Implement Jäkel feedback
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@ -12,6 +12,7 @@
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\usepackage{listings}
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\usepackage{subcaption}
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\usepackage{bbm}
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%
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@ -51,7 +51,7 @@
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
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\citereference{Mac23, 96.33.965}}
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\citereference{Mac24, 96.33.965}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -90,7 +90,7 @@
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
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\citereference{Mac23, 204.33.484}}
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\citereference{Mac24, 204.33.484}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -121,7 +121,7 @@
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
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\citereference{Mac23, 408.33.844}}
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\citereference{Mac24, 408.33.844}}
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\end{subfigure}%
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\vspace*{-2mm}
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@ -190,7 +190,7 @@
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\vspace*{-2mm}
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\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
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\citereference{Mac23, 204.55.187}}
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\citereference{Mac24, 204.55.187}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -221,7 +221,7 @@
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\vspace*{-2mm}
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\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
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\citereference{Mac23, PEGReg252x504}}
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\citereference{Mac24, PEGReg252x504}}
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\end{subfigure}%
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\end{figure}
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\end{minipage}%
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@ -256,8 +256,8 @@
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\vspace*{-1mm}
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\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\end{frame}
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@ -345,7 +345,7 @@ return $\hat{\boldsymbol{c}}$
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\begin{itemize}
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\item Codes: BCH $\left( 31, 11 \right)$; BCH $\left( 31, 26 \right)$;
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\citereference{Mac23, 96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}
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\citereference{Mac24, 96.3.965; 204.33.484; 204.55.187; 408.33.844; PEGReg252x504}
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\item Measured performance: $\sim\SI{10000}{}$ frames/s
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on Intel Core i7-7700HQ @ 2.80GHz; $n=204$
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\item Both algorithms are $\mathcal{O}\left( n \right)$ on average
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@ -389,8 +389,8 @@ return $\hat{\boldsymbol{c}}$
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\smallskip
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\smallskip
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\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\end{frame}
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@ -401,7 +401,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-6mm}
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\begin{itemize}
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\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
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\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
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\item Minimum number of iterations independent of SNR
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\end{itemize}
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@ -496,8 +496,8 @@ return $\hat{\boldsymbol{c}}$
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\end{subfigure}%
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\end{figure}
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\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\end{frame}
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@ -551,7 +551,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
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\citereference{Mac23, 96.3.965}}
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\citereference{Mac24, 96.3.965}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -589,7 +589,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
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\citereference{Mac23, 204.33.484}}
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\citereference{Mac24, 204.33.484}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -627,7 +627,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
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\citereference{Mac23, 408.33.844}}
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\citereference{Mac24, 408.33.844}}
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\end{subfigure}%
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\vspace*{-2mm}
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@ -705,7 +705,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
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\citereference{Mac23, 204.55.187}}
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\citereference{Mac24, 204.55.187}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -743,7 +743,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
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\citereference{Mac23, PEGReg252x504}}
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\citereference{Mac24, PEGReg252x504}}
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\end{subfigure}%
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\end{figure}
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\end{minipage}%
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@ -774,8 +774,8 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-1mm}
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\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\end{frame}
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@ -786,7 +786,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-5mm}
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\begin{itemize}
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\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
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\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
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\item No clear optimum value
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\end{itemize}
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@ -871,8 +871,8 @@ return $\hat{\boldsymbol{c}}$
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\bigskip
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\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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@ -918,7 +918,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$
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\citereference{Mac23, 96.3.965}}
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\citereference{Mac24, 96.3.965}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -949,7 +949,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$
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\citereference{Mac23, 204.33.484}}
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\citereference{Mac24, 204.33.484}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -980,7 +980,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$
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\citereference{Mac23, 408.33.844}}
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\citereference{Mac24, 408.33.844}}
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\end{subfigure}%
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\vspace*{-2mm}
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@ -1044,7 +1044,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$
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\citereference{Mac23, 204.55.187}}
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\citereference{Mac24, 204.55.187}}
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\end{subfigure}%
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\begin{subfigure}[t]{0.33\textwidth}
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\centering
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@ -1075,7 +1075,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-2mm}
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\caption{LDPC code (progressive edge growth construction) with $n=504, k=252$
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\citereference{Mac23, PEGReg252x504}}
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\citereference{Mac24, PEGReg252x504}}
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\end{subfigure}%
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\end{figure}
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\end{minipage}%
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@ -1107,7 +1107,7 @@ return $\hat{\boldsymbol{c}}$
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\vspace*{-1mm}
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\addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\addreference{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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\end{frame}
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@ -783,10 +783,7 @@
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\vspace*{-6mm}
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\begin{itemize}
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\item ``Margulis'' LDPC code with $n = 2640$, $k = 1320$
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\citereference{Mac23, Margulis2640.1320.3}
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\item Comparison of simulation with results from Barman et al.
