From f12bfc8392b2f09416fb2171a4dd0107ebe16722 Mon Sep 17 00:00:00 2001 From: JODBaer Date: Mon, 26 Jul 2021 14:17:05 +0200 Subject: update some files too --- buch/papers/reedsolomon/Makefile | 50 ++++++++++- buch/papers/reedsolomon/dtf.tex | 29 ++++--- buch/papers/reedsolomon/einleitung.tex | 10 +-- buch/papers/reedsolomon/experiments/plot.tex | 2 +- buch/papers/reedsolomon/figures/plotfft.pdf | Bin 0 -> 60217 bytes buch/papers/reedsolomon/figures/polynom2.pdf | Bin 0 -> 20327 bytes buch/papers/reedsolomon/idee.tex | 13 ++- buch/papers/reedsolomon/images/codiert.txt | 96 --------------------- buch/papers/reedsolomon/images/decodiert.txt | 96 --------------------- buch/papers/reedsolomon/images/empfangen.txt | 96 --------------------- buch/papers/reedsolomon/images/fehler.txt | 96 --------------------- buch/papers/reedsolomon/images/locator.txt | 96 --------------------- buch/papers/reedsolomon/images/plotfft.tex | 89 ------------------- buch/papers/reedsolomon/images/polynom2.tex | 49 ----------- buch/papers/reedsolomon/images/signal.txt | 96 --------------------- buch/papers/reedsolomon/images/syndrom.txt | 96 --------------------- buch/papers/reedsolomon/main.tex | 20 ----- buch/papers/reedsolomon/standalone.tex | 30 +++++++ buch/papers/reedsolomon/standalone/standalone.pdf | Bin 0 -> 1782700 bytes buch/papers/reedsolomon/tikz/codiert.txt | 96 +++++++++++++++++++++ buch/papers/reedsolomon/tikz/decodiert.txt | 96 +++++++++++++++++++++ buch/papers/reedsolomon/tikz/empfangen.txt | 96 +++++++++++++++++++++ buch/papers/reedsolomon/tikz/fehler.txt | 96 +++++++++++++++++++++ buch/papers/reedsolomon/tikz/locator.txt | 96 +++++++++++++++++++++ buch/papers/reedsolomon/tikz/plotfft.tex | 99 ++++++++++++++++++++++ buch/papers/reedsolomon/tikz/polynom2.tex | 57 +++++++++++++ buch/papers/reedsolomon/tikz/signal.txt | 96 +++++++++++++++++++++ buch/papers/reedsolomon/tikz/syndrom.txt | 96 +++++++++++++++++++++ 28 files changed, 939 insertions(+), 853 deletions(-) create mode 100644 buch/papers/reedsolomon/figures/plotfft.pdf create mode 100644 buch/papers/reedsolomon/figures/polynom2.pdf delete mode 100644 buch/papers/reedsolomon/images/codiert.txt delete mode 100644 buch/papers/reedsolomon/images/decodiert.txt delete mode 100644 buch/papers/reedsolomon/images/empfangen.txt delete mode 100644 buch/papers/reedsolomon/images/fehler.txt delete mode 100644 buch/papers/reedsolomon/images/locator.txt delete mode 100644 buch/papers/reedsolomon/images/plotfft.tex delete mode 100644 buch/papers/reedsolomon/images/polynom2.tex delete mode 100644 buch/papers/reedsolomon/images/signal.txt delete mode 100644 buch/papers/reedsolomon/images/syndrom.txt create mode 100644 buch/papers/reedsolomon/standalone.tex create mode 100644 buch/papers/reedsolomon/standalone/standalone.pdf create mode 100644 buch/papers/reedsolomon/tikz/codiert.txt create mode 100644 buch/papers/reedsolomon/tikz/decodiert.txt create mode 100644 buch/papers/reedsolomon/tikz/empfangen.txt create mode 100644 buch/papers/reedsolomon/tikz/fehler.txt create mode 100644 buch/papers/reedsolomon/tikz/locator.txt create mode 100644 buch/papers/reedsolomon/tikz/plotfft.tex create mode 100644 buch/papers/reedsolomon/tikz/polynom2.tex create mode 100644 