \end{itemize}
\vspace{3mm}
\end{frame} \end{frame}
@ -514,11 +505,11 @@ return $\boldsymbol{\hat{c}}$
\frametitle{Proximal Decoding: Frame Error Rate} \frametitle{Proximal Decoding: Frame Error Rate}
\begin{itemize} \begin{itemize}
\item Analysis of simulated% \item (3,6) regular LDPC code with $n=204$,\\
\footnote{(3,6) regular LDPC code with $n=204, k=102$ $k=102$ \cite[\text{204.33.484}]{mackay_enc}
\cite[\text{204.33.484}]{mackay_enc}}
BER and FER
\end{itemize} \end{itemize}
\vspace*{-5mm}
\begin{minipage}{.4\textwidth} \begin{minipage}{.4\textwidth}
\centering \centering
@ -538,10 +529,6 @@ for $K$ iterations do
end for end for
return $\boldsymbol{\hat{c}}$ return $\boldsymbol{\hat{c}}$
\end{algorithm} \end{algorithm}
\vspace*{-5mm}
\caption{Proximal decoding algorithm \cite{proximal_paper}}
\end{figure} \end{figure}
\end{minipage}% \end{minipage}%
\begin{minipage}{.6\textwidth} \begin{minipage}{.6\textwidth}
@ -622,9 +609,6 @@ return $\boldsymbol{\hat{c}}$
\addlegendentry{$\gamma = 0.05$} \addlegendentry{$\gamma = 0.05$}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Simulation results for $\omega = 0.05, K=100$}
\label{fig:simulation_results_ber_fer_dfr}
\end{figure} \end{figure}
\end{minipage} \end{minipage}
\end{frame} \end{frame}
@ -634,10 +618,10 @@ return $\boldsymbol{\hat{c}}$
\begin{frame}[t] \begin{frame}[t]
\frametitle{Proximal Decoding: Oscillation of Estimate} \frametitle{Proximal Decoding: Oscillation of Estimate}
\vspace*{-5mm}
\begin{itemize} \begin{itemize}
\item $\nabla L \left( \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right) $ \item Single decoding using the BCH$\left( 7,4 \right) $ code; $E_b / N_0 = \SI{5}{dB}$
and $\nabla h \left( \tilde{\boldsymbol{x}} \right) $ generally end up
in an equilibrium
\end{itemize} \end{itemize}
\begin{figure}[H] \begin{figure}[H]
@ -829,13 +813,13 @@ return $\boldsymbol{\hat{c}}$
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\end{minipage} \end{minipage}
\caption{Internal variables of proximal decoder
as a function of the number of iterations ($n=7$)\footnotemark}
\footnotetext{A single decoding is shown, using the BCH$\left( 7,4 \right) $ code;
$\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$}
\end{figure} \end{figure}
\begin{itemize}
\item $\nabla L \left( \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right) $
and $\nabla h \left( \tilde{\boldsymbol{x}} \right) $ generally end up
in an equilibrium
\end{itemize}
\end{frame} \end{frame}
@ -843,6 +827,8 @@ return $\boldsymbol{\hat{c}}$
\begin{frame}[t] \begin{frame}[t]
\frametitle{Proximal Decoding: Visualization of Gradients} \frametitle{Proximal Decoding: Visualization of Gradients}
\vspace*{-5mm}
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -928,9 +914,9 @@ return $\boldsymbol{\hat{c}}$
\frametitle{Proximal Decoder: Oscillation of $\nabla h\left( \tilde{\boldsymbol{x}} \right) $} \frametitle{Proximal Decoder: Oscillation of $\nabla h\left( \tilde{\boldsymbol{x}} \right) $}
\begin{itemize} \begin{itemize}
\item For larger $n$, the gradient itself starts to oscillate \item Single decoding using a (3,6) regular LDPC code with $n=204, k=102$
\item The dynamic range of the oscillation is highly correlated \cite[\text{204.33.484}]{mackay_enc}
with the probability of a bit error % ; $\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$
\end{itemize} \end{itemize}
\begin{figure} \begin{figure}
@ -963,9 +949,6 @@ return $\boldsymbol{\hat{c}}$
\addlegendentry{$\left(\nabla h \right)_1$} \addlegendentry{$\left(\nabla h \right)_1$}
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Internal variables of proximal decoder as a function of the iteration
($n=204$)\footnotemark}
\end{subfigure}% \end{subfigure}%
\begin{subfigure}[t]{0.5\textwidth} \begin{subfigure}[t]{0.5\textwidth}
\centering \centering
@ -988,15 +971,13 @@ return $\boldsymbol{\hat{c}}$
{res/proximal/extreme_components_20433484_variance.csv}; {res/proximal/extreme_components_20433484_variance.csv};
\end{axis} \end{axis}
\end{tikzpicture} \end{tikzpicture}
\caption{Correlation between bit error and dynamic range of oscillation}
\end{subfigure} \end{subfigure}
\end{figure} \end{figure}
\begin{itemize}
\footnotetext{A single decoding is shown, using a (3,6) regular LDPC code \item For larger $n$, the gradient itself starts to oscillate
with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}; \item Dynamic range of oscillation highly correlated with probability of bit error
$\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$} \end{itemize}
\end{frame} \end{frame}
@ -1119,7 +1100,7 @@ return $\boldsymbol{\hat{c}}$
\vspace*{-0.5cm} \vspace*{-0.5cm}
\begin{itemize} \begin{itemize}
\item Improvement of proximal decoding by adding an ``ML-in-the-List'' step after \item Improvement of proximal decoding by addition of ``ML-in-the-List'' step after
iterating iterating
\end{itemize} \end{itemize}

10
latex/presentations/final/sections/theoretical_background.tex
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@ -9,13 +9,11 @@
\begin{frame}[t] \begin{frame}[t]
\frametitle{Motivation} \frametitle{Motivation}
\begin{itemize} \begin{itemize}
\item The general [ML] decoding problem for linear codes and the general problem \item The general ML decoding problem is NP-complete \cite{ml_np_hard_proof}
of finding the weights of a linear code are both NP-complete \cite{ml_np_hard_proof}.
\item The iterative message–passing algorithms preferred in practice do not guarantee \item The iterative message–passing algorithms preferred in practice do not guarantee
optimality and may fail to decode correctly when the graph contains cycles optimality when the graph contains cycles \cite{ldpc_conv}
\cite{ldpc_conv}. \item The standard message-passing algorithms are often difficult to
\item The standard message-passing algorithms used for decoding LDPC and turbo codes analyze \cite{feldman_thesis}
are often difficult to analyze. \cite{feldman_thesis}
\end{itemize} \end{itemize}
\end{frame} \end{frame}