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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}
\addbibresource{presentation.bib}
\input{common.tex}
\pgfplotsset{
/pgfplots/colormap/mako/.style={

47
latex/presentations/final/sections/comparison.tex
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@ -11,6 +11,10 @@
\begin{frame}[t]
\frametitle{Comparison: Convergence Behavior}
\begin{itemize}
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H]
\centering
@ -53,9 +57,6 @@
\addlegendentry{$E_b / N_0 = \SI{8}{dB}$}
\end{axis}
\end{tikzpicture}
\caption{Average error for $\SI{500000}{}$ decodings,
$\omega = 0.05, \gamma = 0.05, K=200$\footnotemark}
\end{subfigure}%
\begin{subfigure}[t]{0.5\textwidth}
\centering
@ -98,24 +99,24 @@
\addlegendentry{$E_b / N_0 = \SI{4}{dB}$}
\end{axis}
\end{tikzpicture}
\caption{Average error for $\SI{100000}{}$ decodings\protect\footnotemark{}}
\end{subfigure}%
\end{figure}
\footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
\begin{itemize}
\item Minimum number of iterations independant of SNR
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Comparison: Time Complexity}
\vspace*{-5mm}
\begin{itemize}
\item Both algorithms are $\mathcal{O}\left( n \right)$ on average
\item LP decoding implementation significantly faster
\item The points shown are from the following codes: BCH $\left( 31, 11 \right)$;
BCH $\left( 31, 26 \right)$; \\
\cite[\text{96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
\end{itemize}
\begin{figure}[H]
@ -148,16 +149,13 @@
\end{tikzpicture}
\end{figure}
\footnote{The points shown were calculated by evaluating the metadata
of BER simulation results for the following codes:
BCH $\left( 31, 11 \right)$;
BCH $\left( 31, 26 \right)$;
\cite[\text{96.3.965; 204.33.484;
204.55.187; 408.33.844; PEGReg252x504}]{mackay_enc}
}
\begin{itemize}
\item Both algorithms are $\mathcal{O}\left( n \right)$ on average
\item LP decoding implementation significantly faster
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Proximal Decoding: Improvement using \\``ML-in-the-List''}
@ -165,11 +163,7 @@
\vspace{-0.5cm}
\begin{itemize}
\item Comparison of proximal \& improved (correction of $N = \SI{12}{\bit}$)
decoding simulation%
\footnote{(3,6) regular LDPC code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
results
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H]
@ -253,15 +247,12 @@
\addlegendentry{ML}
\addlegendimage{RedOrange, mark=triangle, densely dashed, line width=1pt}
\addlegendentry{Improved}
\addlegendentry{Improved ($N$=12)}
\addlegendimage{RoyalPurple, mark=*, line width=1pt}
\addlegendentry{BP}
\end{axis}
\end{tikzpicture}
\caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, N=12$}
\label{fig:simulation_results_hybrid}
\end{figure}
\end{frame}

65
latex/presentations/final/sections/lp_dec_using_admm.tex
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@ -825,6 +825,13 @@
\begin{frame}[t]
\frametitle{LP Decoding using ADMM}
\begin{itemize}
\item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
\cite[\text{Margulis2640.1320.3}]{mackay_enc}
% ; $K=200, \mu = 3.3, \rho=1.9,
% \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
\end{itemize}
\begin{figure}[H]
\centering
@ -850,23 +857,24 @@
\addlegendentry{BP (Barman et al.)}
\end{axis}
\end{tikzpicture}
\end{figure}
\caption{Comparison of datapoints from Barman et al. with own simulation results%
\protect\footnotemark{}}
\label{fig:admm:results}
\end{figure}%
%
\footnotetext{``Margulis'' LDPC code with $n = 2640$, $k = 1320$
\cite[\text{Margulis2640.1320.3}]{mackay_enc}; $K=200, \mu = 3.3, \rho=1.9,
\epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
}%
%
\begin{itemize}
