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Finished gradient oscillation slide

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Andreas Tsouchlos
2023-01-25 13:26:20 +01:00
parent a894478c86
commit e817b94a2e
4 changed files with 875 additions and 2 deletions
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70
latex/presentations/midterm/sections/examination_results.tex
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@@ -646,7 +646,7 @@ Output $\boldsymbol{\hat{x}}$
\end{tikzpicture}
\end{minipage}
\caption{Internal variables of proximal decoder as a function of $k$\footnotemark}
\caption{Internal variables of proximal decoder as a function of $k$ ($n=7$)\footnotemark}
\footnotetext{A single decoding is shown, using the BCH$\left( 7,4 \right) $ code;
$\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$}
@@ -657,12 +657,78 @@ Output $\boldsymbol{\hat{x}}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{Proximal Decoder: Oscillation of $\nabla h\left( \boldsymbol{x} \right) $}
\setcounter{footnote}{0}
\begin{itemize}
\item For larger $n$, the Gradient itself starts to oscillate
\item The Amplitude of the oscillation seems to be highly correlated
with the probability of a bit error
\end{itemize}
\todo{Add grad oscillation plot}
\todo{Fix $K=200\ne 400$}
\begin{figure}
\centering
\begin{subfigure}[c]{0.5\textwidth}
\centering
\begin{tikzpicture}[scale = 0.85]
\begin{axis}[
grid=both,
xlabel={$k$},
width=8cm,
height=3cm,
scale only axis,
]
\addplot +[mark=none, line width=0.7pt]
table [col sep=comma, x=k, y=comb_r_s_0]
{res/proximal/extreme_components_20433484_combined.csv};
\addplot +[mark=none]
table [col sep=comma, x=k, y=grad_L_0]
{res/proximal/extreme_components_20433484_combined.csv};
\addplot +[mark=none]
table [col sep=comma, x=k, y=grad_h_0]
{res/proximal/extreme_components_20433484_combined.csv};
\addlegendentry{est}
\addlegendentry{$\nabla L$}
\addlegendentry{$\nabla h$}
\end{axis}
\end{tikzpicture}
\caption{Internal variables of proximal decoder as a function of k
($n=204$)\footnotemark}
\end{subfigure}%
\begin{subfigure}[c]{0.5\textwidth}
\centering
\begin{tikzpicture}[scale = 0.85]
\begin{axis}[
point meta min = -1,
point meta max = 1,
grid=both,
xlabel={$Var\left( \nabla h\left( \boldsymbol{x} \right) \right) $},
ylabel={bit error (bool)},
ytick={0, 1},
width=8cm,
height=3cm,
scale only axis,
% colormap/viridis,
]
\addplot [Brown, only marks,]
table [col sep=comma, x=grad_h_vars, y=bit_error]
{res/proximal/extreme_components_20433484_variance.csv};
\end{axis}
\end{tikzpicture}
\caption{Corellation between bit error and amplitude of oscillation}
\end{subfigure}
\end{figure}
\footnotetext{A single decoding is shown, using a (3,6) regular LDPC Code
with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc};
$\gamma = 0.05, \omega = 0.05, E_b / N_0 = \SI{5}{dB}$}
\end{frame}