diff options
Diffstat (limited to 'buch/papers/reedsolomon')
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.aux | 143 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.log | 1198 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.nav | 85 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.out | 8 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.pdf | bin | 0 -> 172860 bytes | |||
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.snm | 1 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.synctex.gz | bin | 0 -> 132775 bytes | |||
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.tex | 58 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/RS presentation/RS_handout.toc | 9 |
9 files changed, 1466 insertions, 36 deletions
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{29}{34}} +\headcommand {\beamer@sectionpages {29}{34}} +\headcommand {\beamer@documentpages {34}} +\headcommand {\gdef \inserttotalframenumber {28}} diff --git a/buch/papers/reedsolomon/RS presentation/RS_handout.out b/buch/papers/reedsolomon/RS presentation/RS_handout.out new file mode 100644 index 0000000..364319e --- /dev/null +++ b/buch/papers/reedsolomon/RS presentation/RS_handout.out @@ -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 Binary files differnew file mode 100644 index 0000000..382049d --- /dev/null +++ b/buch/papers/reedsolomon/RS presentation/RS_handout.pdf 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 Binary files differnew file mode 100644 index 0000000..c28a28a --- /dev/null +++ b/buch/papers/reedsolomon/RS presentation/RS_handout.synctex.gz 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} |