From 4fb52669c9a2d1decdd27a66b0f1a7cf9811fc47 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Fri, 21 Jun 2024 00:05:12 +0200 Subject: [PATCH] =?UTF-8?q?Implement=20J=C3=A4kel=20feedback?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- presentation.tex | 1 + sections/appendix.tex | 60 +++++++------- sections/lp_dec_using_admm.tex | 142 ++++++--------------------------- sections/proximal_decoding.tex | 70 ++++++++-------- 4 files changed, 92 insertions(+), 181 deletions(-) diff --git a/presentation.tex b/presentation.tex index c97395f..3146f7a 100644 --- a/presentation.tex +++ b/presentation.tex @@ -12,6 +12,7 @@ \usepackage{listings} \usepackage{subcaption} +\usepackage{bbm} % diff --git a/sections/appendix.tex b/sections/appendix.tex index 72b63bd..15d031f 100644 --- a/sections/appendix.tex +++ b/sections/appendix.tex @@ -51,7 +51,7 @@ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$ - \citereference{Mac23, 96.33.965}} + \citereference{Mac24, 96.33.965}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -90,7 +90,7 @@ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$ - \citereference{Mac23, 204.33.484}} + \citereference{Mac24, 204.33.484}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -121,7 +121,7 @@ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ - \citereference{Mac23, 408.33.844}} + \citereference{Mac24, 408.33.844}} \end{subfigure}% \vspace*{-2mm} @@ -190,7 +190,7 @@ \vspace*{-2mm} \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$ - \citereference{Mac23, 204.55.187}} + \citereference{Mac24, 204.55.187}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -221,7 +221,7 @@ \vspace*{-2mm} \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$ - \citereference{Mac23, PEGReg252x504}} + \citereference{Mac24, PEGReg252x504}} \end{subfigure}% \end{figure} \end{minipage}% @@ -256,8 +256,8 @@ \vspace*{-1mm} - \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} @@ -345,7 +345,7 @@ return $\hat{\boldsymbol{c}}$ \begin{itemize} \item Codes: BCH $\left( 31, 11 \right)$; BCH $\left( 31, 26 \right)$; - \citereference{Mac23, 96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504} + \citereference{Mac24, 96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504} \item Measured performance: $\sim\SI{10000}{}$ frames/s on Intel Core i7-7700HQ @ 2.80GHz; $n=204$ \item Both algorithms are $\mathcal{O}\left( n \right)$ on average @@ -389,8 +389,8 @@ return $\hat{\boldsymbol{c}}$ \smallskip \smallskip - \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} @@ -401,7 +401,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-6mm} \begin{itemize} - \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484} \item Minimum number of iterations independent of SNR \end{itemize} @@ -496,8 +496,8 @@ return $\hat{\boldsymbol{c}}$ \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} @@ -551,7 +551,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$ - \citereference{Mac23, 96.3.965}} + \citereference{Mac24, 96.3.965}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -589,7 +589,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$ - \citereference{Mac23, 204.33.484}} + \citereference{Mac24, 204.33.484}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -627,7 +627,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ - \citereference{Mac23, 408.33.844}} + \citereference{Mac24, 408.33.844}} \end{subfigure}% \vspace*{-2mm} @@ -705,7 +705,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$ - \citereference{Mac23, 204.55.187}} + \citereference{Mac24, 204.55.187}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -743,7 +743,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$ - \citereference{Mac23, PEGReg252x504}} + \citereference{Mac24, PEGReg252x504}} \end{subfigure}% \end{figure} \end{minipage}% @@ -774,8 +774,8 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-1mm} - \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} @@ -786,7 +786,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-5mm} \begin{itemize} - \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484} \item No clear optimum value \end{itemize} @@ -871,8 +871,8 @@ return $\hat{\boldsymbol{c}}$ \bigskip - \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -918,7 +918,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$ - \citereference{Mac23, 96.3.965}} + \citereference{Mac24, 96.3.965}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -949,7 +949,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$ - \citereference{Mac23, 204.33.484}} + \citereference{Mac24, 204.33.484}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -980,7 +980,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ - \citereference{Mac23, 408.33.844}} + \citereference{Mac24, 408.33.844}} \end{subfigure}% \vspace*{-2mm} @@ -1044,7 +1044,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$ - \citereference{Mac23, 204.55.187}} + \citereference{Mac24, 204.55.187}} \end{subfigure}% \begin{subfigure}[t]{0.33\textwidth} \centering @@ -1075,7 +1075,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-2mm} \caption{LDPC code (progressive edge growth construction) with $n=504, k=252$ - \citereference{Mac23, PEGReg252x504}} + \citereference{Mac24, PEGReg252x504}} \end{subfigure}% \end{figure} \end{minipage}% @@ -1107,7 +1107,7 @@ return $\hat{\boldsymbol{c}}$ \vspace*{-1mm} - \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} diff --git a/sections/lp_dec_using_admm.tex b/sections/lp_dec_using_admm.tex index c30ec6e..e0bf300 100644 --- a/sections/lp_dec_using_admm.tex +++ b/sections/lp_dec_using_admm.tex @@ -783,10 +783,7 @@ \vspace*{-6mm} \begin{itemize} - \item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$ - \citereference{Mac23, Margulis2640.1320.3} - \item Comparison of simulation with results from Barman et al. - \citereference{$\text{Bar}^+\text{13}$} + \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484} \end{itemize} \bigskip @@ -805,124 +802,37 @@ legend pos=outer north east, legend cell align={left}, ] - \addplot[scol0, line width=1pt] - table [col sep=comma, x=SNR, y=FER,] - {res/admm/ber_margulis264013203.csv}; - \addlegendentry{ADMM} - \addplot[scol1, line width=1pt] - table [col sep=comma, x=SNR, y=FER, discard if gt={SNR}{2.2},] - {res/generic/fer_bp_mackay_margulis.csv}; - \addlegendentry{BP \citereference{$\text{Bar}^+\text{13}$}} + + \addplot[scol1, line width=1pt] + table [x=SNR, y=FER, col sep=comma, + discard if not={mu}{3.0}, + discard if gt={SNR}{5.5}] + {res/admm/ber_2d_20433484.csv}; + \addlegendentry{ADMM} + \addplot [KITorange, line width=1pt] + table [x=SNR, y=FER, col sep=comma, + discard if gt={SNR}{5.5}] + {res/generic/bp_20433484.csv}; + + \addlegendentry{BP} + \addplot[black, line width=1pt] + table [col sep=comma, x=SNR, y=FER, + discard if gt={SNR}{5.5}] + {res/generic/fer_ml_20433484.csv}; + \addlegendentry{ML \citereference{HEL+19}} \end{axis} \end{tikzpicture} \end{figure}% - \smallskip + \bigskip + \bigskip \addreferences - {Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. - Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} - {$\text{Bar}^+\text{13}$}{Siddharth Barman et al.: - \emph{Decomposition Methods for Large Scale LP Decoding}. - IEEE Transactions on Information Theory 59.12 (2013), pp. 7870–7886.