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-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.aux37
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.log145
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.nav26
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.out4
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.pdfbin117082 -> 132691 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.snm1
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.synctex.gzbin6763 -> 19501 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.tex109
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.toc4
9 files changed, 235 insertions, 91 deletions
diff --git a/buch/papers/reedsolomon/RS presentation/RS.aux b/buch/papers/reedsolomon/RS presentation/RS.aux
index fff632d..6294c05 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.aux
+++ b/buch/papers/reedsolomon/RS presentation/RS.aux
@@ -22,10 +22,10 @@
\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}}
\HyPL@Entry{1<</P(2)>>}
-\@writefile{toc}{\beamer@sectionintoc {1}{Introduction}{2}{0}{1}}
+\@writefile{toc}{\beamer@sectionintoc {1}{Einführung}{2}{0}{1}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{1}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{1}}}
-\@writefile{nav}{\headcommand {\sectionentry {1}{Introduction}{2}{Introduction}{0}}}
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\@writefile{nav}{\headcommand {\slideentry {1}{0}{1}{2/2}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {2}{2}}}
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@@ -34,8 +34,33 @@
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-\@writefile{nav}{\headcommand {\beamer@partpages {1}{11}}}
-\@writefile{nav}{\headcommand {\beamer@subsectionpages {2}{11}}}
+\HyPL@Entry{11<</P(5)>>}
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\@writefile{nav}{\headcommand {\beamer@sectionpages {2}{11}}}
-\@writefile{nav}{\headcommand {\beamer@documentpages {11}}}
-\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {4}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {2}{11}}}
+\@writefile{nav}{\headcommand {\sectionentry {2}{Polynom Ansatz}{12}{Polynom Ansatz}{0}}}
+\@writefile{snm}{\beamer@slide {ft_discrete}{12}}
+\newlabel{ft_discrete}{{5}{12}{Polynom Ansatz}{Doc-Start}{}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{1}{12/12}{}{0}}}
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+\@writefile{nav}{\headcommand {\beamer@framepages {13}{13}}}
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+\@writefile{nav}{\headcommand {\slideentry {2}{0}{3}{14/15}{}{0}}}
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+\HyPL@Entry{15<</P(8)>>}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{4}{16/16}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {16}{16}}}
+\HyPL@Entry{16<</P(9)>>}
+\@writefile{toc}{\beamer@sectionintoc {3}{Diskrete Fourien Transformation}{17}{0}{3}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {12}{16}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {12}{16}}}
+\@writefile{nav}{\headcommand {\sectionentry {3}{Diskrete Fourien Transformation}{17}{Diskrete Fourien Transformation}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{0}{1}{17/17}{}{0}}}
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+\@writefile{nav}{\headcommand {\beamer@partpages {1}{17}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {17}{17}}}
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+\@writefile{nav}{\headcommand {\beamer@documentpages {17}}}
+\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {9}}}
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
@@ -1,4 +1,4 @@
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File: images/fig2.pdf Graphic file (type pdf)
<use images/fig2.pdf>
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File: images/fig3.pdf Graphic file (type pdf)
<use images/fig3.pdf>
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File: images/fig4.pdf Graphic file (type pdf)
<use images/fig4.pdf>
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File: images/fig5.pdf Graphic file (type pdf)
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<use images/polynom1.pdf>
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+ [14
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<use images/polynom2.pdf>
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+ [15
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+] [16
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(./RS.aux)
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-Output written on RS.pdf (11 pages).
+Output written on RS.pdf (17 pages).
diff --git a/buch/papers/reedsolomon/RS presentation/RS.nav b/buch/papers/reedsolomon/RS presentation/RS.nav
index 3edba3c..22ae94a 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.nav
+++ 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}}
\headcommand {\slideentry {1}{0}{1}{2/2}{}{0}}
\headcommand {\beamer@framepages {2}{2}}
\headcommand {\slideentry {1}{0}{2}{3/9}{}{0}}
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\headcommand {\beamer@sectionpages {2}{11}}
-\headcommand {\beamer@documentpages {11}}
-\headcommand {\gdef \inserttotalframenumber {4}}
+\headcommand {\beamer@subsectionpages {2}{11}}
+\headcommand {\sectionentry {2}{Polynom Ansatz}{12}{Polynom Ansatz}{0}}
+\headcommand {\slideentry {2}{0}{1}{12/12}{}{0}}
+\headcommand {\beamer@framepages {12}{12}}
+\headcommand {\slideentry {2}{0}{2}{13/13}{}{0}}
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+\headcommand {\beamer@framepages {16}{16}}
+\headcommand {\beamer@sectionpages {12}{16}}
+\headcommand {\beamer@subsectionpages {12}{16}}
+\headcommand {\sectionentry {3}{Diskrete Fourien Transformation}{17}{Diskrete Fourien Transformation}{0}}
+\headcommand {\slideentry {3}{0}{1}{17/17}{}{0}}
+\headcommand {\beamer@framepages {17}{17}}
+\headcommand {\beamer@partpages {1}{17}}
+\headcommand {\beamer@subsectionpages {17}{17}}
+\headcommand {\beamer@sectionpages {17}{17}}
+\headcommand {\beamer@documentpages {17}}
+\headcommand {\gdef \inserttotalframenumber {9}}
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
Binary files differ
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
Binary files differ
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}