diff --git a/latex/presentations/final/sections/comparison.tex b/latex/presentations/final/sections/comparison.tex index 5aa3f4b..7781422 100644 --- a/latex/presentations/final/sections/comparison.tex +++ b/latex/presentations/final/sections/comparison.tex @@ -15,8 +15,11 @@ \begin{itemize} \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item Minimum number of iterations independant of SNR \end{itemize} + \bigskip + \begin{figure}[H] \centering @@ -104,11 +107,6 @@ \end{subfigure}% \end{figure} - \begin{itemize} - \item Minimum number of iterations independant of SNR - \end{itemize} - - \bigskip \smallskip \smallskip \smallskip @@ -131,6 +129,8 @@ \item Both algorithms are $\mathcal{O}\left( n \right)$ on average \end{itemize} + \bigskip + \begin{figure}[H] \centering @@ -161,7 +161,6 @@ \end{tikzpicture} \end{figure} - \bigskip \smallskip \smallskip diff --git a/latex/presentations/final/sections/lp_dec_using_admm.tex b/latex/presentations/final/sections/lp_dec_using_admm.tex index 9c988d0..24a1dec 100644 --- a/latex/presentations/final/sections/lp_dec_using_admm.tex +++ b/latex/presentations/final/sections/lp_dec_using_admm.tex @@ -872,10 +872,12 @@ \begin{itemize} \item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$ \citereference{Mac23, Margulis2640.1320.3} -% ; $K=200, \mu = 3.3, \rho=1.9, -% \epsilon_{\text{pri}} = 10^{-5}, \epsilon_{\text{dual}} = 10^{-5}$ + \item Comparison of simulation with results from Barman et al. + \citereference{$\text{Bar}^+\text{13}$} \end{itemize} + \bigskip + \begin{figure}[H] \centering @@ -906,13 +908,8 @@ \end{axis} \end{tikzpicture} \end{figure}% - - \begin{itemize} - \item Comparison of simulation with results from Barman et al. - \citereference{$\text{Bar}^+\text{13}$} - \end{itemize} - \bigskip + \smallskip \addreferences {Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. @@ -932,8 +929,11 @@ \begin{itemize} \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item Similar to $\gamma$ with proximal decoding: no clear optimum \end{itemize} + \bigskip + \begin{figure}[H] \centering @@ -1011,11 +1011,6 @@ \end{subfigure} \end{figure}% - \begin{itemize} - \item Similar to $\gamma$ with proximal decoding: no clear optimum - \end{itemize} - - \bigskip \bigskip \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. @@ -1031,8 +1026,11 @@ \begin{itemize} \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item For lower decoding time, choose low $\mu$ and high $\rho$ \end{itemize} + \bigskip + \begin{figure}[H] \centering @@ -1107,12 +1105,7 @@ \end{tikzpicture} \end{subfigure} \end{figure}% - - \begin{itemize} - \item For lower decoding time, choose low $\mu$ and high $\rho$ - \end{itemize} - \bigskip \smallskip \smallskip \smallskip diff --git a/latex/presentations/final/sections/proximal_decoding.tex b/latex/presentations/final/sections/proximal_decoding.tex index f4e12bc..e1e1519 100644 --- a/latex/presentations/final/sections/proximal_decoding.tex +++ b/latex/presentations/final/sections/proximal_decoding.tex @@ -148,6 +148,7 @@ return $\boldsymbol{\hat{c}}$ \begin{itemize} \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item Comparison of simulation with results of Wadayama et al. \citereference{WT22} \end{itemize} \begin{figure}[H] @@ -207,10 +208,6 @@ return $\boldsymbol{\hat{c}}$ \vspace*{-2mm} - \begin{itemize} - \item Comparison of simulation with results of Wadayama et al. \citereference{WT22} - \end{itemize} - \bigskip \addreference{WT22}{Tadashi Wadayama; Satoshi Takabe: \emph{Proximal Decoding for LDPC @@ -229,8 +226,11 @@ return $\boldsymbol{\hat{c}}$ \begin{itemize} \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item Not great benefit in finding the optimal value for $\gamma$ \end{itemize} + \bigskip + \begin{figure}[H] \centering \hspace*{-3.5cm} @@ -298,10 +298,6 @@ return $\boldsymbol{\hat{c}}$ \end{subfigure} \end{figure} - \begin{itemize} - \item Not great benefit in finding the optimal value for $\gamma$ - \end{itemize} - \bigskip \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. @@ -654,8 +650,13 @@ return $\boldsymbol{\hat{c}}$ \begin{itemize} \item Single decoding using the BCH$\left( 7,4 \right) $ code; $E_b / N_0 = \SI{5}{dB}$ + \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} + \bigskip + \begin{figure}[H] \centering \begin{minipage}[c]{0.25\textwidth} @@ -846,12 +847,6 @@ return $\boldsymbol{\hat{c}}$ \end{tikzpicture} \end{minipage} \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} @@ -948,9 +943,12 @@ return $\boldsymbol{\hat{c}}$ \begin{itemize} \item Single decoding using a (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} -% ; $\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$ + \item For larger $n$, the gradient itself starts to oscillate + \item Dynamic range of oscillation highly correlated with probability of bit error \end{itemize} + \bigskip + \begin{figure} \centering @@ -1005,13 +1003,7 @@ return $\boldsymbol{\hat{c}}$ \end{tikzpicture} \end{subfigure} \end{figure} - - \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} - \bigskip \bigskip \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. @@ -1200,6 +1192,7 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d \begin{itemize} \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item Up to $\sim \SI{1}{dB}$ improvement \end{itemize} \begin{figure}[H] @@ -1300,10 +1293,6 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d \end{tikzpicture} \end{figure} - \begin{itemize} - \item Up to $\sim \SI{1}{dB}$ improvement - \end{itemize} - \bigskip \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. diff --git a/latex/presentations/final/sections/theoretical_background.tex b/latex/presentations/final/sections/theoretical_background.tex index 6f42622..9c98d59 100644 --- a/latex/presentations/final/sections/theoretical_background.tex +++ b/latex/presentations/final/sections/theoretical_background.tex @@ -149,7 +149,7 @@ \vspace{5mm} \begin{itemize} - \item Usage of ''$\sim$`` to denote change in domain, e.g. + \item Usage of ''$\sim$`` to denote change in domain, e.g.: \end{itemize} \vspace*{-2mm} @@ -223,8 +223,6 @@ draw, circle, inner sep=0pt, minimum size=4pt] (f) at (0.7, 0.7, 1) {}; \node[color=KITgreen, right=0cm of f] {$\tilde{\boldsymbol{c}}$}; \end{tikzpicture} - - \caption{Hypercube ($n=3$) with valid codewords for single parity-check code} \end{figure} \end{minipage} \end{frame}