From 61a39fe2f65b87331c494bd41e8ca9a252d3f1bb Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Wed, 19 Apr 2023 23:29:19 +0200 Subject: [PATCH] Finished corrections --- .../final/sections/comparison.tex | 33 ++++++++++--------- .../final/sections/conclusion.tex | 16 +++++++-- .../final/sections/lp_dec_using_admm.tex | 13 ++++---- .../final/sections/proximal_decoding.tex | 8 ++--- 4 files changed, 42 insertions(+), 28 deletions(-) diff --git a/latex/presentations/final/sections/comparison.tex b/latex/presentations/final/sections/comparison.tex index 7781422..b521e50 100644 --- a/latex/presentations/final/sections/comparison.tex +++ b/latex/presentations/final/sections/comparison.tex @@ -15,7 +15,7 @@ \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 + \item Minimum number of iterations independent of SNR \end{itemize} \bigskip @@ -137,24 +137,27 @@ \begin{tikzpicture} \begin{axis}[ grid=both, - xlabel={$n$}, ylabel={time per frame (s)}, + xlabel={$n$}, ylabel={time per frame (ms)}, legend style={at={(0.05,0.6)},anchor=south west}, legend cell align={left}, width=0.43\textwidth, height=0.32\textwidth, ] \addplot[RedOrange, only marks, mark=square*] - table [col sep=comma, x=n, y=spf] + table [col sep=comma, x=n, y=spf, + y expr=\thisrow{spf} * 1000] {res/proximal/fps_vs_n.csv}; \addlegendentry{proximal} \addplot[Gray, only marks, mark=*] - table [col sep=comma, x=n, y=spf] + table [col sep=comma, x=n, y=spf, + y expr=\thisrow{spf} * 1000] {res/hybrid/fps_vs_n.csv}; - \addlegendentry{improved ($\SI{12}{\bit}$)} + \addlegendentry{improved ($N=12$)} \addplot[NavyBlue, only marks, mark=triangle*] - table [col sep=comma, x=n, y=spf] + table [col sep=comma, x=n, y=spf, + y expr=\thisrow{spf} * 1000] {res/admm/fps_vs_n.csv}; \addlegendentry{ADMM} \end{axis} @@ -617,7 +620,7 @@ while stopping critierion unfulfilled do \textbf{prox}_{\gamma h}\left( \boldsymbol{r} \right)} $|\Suppressnumber| |\Reactivatenumber| end while -return $\boldsymbol{s}$ +return $\hat{\boldsymbol{c}}$ \end{algorithm} \end{subfigure}\hfill% \begin{subfigure}[b]{0.5\textwidth} @@ -652,7 +655,7 @@ while stopping criterion unfulfilled do $\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j + \tilde{\boldsymbol{c}} - \boldsymbol{z}_j, \hspace{14.5mm}\forall j\in\mathcal{J}$ end while -return $\tilde{\boldsymbol{c}}$ +return $\hat{\boldsymbol{c}}$ \end{algorithm} \end{subfigure}% \end{figure}% @@ -663,7 +666,7 @@ return $\tilde{\boldsymbol{c}}$ \begin{frame}[t, fragile] \frametitle{Comparison: Algorithm Structure} - \vspace*{-1cm} + \vspace*{-0.6cm} \begin{figure}[h] \centering @@ -674,12 +677,12 @@ return $\tilde{\boldsymbol{c}}$ \begin{algorithm}[caption={}, label={},] Initialize $\boldsymbol{r}, \boldsymbol{s}, \omega, \gamma$ while stopping critierion unfulfilled do - for j in $\mathcal{J}$ do + for $j$ in $\mathcal{J}$ do $p_j \leftarrow \prod_{i\in N_c\left( j \right) } r_i $ $\textcolor{KITblue}{M_{j\to i} \leftarrow p_j^2 - p_j}$|\Suppressnumber| |\vspace{0.7mm}\Reactivatenumber| end for - for i in $\mathcal{I}$ do + for $i$ in $\mathcal{I}$ do $s_i \leftarrow s_i + \gamma \left[ 4\left( s_i^2 - 1 \right)s_i \phantom{\frac{4}{s_i}}\right.$|\Suppressnumber| |\Reactivatenumber|$\left.+ \frac{4}{s_i}\sum_{j\in N_v\left( i \right) } @@ -687,7 +690,7 @@ while stopping critierion unfulfilled do $r_i \leftarrow r_i + \omega \left( s_i - y_i \right)$ end for end while -return $\boldsymbol{s}$ +return $\hat{\boldsymbol{c}}$ \end{algorithm} \end{subfigure}% \hfill @@ -697,7 +700,7 @@ return $\boldsymbol{s}$ \begin{algorithm}[caption={}, label={},] Initialize $\tilde{\boldsymbol{c}}, \boldsymbol{z}, \boldsymbol{u}, \boldsymbol{\gamma}, \rho$ while stopping criterion unfulfilled do - for j in $\mathcal{J}$ do + for $j$ in $\mathcal{J}$ do $\boldsymbol{z}_j \leftarrow \Pi_{P_{d_j}}\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}} + \boldsymbol{u}_j\right)$ $\boldsymbol{u}_j \leftarrow \boldsymbol{u}_j + \boldsymbol{T}_j\tilde{\boldsymbol{c}} @@ -705,14 +708,14 @@ while stopping criterion unfulfilled do $\textcolor{KITblue}{M_{j\to i} \leftarrow \left( z_j \right)_i - \left( u_j \right)_i, \hspace{3mm} \forall i \in N_c\left( j \right)}$ end for - for i in $\mathcal{I}$ do + for $i$ in $\mathcal{I}$ do $\tilde{c}_i \leftarrow \frac{1}{d_i} \left(\sum_{j\in N_v\left( i \right) } M_{j\to