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Incorporated proposals from test presentation; Fixed pseudocode listings

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Andreas Tsouchlos 2023-01-27 02:30:41 +01:00
parent a3c1adf3db
commit 052bb57834
4 changed files with 23 additions and 13 deletions
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2
latex/presentations/midterm/presentation.tex
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@ -196,7 +196,7 @@
basicstyle=\normalfont, basicstyle=\normalfont,
columns=fullflexible, columns=fullflexible,
keywordstyle=\color{black}\bfseries, keywordstyle=\color{black}\bfseries,
keywords={a, for, end, do, return, b} % add the keywords you want, or load keywords={a, for, end, do, return, if, b} % add the keywords you want, or load
% a language as Rubens explains in his comment above. % a language as Rubens explains in his comment above.
numbers=left, numbers=left,
xleftmargin=.04\textwidth, xleftmargin=.04\textwidth,

8
latex/presentations/midterm/sections/decoding_algorithms.tex
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@ -16,7 +16,7 @@
= \argmax_{x\in\mathbb{R}^n} = \argmax_{x\in\mathbb{R}^n}
f_{\boldsymbol{Y}}\left( \boldsymbol{y} | \boldsymbol{x} \right) f_{\boldsymbol{Y}}\left( \boldsymbol{y} | \boldsymbol{x} \right)
f_{\boldsymbol{X}}\left( \boldsymbol{x} \right) f_{\boldsymbol{X}}\left( \boldsymbol{x} \right)
= \argmax_{x\in\mathbb{R^n}} = \argmax_{x\in\mathbb{R}^n}
e^{-L\left( \boldsymbol{y} | \boldsymbol{x}\right)} e^{-L\left( \boldsymbol{y} | \boldsymbol{x}\right)}
f_{\boldsymbol{X}}\left( \boldsymbol{x} \right) f_{\boldsymbol{X}}\left( \boldsymbol{x} \right)
\end{align*} \end{align*}
@ -70,7 +70,7 @@
\left( \boldsymbol{y} | \boldsymbol{x} \right) \right) \left( \boldsymbol{y} | \boldsymbol{x} \right) \right)
\end{align*} \end{align*}
\note{Notational difference between $f$ and $f_X$ or $f_Y$} \note{Notational difference between $f$ and $f_X$ or $f_Y$}
\item Code proximal operator \cite{proximal_algorithms}: \item Proximal operator \cite{proximal_algorithms}:
\begin{align*} \begin{align*}
\text{prox}_{\gamma h} \left( \boldsymbol{x} \right) &\equiv \text{prox}_{\gamma h} \left( \boldsymbol{x} \right) &\equiv
\argmin_{\boldsymbol{t}\in\mathbb{R}^n} \left( \argmin_{\boldsymbol{t}\in\mathbb{R}^n} \left(
@ -108,7 +108,9 @@ for $K$ iterations do
$\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\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{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
$\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
If $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$, then return $\boldsymbol{\hat{c}}$ if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do
return $\boldsymbol{\hat{c}}$
end if
end for end for
return $\boldsymbol{\hat{c}}$ return $\boldsymbol{\hat{c}}$
\end{algorithm} \end{algorithm}

24
latex/presentations/midterm/sections/examination_results.tex
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@ -410,7 +410,9 @@ for $K$ iterations do
$\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\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{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
$\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
If $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$, then return $\boldsymbol{\hat{c}}$ if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do
return $\boldsymbol{\hat{c}}$
end if
end for end for
return $\boldsymbol{\hat{c}}$ return $\boldsymbol{\hat{c}}$
\end{algorithm} \end{algorithm}
@ -981,6 +983,8 @@ return $\boldsymbol{\hat{c}}$
\frametitle{Proximal Decoding: Improvement using ``ML-on-List''} \frametitle{Proximal Decoding: Improvement using ``ML-on-List''}
\setcounter{footnote}{0} \setcounter{footnote}{0}
\vspace*{-0.5cm}
\begin{itemize} \begin{itemize}
\item Improvement of proximal decoding by adding an ``ML-on-list'' step after iterating \item Improvement of proximal decoding by adding an ``ML-on-list'' step after iterating
\end{itemize} \end{itemize}
@ -991,13 +995,15 @@ return $\boldsymbol{\hat{c}}$
\begin{figure} \begin{figure}
\centering \centering
\begin{algorithm}[caption={}, label={}] \begin{algorithm}[caption={}, label={}, basicstyle=\fontsize{9.5}{11.5}\selectfont]
$\boldsymbol{s} \leftarrow \boldsymbol{0}$ $\boldsymbol{s} \leftarrow \boldsymbol{0}$
for $K$ iterations do for $K$ iterations do
$\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\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{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
$\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
If $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$, then return $\boldsymbol{\hat{c}}$ if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$ do
return $\boldsymbol{\hat{c}}$
end if
end for end for
return $\boldsymbol{\hat{c}}$ return $\boldsymbol{\hat{c}}$
\end{algorithm} \end{algorithm}
@ -1011,18 +1017,20 @@ return $\boldsymbol{\hat{c}}$
\begin{figure} \begin{figure}
\centering \centering
\begin{algorithm}[caption={}, label={}] \begin{algorithm}[caption={}, label={}, basicstyle=\fontsize{9.5}{11.5}\selectfont]
$\boldsymbol{s} \leftarrow \boldsymbol{0}$ $\boldsymbol{s} \leftarrow \boldsymbol{0}$
for $K$ iterations do for $K$ iterations do
$\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $ $\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{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
$\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $ $\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
If $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$, then return $\boldsymbol{\hat{c}}$ if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$
return $\boldsymbol{\hat{c}}$
end if
end for end for
$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$ $\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits.}}$
$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{c}}_n\text{ of }\boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified.}}$ $\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{c}}_i\text{ of }\boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified.}}$
$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{c}}_n, \boldsymbol{\hat{c}} \right) \forall n \in \left[ 1 : N-1 \right]}$ $\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{c}}_i, \boldsymbol{\hat{c}} \right) \text{ for all valid codewords } \boldsymbol{\tilde{c}}_i}$
$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_n\text{ with lowest }d_H\left( \boldsymbol{ \tilde{c}}_n, \boldsymbol{\hat{c}} \right)}$ $\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_i\text{ with lowest }d_H\left( \boldsymbol{ \tilde{c}}_i, \boldsymbol{\hat{c}} \right)}$
\end{algorithm} \end{algorithm}
\caption{Improved proximal decoding algorithm} \caption{Improved proximal decoding algorithm}

2
latex/presentations/midterm/sections/forthcoming_examination.tex
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@ -3,7 +3,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Forth Exam LP Decoding}% \subsection{LP Decoding}%
\label{sub:Forth Exam LP Decoding} \label{sub:Forth Exam LP Decoding}
\begin{frame}[t] \begin{frame}[t]