\item Comparison of simulation with results from Barman et al. \cite{original_admm}
\end{itemize}
\end{frame}
\begin{frame}[t]
\frametitle{LP Decoding using ADMM}
\begin{itemize}
\item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
\cite[\text{Margulis2640.1320.3}]{mackay_enc}
% ; $K=200, \mu = 3.3, \rho=1.9,
% \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
\end{itemize}
\begin{figure}[H]
\centering
@ -896,18 +904,11 @@
\addlegendentry{BP (Barman et al.)}
\end{axis}
\end{tikzpicture}
\caption{Comparison of datapoints from Barman et al. with own simulation results%
\protect\footnotemark{}}
\label{fig:admm:results}
\end{figure}%
%
\footnotetext{``Margulis'' LDPC code with $n = 2640$, $k = 1320$
\cite[\text{Margulis2640.1320.3}]{mackay_enc}; $K=200, \mu = 3.3, \rho=1.9,
\epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$
}%
%
\begin{itemize}
\item Comparison of simulation with results from Barman et al. \cite{original_admm}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -915,6 +916,10 @@
\frametitle{LP Decoding using ADMM: Choice of Penalty\\
Parameters}
\begin{itemize}
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H]
\centering
@ -990,13 +995,11 @@
\end{axis}
\end{tikzpicture}
\end{subfigure}
\caption{Relation between $\mu$ and $\rho$ and decoding performance%
\protect\footnotemark{}}
\end{figure}%
\footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
\begin{itemize}
\item Similar to $\gamma$ with proximal decoding: no clear optimum
\end{itemize}
\end{frame}
@ -1005,6 +1008,10 @@
\frametitle{LP Decoding using ADMM: Choice of Penalty\\
Parameters}
\begin{itemize}
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H]
\centering
@ -1078,12 +1085,10 @@
\end{axis}
\end{tikzpicture}
\end{subfigure}
\caption{Relation between $\mu$ and $\rho$ and speed of convergence%
\protect\footnotemark{}}
\end{figure}%
\footnotetext{Simulation performed with (3,6) regular LDPC code with $n=204, k=102$
\cite[Code: 204.33.484]{mackay_enc}}
\begin{itemize}
\item For lower decoding time, choose low $\mu$ and high $\rho$
\end{itemize}
\end{frame}

79
latex/presentations/final/sections/proximal_decoding.tex
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@ -129,12 +129,9 @@ return $\boldsymbol{\hat{c}}$
\begin{frame}[t]
\frametitle{Proximal Decoding: Bit Error Rate and Performance}
\vspace*{-0.5cm}
\begin{itemize}
\item Comparison of simulation%
\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}
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H]
@ -190,11 +187,12 @@ return $\boldsymbol{\hat{c}}$
\end{axis}
\end{tikzpicture}
\caption{Simulation results for $\omega = 0.05, K=100$}
\label{fig:sim_results_prox}
\end{figure}
\begin{itemize}
\item Comparison of simulation with results of Wadayama et al. \cite{proximal_paper}
\end{itemize}
% \vspace*{-0.5cm}
% \begin{itemize}
% \item $\mathcal{O}\left(n \right) $ time complexity - same as BP;
@ -211,10 +209,7 @@ return $\boldsymbol{\hat{c}}$
\frametitle{Proximal Decoding: Choice of $\gamma$}
\begin{itemize}
\item Simulation%
\footnote{(3,6) regular LDPC code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}}
results for different values of $\gamma$
\item (3,6) regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\begin{figure}[H]
@ -282,15 +277,11 @@ return $\boldsymbol{\hat{c}}$
\end{axis}
\end{tikzpicture}
\end{subfigure}
\caption{BER for $\omega = 0.05, K=100$}
\label{fig:ber_3d}
\end{figure}
\begin{itemize}
\item Not great benefit in finding the optimal value for $\gamma$
\end{itemize}
\vspace{3mm}
\end{frame}
@ -514,12 +505,12 @@ return $\boldsymbol{\hat{c}}$
\frametitle{Proximal Decoding: Frame Error Rate}
\begin{itemize}
\item Analysis of simulated%