} + {Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} + {Hel+19}{Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft, + Stefan Ruzika, and Norbert Wehn. \emph{Database of Channel Codes and + ML Simulation Results}. June 2024. URL: \url{www.rptu.de/channel-codes}} \stopreferences \end{frame} -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\begin{frame}[t] -% \frametitle{LP Decoding using ADMM: Choice of Penalty\\ -% Parameters} -% -% \vspace*{-5mm} -% -% \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 -% -% \begin{subfigure}[c]{0.48\textwidth} -% \centering -% -% \begin{tikzpicture} -% \begin{axis}[ -% grid=both, -% xlabel={$\mu$}, ylabel={Average \# of iterations}, -% width=0.8\textwidth, -% height=0.6\textwidth, -% ] -% \addplot[ForestGreen, line width=1pt, densely dashed, mark=*] -% table [col sep=comma, x=mu, y=k_avg, -% discard if not={SNR}{2.0},] -% {res/admm/mu_kavg_20433484.csv}; -% \addplot[NavyBlue, line width=1pt, densely dashed, mark=*] -% table [col sep=comma, x=mu, y=k_avg, -% discard if not={SNR}{3.0},] -% {res/admm/mu_kavg_20433484.csv}; -% \addplot[RedOrange, line width=1pt, densely dashed, mark=*] -% table [col sep=comma, x=mu, y=k_avg, -% discard if not={SNR}{4.0},] -% {res/admm/mu_kavg_20433484.csv}; -% \end{axis} -% \end{tikzpicture} -% \end{subfigure}% -% \begin{subfigure}[c]{0.48\textwidth} -% \centering -% -% \begin{tikzpicture} -% \begin{axis}[ -% grid=both, -% xlabel={$\rho$}, ylabel={Average \# of iterations}, -% width=0.8\textwidth, -% height=0.6\textwidth, -% ] -% \addplot[ForestGreen, line width=1pt, densely dashed, mark=*] -% table [col sep=comma, x=rho, y=k_avg, -% discard if not={SNR}{2.0},] -% {res/admm/rho_kavg_20433484.csv}; -% \addplot[NavyBlue, line width=1pt, densely dashed, mark=*] -% table [col sep=comma, x=rho, y=k_avg, -% discard if not={SNR}{3.0},] -% {res/admm/rho_kavg_20433484.csv}; -% \addplot[RedOrange, line width=1pt, densely dashed, mark=*] -% table [col sep=comma, x=rho, y=k_avg, -% discard if not={SNR}{4.0},] -% {res/admm/rho_kavg_20433484.csv}; -% \end{axis} -% \end{tikzpicture} -% \end{subfigure}% -% -% \begin{subfigure}[t]{\textwidth} -% \centering -% -% \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, line width=1pt, densely dashed, mark=*} -% \addlegendentry{$E_b / N_0 = \SI{2}{dB}$} -% \addlegendimage{RedOrange, line width=1pt, densely dashed, mark=*} -% \addlegendentry{$E_b / N_0 = \SI{3}{dB}$} -% \addlegendimage{NavyBlue, line width=1pt, densely dashed, mark=*} -% \addlegendentry{$E_b / N_0 = \SI{4}{dB}$} -% \end{axis} -% \end{tikzpicture} -% \end{subfigure} -% \end{figure}% -% -% \smallskip -% \smallskip -% \smallskip -% -% \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} -% diff --git a/sections/proximal_decoding.tex b/sections/proximal_decoding.tex index 10441af..015a886 100644 --- a/sections/proximal_decoding.tex +++ b/sections/proximal_decoding.tex @@ -126,7 +126,7 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$ for $K$ iterations do $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $ - $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ + $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$ if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do return $\boldsymbol{\hat{c}}$ end if @@ -146,7 +146,7 @@ return $\boldsymbol{\hat{c}}$ \vspace*{-7mm} \begin{itemize} - \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484} \item Comparison of simulation with results of Wadayama et al. \citereference{WT22} \end{itemize} @@ -156,7 +156,7 @@ return $\boldsymbol{\hat{c}}$ \begin{tikzpicture} \begin{axis}[ grid=both, grid style={line width=.1pt}, - xlabel={$E_b / N_0$ (dB)}, ylabel={BER}, + xlabel={$E_b / N_0$ (dB)}, ylabel={FER}, ymode=log, legend pos=outer north east, width=0.45\textwidth, @@ -202,8 +202,8 @@ return $\boldsymbol{\hat{c}}$ \addreference{WT22}{Tadashi Wadayama; Satoshi Takabe: \emph{Proximal Decoding for LDPC Codes}. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences advpub (2022), 2022TAP0002.