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\citereference{$\text{Bar}^+\text{13}$}
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\item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac24, 204.33.484}
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\end{itemize}
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\bigskip
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@ -805,124 +802,37 @@
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legend pos=outer north east,
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legend cell align={left},
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]
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\addplot[scol0, line width=1pt]
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table [col sep=comma, x=SNR, y=FER,]
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{res/admm/ber_margulis264013203.csv};
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\addlegendentry{ADMM}
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\addplot[scol1, line width=1pt]
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table [col sep=comma, x=SNR, y=FER, discard if gt={SNR}{2.2},]
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{res/generic/fer_bp_mackay_margulis.csv};
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\addlegendentry{BP \citereference{$\text{Bar}^+\text{13}$}}
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\addplot[scol1, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if not={mu}{3.0},
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discard if gt={SNR}{5.5}]
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{res/admm/ber_2d_20433484.csv};
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\addlegendentry{ADMM}
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\addplot [KITorange, line width=1pt]
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table [x=SNR, y=FER, col sep=comma,
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discard if gt={SNR}{5.5}]
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{res/generic/bp_20433484.csv};
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\addlegendentry{BP}
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\addplot[black, line width=1pt]
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table [col sep=comma, x=SNR, y=FER,
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discard if gt={SNR}{5.5}]
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{res/generic/fer_ml_20433484.csv};
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\addlegendentry{ML \citereference{HEL+19}}
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\end{axis}
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\end{tikzpicture}
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\end{figure}%
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\smallskip
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\bigskip
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\bigskip
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\addreferences
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{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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{$\text{Bar}^+\text{13}$}{Siddharth Barman et al.:
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\emph{Decomposition Methods for Large Scale LP Decoding}.
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IEEE Transactions on Information Theory 59.12 (2013), pp. 7870–7886.}
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{Mac24}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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June 2024. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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{Hel+19}{Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft,
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Stefan Ruzika, and Norbert Wehn. \emph{Database of Channel Codes and
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ML Simulation Results}. June 2024. URL: \url{www.rptu.de/channel-codes}}
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\stopreferences
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\end{frame}
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\begin{frame}[t]
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% \frametitle{LP Decoding using ADMM: Choice of Penalty\\
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% Parameters}
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%
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% \vspace*{-5mm}
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%
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% \begin{itemize}
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% \item (3,6) regular LDPC code with $n=204, k=102$ \citereference{Mac23, 204.33.484}
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% \item For lower decoding time, choose low $\mu$ and high $\rho$
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% \end{itemize}
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%
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% \bigskip
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%
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% \begin{figure}[H]
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% \centering
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%
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% \begin{subfigure}[c]{0.48\textwidth}
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% \centering
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%
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% \begin{tikzpicture}
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% \begin{axis}[
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% grid=both,
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% xlabel={$\mu$}, ylabel={Average \# of iterations},
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% width=0.8\textwidth,
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% height=0.6\textwidth,
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% ]
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% \addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
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% table [col sep=comma, x=mu, y=k_avg,
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% discard if not={SNR}{2.0},]
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% {res/admm/mu_kavg_20433484.csv};
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% \addplot[NavyBlue, line width=1pt, densely dashed, mark=*]
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% table [col sep=comma, x=mu, y=k_avg,
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% discard if not={SNR}{3.0},]
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% {res/admm/mu_kavg_20433484.csv};
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% \addplot[RedOrange, line width=1pt, densely dashed, mark=*]
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% table [col sep=comma, x=mu, y=k_avg,
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% discard if not={SNR}{4.0},]
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% {res/admm/mu_kavg_20433484.csv};
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% \end{axis}
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% \end{tikzpicture}
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% \end{subfigure}%
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% \begin{subfigure}[c]{0.48\textwidth}
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% \centering
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%
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% \begin{tikzpicture}
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% \begin{axis}[
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% grid=both,
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% xlabel={$\rho$}, ylabel={Average \# of iterations},
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% width=0.8\textwidth,
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% height=0.6\textwidth,
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% ]
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% \addplot[ForestGreen, line width=1pt, densely dashed, mark=*]
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% table [col sep=comma, x=rho, y=k_avg,
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% discard if not={SNR}{2.0},]
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% {res/admm/rho_kavg_20433484.csv};
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% \addplot[NavyBlue, line width=1pt, densely dashed, mark=*]
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% table [col sep=comma, x=rho, y=k_avg,
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% discard if not={SNR}{3.0},]
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% {res/admm/rho_kavg_20433484.csv};
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% \addplot[RedOrange, line width=1pt, densely dashed, mark=*]
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% table [col sep=comma, x=rho, y=k_avg,
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% discard if not={SNR}{4.0},]
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% {res/admm/rho_kavg_20433484.csv};
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% \end{axis}
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% \end{tikzpicture}
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% \end{subfigure}%
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%
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% \begin{subfigure}[t]{\textwidth}
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% \centering
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%
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% \begin{tikzpicture}
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% \begin{axis}[hide axis,
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% xmin=10, xmax=50,
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% ymin=0, ymax=0.4,
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% legend columns=3,
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% legend style={draw=white!15!black,legend cell align=left}]
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%
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% \addlegendimage{ForestGreen, line width=1pt, densely dashed, mark=*}
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% \addlegendentry{$E_b / N_0 = \SI{2}{dB}$}
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% \addlegendimage{RedOrange, line width=1pt, densely dashed, mark=*}
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% \addlegendentry{$E_b / N_0 = \SI{3}{dB}$}
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% \addlegendimage{NavyBlue, line width=1pt, densely dashed, mark=*}
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% \addlegendentry{$E_b / N_0 = \SI{4}{dB}$}
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% \end{axis}
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% \end{tikzpicture}
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% \end{subfigure}
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% \end{figure}%
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%
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% \smallskip
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% \smallskip
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% \smallskip
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%
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% \addreference{Mac23}{David J.C. MacKay: \emph{Encyclopedia of Sparse Graph Codes}.
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% Jan. 2023. URL: \url{http://www.inference.org.uk/mackay/codes/data.html}.}
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%\end{frame}
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%
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@ -126,7 +126,7 @@ $\boldsymbol{s} \leftarrow \boldsymbol{0}$
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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}
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user