\footnote{(3,6) regular LDPC code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}}
BER and FER
\item (3,6) regular LDPC code with $n=204$,\\
$k=102$ \cite[\text{204.33.484}]{mackay_enc}
\end{itemize}
\vspace*{-5mm}
\begin{minipage}{.4\textwidth}
\centering
@ -538,10 +529,6 @@ for $K$ iterations do
end for
return $\boldsymbol{\hat{c}}$
\end{algorithm}
\vspace*{-5mm}
\caption{Proximal decoding algorithm \cite{proximal_paper}}
\end{figure}
\end{minipage}%
\begin{minipage}{.6\textwidth}
@ -622,9 +609,6 @@ return $\boldsymbol{\hat{c}}$
\addlegendentry{$\gamma = 0.05$}
\end{axis}
\end{tikzpicture}
\caption{Simulation results for $\omega = 0.05, K=100$}
\label{fig:simulation_results_ber_fer_dfr}
\end{figure}
\end{minipage}
\end{frame}
@ -634,10 +618,10 @@ return $\boldsymbol{\hat{c}}$
\begin{frame}[t]
\frametitle{Proximal Decoding: Oscillation of Estimate}
\vspace*{-5mm}
\begin{itemize}
\item $\nabla L \left( \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right) $
and $\nabla h \left( \tilde{\boldsymbol{x}} \right) $ generally end up
in an equilibrium
\item Single decoding using the BCH$\left( 7,4 \right) $ code; $E_b / N_0 = \SI{5}{dB}$
\end{itemize}
\begin{figure}[H]
@ -829,13 +813,13 @@ return $\boldsymbol{\hat{c}}$
\end{axis}
\end{tikzpicture}
\end{minipage}
\caption{Internal variables of proximal decoder
as a function of the number of iterations ($n=7$)\footnotemark}
\footnotetext{A single decoding is shown, using the BCH$\left( 7,4 \right) $ code;
$\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$}
\end{figure}
\begin{itemize}
\item $\nabla L \left( \boldsymbol{y} \mid \tilde{\boldsymbol{x}} \right) $
and $\nabla h \left( \tilde{\boldsymbol{x}} \right) $ generally end up
in an equilibrium
\end{itemize}
\end{frame}
@ -843,6 +827,8 @@ return $\boldsymbol{\hat{c}}$
\begin{frame}[t]
\frametitle{Proximal Decoding: Visualization of Gradients}
\vspace*{-5mm}
\begin{figure}[H]
\centering
@ -928,9 +914,9 @@ return $\boldsymbol{\hat{c}}$
\frametitle{Proximal Decoder: Oscillation of $\nabla h\left( \tilde{\boldsymbol{x}} \right) $}
\begin{itemize}
\item For larger $n$, the gradient itself starts to oscillate
\item The dynamic range of the oscillation is highly correlated
with the probability of a bit error
\item Single decoding using a (3,6) regular LDPC code with $n=204, k=102$
\cite[\text{204.33.484}]{mackay_enc}
% ; $\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$
\end{itemize}
\begin{figure}
@ -963,9 +949,6 @@ return $\boldsymbol{\hat{c}}$
\addlegendentry{$\left(\nabla h \right)_1$}
\end{axis}
\end{tikzpicture}
\caption{Internal variables of proximal decoder as a function of the iteration
($n=204$)\footnotemark}
\end{subfigure}%
\begin{subfigure}[t]{0.5\textwidth}
\centering
@ -988,15 +971,13 @@ return $\boldsymbol{\hat{c}}$
{res/proximal/extreme_components_20433484_variance.csv};
\end{axis}
\end{tikzpicture}
\caption{Correlation between bit error and dynamic range of oscillation}
\end{subfigure}
\end{figure}
\footnotetext{A single decoding is shown, using a (3,6) regular LDPC code
with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc};
$\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$}
\begin{itemize}
\item For larger $n$, the gradient itself starts to oscillate
\item Dynamic range of oscillation highly correlated with probability of bit error
\end{itemize}
\end{frame}
@ -1119,7 +1100,7 @@ return $\boldsymbol{\hat{c}}$
\vspace*{-0.5cm}
\begin{itemize}
\item Improvement of proximal decoding by adding an ``ML-in-the-List'' step after
\item Improvement of proximal decoding by addition of ``ML-in-the-List'' step after
iterating
\end{itemize}

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