} - \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}} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}} \end{frame} @@ -431,7 +431,7 @@ return $\boldsymbol{\hat{c}}$ \begin{itemize} \item (3,6) regular LDPC code with $n=204$,\\ - $k=102$ \citereference{Mac23, 204.33.484} + $k=102$ \citereference{Mac24, 204.33.484} \end{itemize} \vspace*{-2mm} @@ -447,7 +447,7 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$ for $K$ iterations do $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $ - $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ + $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$ if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do return $\boldsymbol{\hat{c}}$ end if @@ -458,8 +458,8 @@ return $\boldsymbol{\hat{c}}$ \vspace*{-4mm} \hspace*{-4mm} - \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{minipage}% \begin{minipage}{.6\textwidth} \centering @@ -845,7 +845,7 @@ 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} + \citereference{Mac24, 204.33.484} \item For larger $n$, the gradient itself starts to oscillate \item Amplitude of oscillation highly correlated to probability of bit error \end{itemize} @@ -906,8 +906,8 @@ return $\boldsymbol{\hat{c}}$ \bigskip - \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} @@ -1047,7 +1047,7 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$ for $K$ iterations do $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $ - $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ + $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$ if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do return $\boldsymbol{\hat{c}}$ end if @@ -1070,13 +1070,13 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$ for $K$ iterations do $\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $ - $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ + $\boldsymbol{\hat{c}} \leftarrow \mathbbm{1}_{\left\{ \boldsymbol{s} \le 0 \right\}}$ if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ return $\boldsymbol{\hat{c}}$ end if end for $\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits}}$ -$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with }N\text{ bits modified}}$ +$\textcolor{KITblue}{L' := \left\{ \text{Variations } \boldsymbol{\hat{c}}_l\text{ of }\boldsymbol{\hat{c}}\text{ with }N\text{ bits modified} \right\}}$ $\textcolor{KITblue}{\text{Compute }\boldsymbol{y}^\text{T}\boldsymbol{ \hat{c}}_l \text{ for all codewords } \boldsymbol{\hat{c}}_l}$ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest }\boldsymbol{y}^\text{T}\boldsymbol{ \hat{c}}_l \text{, prioritizing valid codewords}}$ \end{algorithm} @@ -1091,7 +1091,7 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest } \vspace{-0.6cm} \begin{itemize} - \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484} \item Up to $\sim \SI{1}{dB}$ improvement \end{itemize} @@ -1195,8 +1195,8 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest } \bigskip - \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -1206,7 +1206,7 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest } \vspace*{-5mm} \begin{itemize} - \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484} \item Chosen parameters: $\gamma = 0.05$ \end{itemize} @@ -1255,8 +1255,8 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest } \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame} @@ -1267,7 +1267,7 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest } \vspace*{-5mm} \begin{itemize} - \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484} + \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484} \item Chosen parameters: $N=8, \gamma = 0.05$ \end{itemize} @@ -1403,26 +1403,26 @@ $\textcolor{KITblue}{\textbf{return }\boldsymbol{\hat{c}}_l\text{ with highest } \centering \begin{tabular}{c c c c c c} - $E_b/N_0$ & \shortstack{List size\\ mean} & \shortstack{List size\\ var.} \\ + $E_b/N_0$ (dB) & \shortstack{List size\\ mean} \\ \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 + 1.0 & 1.0 \\ + 1.5 & 1.0 \\ + 2.0 & 1.0 \\ + 2.5 & 1.0 \\ + 3.0 & 1.0 \\ + 3.5 & 1.0 \\ + 4.0 & 1.0 \\ + 4.5 & 1.0 \\ + 5.0 & 1.0 \\ + 5.5 & 1.0 \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}.} + \addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}. + June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.} \end{frame}