buch/papers/reedsolomon/tikz/signal.txt create mode 100644 buch/papers/reedsolomon/tikz/syndrom.txt (limited to 'buch/papers') diff --git a/buch/papers/reedsolomon/Makefile b/buch/papers/reedsolomon/Makefile index 9c96e88..25fd98b 100644 --- a/buch/papers/reedsolomon/Makefile +++ b/buch/papers/reedsolomon/Makefile @@ -4,6 +4,52 @@ # (c) 2020 Prof Dr Andreas Mueller # -images: - @echo "no images to be created in reedsolomon" +SOURCES := \ + anwendungen.tex \ + codebsp.tex \ + decmitfehler.tex \ + decohnefehler.tex \ + dtf.tex \ + einleitung.tex \ + endlichekoerper.tex \ + hilfstabellen.tex \ + idee.tex \ + main.tex \ + packages.tex \ + rekonstruktion.tex \ + restetabelle1.tex \ + restetabelle2.tex \ + standalone.tex \ + zusammenfassung.tex + +TIKZFIGURES := \ + tikz/polynom2.tex \ + tikz/plotfft.tex + +FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) + + +all: images standalone + + +.PHONY: images +images: $(FIGURES) + +figures/%.pdf: tikz/%.tex + mkdir -p figures + pdflatex --output-directory=figures $< + +.PHONY: standalone +standalone: standalone.tex $(SOURCES) $(FIGURES) + mkdir -p standalone + cd ../..; \ + pdflatex \ + --halt-on-error \ + --shell-escape \ + --output-directory=papers/reedsolomon/standalone \ + papers/reedsolomon/standalone.tex; + cd standalone; \ + bibtex standalone; \ + makeindex standalone; + diff --git a/buch/papers/reedsolomon/dtf.tex b/buch/papers/reedsolomon/dtf.tex index a111527..62e44cc 100644 --- a/buch/papers/reedsolomon/dtf.tex +++ b/buch/papers/reedsolomon/dtf.tex @@ -14,20 +14,27 @@ wobei sie dann bei späteren Berchnungen ganz nützlich ist. \subsection{Diskrete Fourientransformation Zusamenhang \label{reedsolomon:subsection:dtfzusamenhang}} Die Diskrete Fourientransformation ist definiert als - \[ - \label{ft_discrete} +\begin{equation} \hat{c}_{k} = \frac{1}{N} \sum_{n=0}^{N-1} {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn} - \] + \label{reedsolomon:DFT} +\end{equation} + , wenn man nun - \[ - w = e^{-\frac{2\pi j}{N} k} - \] +\begin{equation} + w = + e^{-\frac{2\pi j}{N} k} + \label{reedsolomon:DFT_summand} +\end{equation} + ersetzte, und $N$ konstantbleibt, erhält man - \[ - \hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N) - \] +\begin{equation} + \hat{c}_{k}= + \frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N) + \label{reedsolomon:DFT_polynom} +\end{equation} + was überaust ähnlich zu unserem Polynomidee ist. \subsection{Übertragungsabfolge \label{reedsolomon:subsection:Übertragungsabfolge}} @@ -47,8 +54,8 @@ Das heisst alle information ist in alle Zahlenvorhanden. \begin{figure} \centering \resizebox{0.9\textwidth}{!}{ - %\includegraphics[width=0.5\textwidth]{papers/reedsolomon/images/plot.pdf} - \input{papers/reedsolomon/images/plotfft.tex} + \includegraphics[width=\textwidth]{papers/reedsolomon/figures/plotfft} + %\input{papers/reedsolomon/images/plotfft.tex} } \caption{Übertragungsabfolge \ref{reedsolomon:subsection:Übertragungsabfolge}} \label{fig:sendorder} diff --git a/buch/papers/reedsolomon/einleitung.tex b/buch/papers/reedsolomon/einleitung.tex index 2b1d878..074df05 100644 --- a/buch/papers/reedsolomon/einleitung.tex +++ b/buch/papers/reedsolomon/einleitung.tex @@ -7,13 +7,11 @@ \label{reedsolomon:section:einleitung}} \rhead{Einleitung} Der