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Minor changes to presentation

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Andreas Tsouchlos 2025-05-12 23:36:26 +02:00
parent 4b3d39e605
commit 9092f31ea8
1 changed files with 20 additions and 33 deletions
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src/2025-03-28/presentation.tex
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@ -390,8 +390,8 @@ Homotopy Continuation Methods}
\end{array}\right] \\
G(\bm{x}) &= \left[
\begin{array}{c}
x_1 - y_1\\
x_2 - y_2
x_1\\
x_2
\end{array}\right]\\
H(\bm{x}, t) &= (1-t)G(\bm{x}) + tF(\bm{x})
\end{align*}
@ -485,6 +485,17 @@ func decode(y) {
\begin{frame}[fragile]
\frametitle{Simulation results}
\vspace*{-5mm}
\begin{itemize}
\item Simulation using the all-zeros codeword
\item Newton homotopy:
\begin{gather*}
G(\bm{x}) = F(x) - F(\bm{y}) \hspace{5mm} \Rightarrow
\hspace{5mm} H(\bm{x}) = F(\bm{x}) - (1 - t) F(\bm{y})
\end{gather*}
\end{itemize}
\begin{figure}[H]
\centering
@ -503,17 +514,9 @@ func decode(y) {
legend pos= south west,
xmax=6
]
% \addplot+[scol0, densely dashed, mark=none, line
% width=1pt, forget plot]
% table[col sep=comma, x=SNR, y=FER]
% {\res/bch_31_26_hc.csv};
% \addplot+[scol0, mark=none, line width=1pt]
% table[col sep=comma, x=SNR, y=BER]
% {\res/bch_31_26_hc.csv};
% \addlegendentry{Homotopy continuation}
%
\addplot+[scol0, densely dashed, mark=none, line width=1pt,
forget plot]
\addplot+[scol0, densely dashed, mark=none, line
width=1pt, forget plot]
table[col sep=comma, x=SNR, y=FER]
{\res/bch_31_26_hc.csv};
\addplot+[scol0, mark=none, line width=1pt]
@ -532,19 +535,8 @@ func decode(y) {
{\res/bch_31_26_proximal.csv};
\addlegendentry{Proximal decoding}
% \addplot+[scol2, densely dashed, mark=none, line
% width=1pt, forget plot]
% table[col sep=comma, x=SNR, y=FER]
% {\res/bch_31_26_ml.csv};
% \addplot+[scol2, mark=none, line width=1pt]
% table[col sep=comma, x=SNR, y=BER]
% {\res/bch_31_26_ml.csv};
\addlegendentry{ML}
% \addplot+[mark=none, line width=1pt]
% table[col sep=comma, x=SNR, y=DFR]
% {\res/bch_31_11.csv};
% \addlegendentry{DFR}
\end{axis}
\end{tikzpicture}
@ -553,7 +545,7 @@ func decode(y) {
\begin{subfigure}[c]{0.48\textwidth}
\centering
\vspace*{-20mm}
\vspace*{-17mm}
\begin{tabular}{rl|ccccc}
Parameter & Value \\ \hline
@ -565,15 +557,10 @@ func decode(y) {
\end{tabular}
\bigskip
\smallskip
\begin{itemize}
\item Newton homotopy:
\begin{align*}
G(\bm{x}) &= F(x) - F(\bm{y}) \\
H(\bm{x}) &= (1-t)G(\bm{x}) - tF(\bm{x})\\
&= F(\bm{x}) - (1 - t) F(\bm{y})
\end{align*}
\end{itemize}
(No comprehensive investigation into choice of parameters
completed yet)
\end{subfigure}
\end{figure}
\end{frame}