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-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.aux143
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.log1198
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.nav85
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.out8
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.pdfbin0 -> 172860 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.snm1
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.synctex.gzbin0 -> 132775 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.tex58
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS_handout.toc9
9 files changed, 1466 insertions, 36 deletions
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@@ -0,0 +1,8 @@
+\BOOKMARK [2][]{Outline0.1}{Einführung}{}% 1
+\BOOKMARK [2][]{Outline0.2}{Polynom\040Ansatz}{}% 2
+\BOOKMARK [2][]{Outline0.3}{Diskrete\040Fourier\040Transformation}{}% 3
+\BOOKMARK [2][]{Outline0.4}{Reed-Solomon in Endlichen Körpern}{}% 4
+\BOOKMARK [2][]{Outline0.5}{Codierung\040eines\040Beispiels}{}% 5
+\BOOKMARK [2][]{Outline0.6}{Decodierung\040ohne\040Fehler}{}% 6
+\BOOKMARK [2][]{Outline0.7}{Decodierung\040mit\040Fehler}{}% 7
+\BOOKMARK [2][]{Outline0.8}{Nachricht\040Rekonstruieren}{}% 8
diff --git a/buch/papers/reedsolomon/RS presentation/RS_handout.pdf b/buch/papers/reedsolomon/RS presentation/RS_handout.pdf
new file mode 100644
index 0000000..382049d
--- /dev/null
+++ b/buch/papers/reedsolomon/RS presentation/RS_handout.pdf
Binary files differ
diff --git a/buch/papers/reedsolomon/RS presentation/RS_handout.snm b/buch/papers/reedsolomon/RS presentation/RS_handout.snm
new file mode 100644
index 0000000..1796304
--- /dev/null
+++ b/buch/papers/reedsolomon/RS presentation/RS_handout.snm
@@ -0,0 +1 @@
+\beamer@slide {ft_discrete}{13}
diff --git a/buch/papers/reedsolomon/RS presentation/RS_handout.synctex.gz b/buch/papers/reedsolomon/RS presentation/RS_handout.synctex.gz
new file mode 100644
index 0000000..c28a28a
--- /dev/null
+++ b/buch/papers/reedsolomon/RS presentation/RS_handout.synctex.gz
Binary files differ
diff --git a/buch/papers/reedsolomon/RS presentation/RS_handout.tex b/buch/papers/reedsolomon/RS presentation/RS_handout.tex
index 863b3a2..1cbb6ef 100644
--- a/buch/papers/reedsolomon/RS presentation/RS_handout.tex
+++ b/buch/papers/reedsolomon/RS presentation/RS_handout.tex
@@ -25,38 +25,29 @@
\begin{frame}
\frametitle{Reed-Solomon-Code:}
\begin{itemize}
- \visible<1->{\item Für Übertragung von Daten}
- \visible<2->{\item Ermöglicht Korrektur von Übertragungsfehler}
- \visible<3->{\item Wird verwendet in: CD, QR-Codes, Voyager-Sonde, etc.}
+ \item Für Übertragung von Daten
+ \item Ermöglicht Korrektur von Übertragungsfehler
+ \item Wird verwendet in: CD, QR-Codes, Voyager-Sonde, etc.
\end{itemize}
\end{frame}
%-------------------------------------------------------------------------------
\section{Polynom Ansatz}
\begin{frame}
\begin{itemize}
- \item Beispiel $2, 1, 5$ versenden und auf 2 Fehler absichern
+ \item $2, 1, 5$ versenden und auf 2 Fehler absichern
\end{itemize}
- \end{frame}
- \begin{frame}
\frametitle{Beispiel}
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>{
- Versende $ (p(1),p(2),\dots,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>{
- Versende $ (p(1),p(2),\dots,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}
- \newline
- \textcolor{green}{7} Zahlen versenden, um \textcolor{blue}{3} Zahlen gegen \textcolor{red}{2} Fehlern abzusichern.}
+ \newline
+ Versende $ (p(1),p(2),\dots,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}
+ \newline
+ \textcolor{green}{7} Zahlen versenden, um \textcolor{blue}{3} Zahlen gegen \textcolor{red}{2} Fehlern abzusichern.
\end{frame}
%-------------------------------------------------------------------------------
\begin{frame}
@@ -68,18 +59,14 @@
\hline
3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\
4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\
-\visible<1->{3}&
-\visible<1->{3}&
-\visible<1->{9 Werte eines Polynoms vom Grad 2} \\
+ 3& 3& 9 Werte eines Polynoms vom Grad 2 \\
&&\\
-\visible<1->{$k$} &
-\visible<1->{$t$} &
-\visible<1->{$k+2t$ Werte eines Polynoms vom Grad $k-1$} \\
+ $k$ & $t$ & $k+2t$ Werte eines Polynoms vom Grad $k-1$ \\
\hline
&&\\
&&\\
\multicolumn{3}{l} {
- \visible<1>{Ausserdem können bis zu $2t$ Fehler erkannt werden!}
+ Ausserdem können bis zu $2t$ Fehler erkannt werden!
}
\end{tabular}
\end{center}
@@ -127,23 +114,23 @@
\frametitle{Diskrete Fourier Transformation}
\begin{itemize}
\item Diskrete Fourier-Transformation gegeben durch:
- \visible<1->{
+
\[
\label{ft_discrete}
\hat{c}_{k}
= \frac{1}{N} \sum_{n=0}^{N-1}
{f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn}
- \]}
- \visible<2->{
+ \]
+
\item Ersetzte
\[
w = e^{-\frac{2\pi j}{N} k}
- \]}
- \visible<3->{
+ \]
+
\item 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{itemize}
\end{frame}
@@ -177,10 +164,9 @@
\frametitle{Probleme und Fragen}
Wie wird der Fehler lokalisiert?
- \visible<2>{
\newline
Indem in einem endlichen Körper gerechnet wird.
- }
+
\end{frame}
%-------------------------------------------------------------------------------
diff --git a/buch/papers/reedsolomon/RS presentation/RS_handout.toc b/buch/papers/reedsolomon/RS presentation/RS_handout.toc
new file mode 100644
index 0000000..ce1bdc2
--- /dev/null
+++ b/buch/papers/reedsolomon/RS presentation/RS_handout.toc
@@ -0,0 +1,9 @@
+\babel@toc {ngerman}{}
+\beamer@sectionintoc {1}{Einführung}{2}{0}{1}
+\beamer@sectionintoc {2}{Polynom Ansatz}{3}{0}{2}
+\beamer@sectionintoc {3}{Diskrete Fourier Transformation}{5}{0}{3}
+\beamer@sectionintoc {4}{Reed-Solomon in Endlichen Körpern}{16}{0}{4}
+\beamer@sectionintoc {5}{Codierung eines Beispiels}{18}{0}{5}
+\beamer@sectionintoc {6}{Decodierung ohne Fehler}{20}{0}{6}
+\beamer@sectionintoc {7}{Decodierung mit Fehler}{23}{0}{7}
+\beamer@sectionintoc {8}{Nachricht Rekonstruieren}{29}{0}{8}