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Andreas Tsouchlos 2022-12-20 14:58:14 +01:00
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latex/presentations/midterm/sections/theoretical_background.tex
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@ -46,7 +46,8 @@
\item All simulations are performed with BPSK Modulation: \item All simulations are performed with BPSK Modulation:
\begin{align*} \begin{align*}
x\left[ k \right] = \left( -1 \right)^{c\left[ k \right] }, 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\} \hspace{5mm} \boldsymbol{c} \in \mathbb{F}_2^n,
\hspace{2mm} k\in \left\{ 1, \ldots, n \right\}
\end{align*} \end{align*}
\item The used channel model is AWGN: \item The used channel model is AWGN:
\begin{align*} \begin{align*}
@ -176,9 +177,11 @@
\end{align*} \end{align*}
\item Relaxed polytope representation: \item Relaxed polytope representation:
\begin{align*} \begin{align*}
\sum_{i\in \left( N\left( j \right) \setminus S\right) }f_i + \sum_{i\in S} \left( 1 - f_i \right) \ge 1 \sum_{i\in \left( N\left( j \right) \setminus S\right) } f_i
+ \sum_{i\in S} \left( 1 - f_i \right) \ge 1
\end{align*} \end{align*}
``$\boldsymbol{f}$ is separated by at least one bitflip from all illegal configurations'' ``$\boldsymbol{f}$ is separated by at least one bitflip
from all illegal configurations''
\end{itemize} \end{itemize}
\end{minipage}% \end{minipage}%
\hfill% \hfill%