Persentation stand 17:30

9 files changed, 235 insertions, 91 deletions

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index fff632d..6294c05 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.aux
+++ b/buch/papers/reedsolomon/RS presentation/RS.aux
@@ -22,10 +22,10 @@
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diff --git a/buch/papers/reedsolomon/RS presentation/RS.log b/buch/papers/reedsolomon/RS presentation/RS.log
index 824b9b5..342b031 100644
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+++ b/buch/papers/reedsolomon/RS presentation/RS.log
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diff --git a/buch/papers/reedsolomon/RS presentation/RS.nav b/buch/papers/reedsolomon/RS presentation/RS.nav
index 3edba3c..22ae94a 100644
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+++ b/buch/papers/reedsolomon/RS presentation/RS.nav
@@ -2,15 +2,31 @@
 \headcommand {\beamer@framepages {1}{1}}
 \headcommand {\beamer@sectionpages {1}{1}}
 \headcommand {\beamer@subsectionpages {1}{1}}
-\headcommand {\sectionentry {1}{Introduction}{2}{Introduction}{0}}
+\headcommand {\sectionentry {1}{Einführung}{2}{Einführung}{0}}
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 \headcommand {\beamer@framepages {2}{2}}
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+\headcommand {\beamer@subsectionpages {12}{16}}
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diff --git a/buch/papers/reedsolomon/RS presentation/RS.out b/buch/papers/reedsolomon/RS presentation/RS.out
index dec2d7d..597a5f8 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.out
+++ b/buch/papers/reedsolomon/RS presentation/RS.out
@@ -1 +1,3 @@
-\BOOKMARK [2][]{Outline0.1}{Introduction}{}% 1
+\BOOKMARK [2][]{Outline0.1}{Einführung}{}% 1
+\BOOKMARK [2][]{Outline0.2}{Polynom\040Ansatz}{}% 2
+\BOOKMARK [2][]{Outline0.3}{Diskrete\040Fourien\040Transformation}{}% 3
diff --git a/buch/papers/reedsolomon/RS presentation/RS.pdf b/buch/papers/reedsolomon/RS presentation/RS.pdf
index 10719b7..f49671f 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.pdf
+++ b/buch/papers/reedsolomon/RS presentation/RS.pdf
diff --git a/buch/papers/reedsolomon/RS presentation/RS.snm b/buch/papers/reedsolomon/RS presentation/RS.snm
index e69de29..8b82641 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.snm
+++ b/buch/papers/reedsolomon/RS presentation/RS.snm
@@ -0,0 +1 @@
+\beamer@slide {ft_discrete}{12}
diff --git a/buch/papers/reedsolomon/RS presentation/RS.synctex.gz b/buch/papers/reedsolomon/RS presentation/RS.synctex.gz
index 2fe95de..96af4cc 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.synctex.gz
+++ b/buch/papers/reedsolomon/RS presentation/RS.synctex.gz
diff --git a/buch/papers/reedsolomon/RS presentation/RS.tex b/buch/papers/reedsolomon/RS presentation/RS.tex
index fb822da..9bdf947 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.tex
+++ b/buch/papers/reedsolomon/RS presentation/RS.tex
@@ -19,10 +19,15 @@
 	\begin{frame}[plain]
 		\maketitle
 	\end{frame}
-	\section{Introduction}
+	\section{Einführung}
 	\begin{frame}
 		\frametitle{Idee}
-		
+		\begin{itemize}
+		\item Reed-Solomon-Code beschäftigt sich mit der Übertragung von Daten
+		und deren Fehler Erkennung.
+		\item Idee Fourier Transformieren und dann senden.
+		\item Danach Empfangen und Rücktransformieren.
+		\end{itemize}
 	\end{frame}
 
