70 lines
2.2 KiB
TeX
70 lines
2.2 KiB
TeX
\section{Theoretical Background}%
|
|
\label{sec:Theoretical Background}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\subsection{Motivation}%
|
|
\label{sub:Motivation}
|
|
|
|
\begin{frame}[t]
|
|
\frametitle{Motivation}
|
|
|
|
\todo{TODO}
|
|
\end{frame}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\subsection{Presumptions}%
|
|
\label{sub:Presumptions}
|
|
|
|
\begin{frame}[t]
|
|
\frametitle{Channel \& Modulation}
|
|
|
|
\tikzstyle{mapper} = [rectangle, minimum width=1.5cm, rounded corners=0.1cm, minimum height=0.7cm, text centered, draw=black, fill=KITgreen!80]
|
|
\begin{figure}[htpb]
|
|
\centering
|
|
|
|
\begin{tikzpicture}[scale=1, transform shape]
|
|
\node (in) {$c\left[ k \right] $};
|
|
\node[mapper, right=0.5cm of in] (bpskmap) {Mapper};
|
|
\node[right=1.5cm of bpskmap, draw, circle, inner sep=0pt, minimum size=0.5cm] (add) {$+$};
|
|
\node[right=0.5cm of add] (out) {$y\left[ k \right] $};
|
|
\node[below=0.5cm of add] (noise) {$n\left[ k \right] $};
|
|
|
|
\node at ($(bpskmap.east)!0.5!(add.west) + (0,0.3cm)$) {$x\left[ k \right] $};
|
|
|
|
\draw[->] (in) -- (bpskmap);
|
|
\draw[->] (bpskmap) -- (add);
|
|
\draw[->] (add) -- (out);
|
|
\draw[->] (noise) -- (add);
|
|
\end{tikzpicture}
|
|
\end{figure}
|
|
|
|
\begin{itemize}
|
|
\item All simulations are performed with BPSK Modulation:
|
|
\begin{align*}
|
|
x\left[ k \right] = \left( -1 \right)^{c\left[ k \right] }, \hspace{5mm} \boldsymbol{c} \in \mathbb{F}_2^n, \hspace{2mm} k\in \left\{ 1, \ldots, n \right\}
|
|
\end{align*}
|
|
\item The used channel model is AWGN:
|
|
\begin{align*}
|
|
\boldsymbol{y} = \boldsymbol{x} + \boldsymbol{n},
|
|
\hspace{5mm}\boldsymbol{n}\sim \mathcal{N}
|
|
\left(0,\frac{1}{2}\left(\frac{k}{n}\frac{E_b}{N_0}\right)^{-1}\right),
|
|
\hspace{2mm} \boldsymbol{y}, \boldsymbol{n} \in \mathbb{R}^n
|
|
\end{align*}
|
|
\todo{Why $\frac{1}{2}$}
|
|
\end{itemize}
|
|
\end{frame}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
\subsection{LP Decoding}%
|
|
\label{sub:LP Decoding}
|
|
|
|
\begin{frame}[t]
|
|
\frametitle{LP Decoding}
|
|
|
|
\todo{TODO}
|
|
\end{frame}
|
|
|