i} - \frac{\gamma_i}{\mu} \right)$|\Suppressnumber| |\vspace{7mm}\Reactivatenumber| end for end while -return $\tilde{\boldsymbol{c}}$ +return $\hat{\boldsymbol{c}}$ \end{algorithm} \end{subfigure}% \end{figure}% diff --git a/latex/presentations/final/sections/conclusion.tex b/latex/presentations/final/sections/conclusion.tex index c63f302..949fb85 100644 --- a/latex/presentations/final/sections/conclusion.tex +++ b/latex/presentations/final/sections/conclusion.tex @@ -1,5 +1,5 @@ \section{Conclusion and Outlook}% -\label{sec:Comparison} +\label{sec:Conclusion} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -19,8 +19,18 @@ \end{itemize} \item Comparison \begin{itemize} - \item based on simulation results - \item based on their theoretical structure + \item Based on simulation results + \item Based on their theoretical structure + \end{itemize} + \end{itemize} + + \bigskip + + \begin{itemize} + \item Future work + \begin{itemize} + \item Usage of adaptive LP decoding to lower runtime or approximate ML performance + \item Combination of proximal and LP decoding \end{itemize} \end{itemize} \end{frame} diff --git a/latex/presentations/final/sections/lp_dec_using_admm.tex b/latex/presentations/final/sections/lp_dec_using_admm.tex index 24a1dec..c0b4bc6 100644 --- a/latex/presentations/final/sections/lp_dec_using_admm.tex +++ b/latex/presentations/final/sections/lp_dec_using_admm.tex @@ -688,14 +688,14 @@ \item Iterative algorithm: \begin{alignat*}{3} \tilde{\boldsymbol{c}} &\leftarrow \argmin_{\tilde{\boldsymbol{c}}} - \left( \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}} + \boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}} + \frac{\mu}{2}\sum_{j\in\mathcal{J}} \left\Vert \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j - + \boldsymbol{u}_j \right\Vert \right) \\ + + \boldsymbol{u}_j \right\Vert \\ \boldsymbol{z}_j &\leftarrow \argmin_{\boldsymbol{z}_j} - \left( g\left( \boldsymbol{z}_j \right) + g\left( \boldsymbol{z}_j \right) + \frac{\mu}{2} \left\Vert \boldsymbol{T}_j \tilde{\boldsymbol{c}} - - \boldsymbol{z}_j + \boldsymbol{u}_j \right\Vert \right), + - \boldsymbol{z}_j + \boldsymbol{u}_j \right\Vert, \hspace{5mm} &&\forall j\in\mathcal{J} \\ \boldsymbol{u}_j &\leftarrow \boldsymbol{u}_j + \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j, @@ -729,7 +729,7 @@ % \boldsymbol{z}_j \right)_i$.\\ % The same is true for $\left( \boldsymbol{u}_j \right)_i$}: - \vspace*{-3mm} + \vspace*{-4mm} \begin{alignat*}{3} \tilde{c}_i &\leftarrow \frac{1}{\left| N_v\left( i \right) \right|} \left( @@ -759,7 +759,7 @@ \end{itemize} \bigskip - \smallskip + \bigskip \addreferences {$\text{Bar}^+\text{13}$}{Siddharth Barman et al.: @@ -890,6 +890,7 @@ height=0.325\textwidth, %legend style={at={(0.03,0.04)},anchor=south west}, legend pos=outer north east, + legend cell align={left}, ] \addplot[Emerald, line width=1pt, mark=*] table [col sep=comma, x=SNR, y=FER, diff --git a/latex/presentations/final/sections/proximal_decoding.tex b/latex/presentations/final/sections/proximal_decoding.tex index e1e1519..8199780 100644 --- a/latex/presentations/final/sections/proximal_decoding.tex +++ b/latex/presentations/final/sections/proximal_decoding.tex @@ -226,7 +226,7 @@ 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 $\gamma$ + \item Observation: not great benefit in finding the optimal value for $\gamma$ \end{itemize} \bigskip @@ -936,7 +936,7 @@ return $\boldsymbol{\hat{c}}$ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}[t] - \frametitle{Proximal Decoder: Oscillation of $\nabla h\left( \tilde{\boldsymbol{x}} \right) $} + \frametitle{Proximal Decoding: Improvement} \vspace*{-3mm} @@ -1175,8 +1175,8 @@ for $K$ iterations do return $\boldsymbol{\hat{c}}$ end if end for -$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$ -$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified.}}$ +$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits}}$ +$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with }N\text{ bits modified}}$ $\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \hat{c}}_l, \boldsymbol{\hat{c}} \right) \text{ for all valid codewords } \boldsymbol{\hat{c}}_l}$ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with lowest }d_H\left( \boldsymbol{ \hat{c}}_l, \boldsymbol{\hat{c}} \right)}$ \end{algorithm}