 	\begin{frame}
@@ -50,20 +55,100 @@
 			}
 	\end{figure}
 	\end{frame}
+	
 
 	\begin{frame}
-		Übertragen von den Zahlen 
-		\textcolor{blue}{2}, \textcolor{blue}{1}, \textcolor{blue}{5} 
-		als $ p(x) = \textcolor{blue}{2}x^2 + \textcolor{blue}{1}x + \textcolor{blue}{5} $.\newline
-		Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8}, 
-			\textcolor{green}{15}, \textcolor{green}{26},
-			\textcolor{green}{ 41}, \textcolor{green}{60}, 
-			\textcolor{green}{83}, \textcolor{green}{110})$
+		\uncover<1->{
+			Wie ist die Anzahl 0 definiert zum mitgeben?
+			Indem die Polymereigenschaft genutzt werden.
+		}
+		\uncover<2->{
+			Wie wird der Fehler lokalisiert?
+			Indem in einem Endlichen Körper gerechnet wird.
+		}
+		
+	\end{frame}	
+
+\section{Polynom Ansatz}
+	\begin{frame}
+		Die Diskrite Fouren Transformation ist so gegeben
+		\[
+			\label{ft_discrete}
+			\hat{c}_{k} 
+			= \frac{1}{N} \sum_{n=0}^{N-1}
+			{f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn}
+		\].
+		
+			\[
+			w = e^{-\frac{2\pi j}{N} k}
+			\]
+			Wenn $N$ konstant:
+			\[
+			\hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N)
+			\]
+	\end{frame}
+
+	\begin{frame}
+		Beispiel 2, 1, 5 Versenden und auf 2 Fehler absichern.
+	\end{frame}
+	\begin{frame}
+		Übertragen von 
+		${f}_2=$\textcolor{blue}{2}, ${f}_1$\textcolor{blue}{1}, ${f}_0$\textcolor{blue}{5} 
+		als $ p(w) = \textcolor{blue}{2}w^2 + \textcolor{blue}{1}w + \textcolor{blue}{5} $.
+
 		\only<1>{
-		\includegraphics[]{images/polynom1.pdf}}
+		Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8}, 
+		\textcolor{green}{15}, \textcolor{green}{26},
+		\textcolor{green}{ 41}, \textcolor{green}{60}, 
+		\textcolor{green}{83}, \textcolor{green}{110})$	
+		\includegraphics[scale = 1.2]{images/polynom1.pdf}}
 		\only<2>{
-		\includegraphics[]{images/polynom2.pdf}}
+		Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8}, 
+		\textcolor{red}{50}, \textcolor{red}{37},
+		\textcolor{green}{ 41}, \textcolor{green}{60}, 
+		\textcolor{green}{83}, \textcolor{green}{110})$
+		\includegraphics[scale = 1.2]{images/polynom2.pdf}
+		\textcolor{green}{7} Zahlen versenden, um \textcolor{blue}{3} Zahlen gegen \textcolor{red}{2} Fehlern abzusichern.}
+	\end{frame}
+	
+	\begin{frame}
+	\frametitle{Parameter}
+	\begin{center}
+		\begin{tabular}{ c c c } 
+			\hline
+			"Nutzlast" & Fehler & Versenden \\
+			\hline 
+			3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\ 
+			4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\ 
+			3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\ 
+			&&\\
+			k & t & k+2t Werte eines Polynoms vom Grad k-1 \\ 
+			\hline
+		\end{tabular}
+	\end{center}
+	\end{frame}
+\section{Diskrete Fourien Transformation}
+	\begin{frame}
+	\[
+		\begin{pmatrix}
+			\hat{c}_1 \\\hat{c}_2 \\\hat{c}_3 \\ \vdots \\\hat{c}_n
+		\end{pmatrix}
+		=
+		\begin{pmatrix}
+			w^0 & w^0   & w^0  & \dots  &w^0     \\
+			w^0 & w^1   &w^2   & \dots  &w^n     \\ 
+			w^0 & w^2   &w^4   & \dots  &w^{2n}  \\ 
+			\vdots   & \vdots     &\vdots     &\ddots  &\vdots       \\
+			w^0 & w^{1n}&w^{2n}& \dots  &w^{n}  \\ 
+		\end{pmatrix}
+		\begin{pmatrix}
+			\textcolor{blue}{5}  	\\
+			\textcolor{blue}{1}	\\
+			\textcolor{blue}{2}	\\	 
+		 \vdots  \\
+		 	0  \\ 
+		\end{pmatrix}
+	\]
 	\end{frame}
-
 	
 \end{document}
\ No newline at end of file
diff --git a/buch/papers/reedsolomon/RS presentation/RS.toc b/buch/papers/reedsolomon/RS presentation/RS.toc
index 32e7e8d..ff200c6 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.toc
+++ b/buch/papers/reedsolomon/RS presentation/RS.toc
@@ -1,2 +1,4 @@
 \babel@toc {ngerman}{}
-\beamer@sectionintoc {1}{Introduction}{2}{0}{1}
+\beamer@sectionintoc {1}{Einführung}{2}{0}{1}
+\beamer@sectionintoc {2}{Polynom Ansatz}{12}{0}{2}
+\beamer@sectionintoc {3}{Diskrete Fourien Transformation}{17}{0}{3}