Reed-Solomon-Code ist entstanden um, -das Problem der Fehler, bei der Datenübertragung, zu lösen. -In diesem Abschnitt wird möglichst verständlich die mathematische Abfolge, Funktion oder Algorithmus erklärt. +das Problem der Fehler bei der Datenübertragung, zu lösen. +In diesem Abschnitt wird möglichst verständlich die mathematische Abfolge, +Funktion oder Algorithmus des Reed-Solomon-Code erklärt. Es wird jedoch nicht auf die technische Umsetzung oder Implementierung eingegangen. -Um beim Datenübertragen Fehler zu erkennen, könnte man die Daten jeweils doppelt senden, -und so jeweilige Fehler zu erkennen. -Doch nur schon um weinige Fehler zu erkennen werden überproportional viele Daten doppelt und dreifach gesendet. -Der Reed-Solomon-Code macht dies auf eine andere, clevere Weise. + diff --git a/buch/papers/reedsolomon/experiments/plot.tex b/buch/papers/reedsolomon/experiments/plot.tex index 2196c82..4b156bb 100644 --- a/buch/papers/reedsolomon/experiments/plot.tex +++ b/buch/papers/reedsolomon/experiments/plot.tex @@ -90,7 +90,7 @@ \draw[ultra thick, ->] (zoom) to[out=180, in=90] (syndrom.north); %item - \node[circle, draw, fill =lightgray] at (signal.north west)+(1,0) {1}; + \node[circle, draw, fill =lightgray] at (signal.north west) {1}; \node[circle, draw, fill =lightgray] at (codiert.north west) {2}; \node[circle, draw, fill =lightgray] at (fehler.north west) {3}; \node[circle, draw, fill =lightgray] at (empfangen.north west) {4}; diff --git a/buch/papers/reedsolomon/figures/plotfft.pdf b/buch/papers/reedsolomon/figures/plotfft.pdf new file mode 100644 index 0000000..27992c9 Binary files /dev/null and b/buch/papers/reedsolomon/figures/plotfft.pdf differ diff --git a/buch/papers/reedsolomon/figures/polynom2.pdf b/buch/papers/reedsolomon/figures/polynom2.pdf new file mode 100644 index 0000000..ae68385 Binary files /dev/null and b/buch/papers/reedsolomon/figures/polynom2.pdf differ diff --git a/buch/papers/reedsolomon/idee.tex b/buch/papers/reedsolomon/idee.tex index 39adbbf..e18ccd2 100644 --- a/buch/papers/reedsolomon/idee.tex +++ b/buch/papers/reedsolomon/idee.tex @@ -1,15 +1,22 @@ % -% teil1.tex -- Beispiel-File für das Paper +% idee.tex -- Beispiel-File für das Paper % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Idee \label{reedsolomon:section:idee}} \rhead{Problemstellung} +Um beim Datenübertragen Fehler zu erkennen, könnte man die Daten jeweils doppelt senden, +und so jeweilige Fehler zu erkennen. +Doch nur schon um Fehler zu erkennen werden überproportional viele Daten doppelt und dreifach gesendet. +Der Reed-Solomon-Code macht dies auf eine andere, clevere Weise. Das Problem liegt darin Informationen, Zahlen, zu Übertragen und Fehler zu erkennen. Beim Reed-Solomon-Code kann man nicht nur Fehler erkennen, man kann sogar einige Fehler korrigieren. +Der unterschied des Fehler erkennen und korrigiren, ist das beim Erkennen nur die Frage kommt hat es Fehler oder keine, +beim korrigieren muss man den Fehler erkennun und dann zusätzlich noch den original Wert rekonstruieren. +Auch eine variante wäre es die Daten nach einem Fehler einfach nochmals zu senden, was bei Reed-Solomon-Code-Anwendungen nicht immer sinnvolll ist. \ref(reedsolomon:section:anwendung) \rhead{Polynom-Ansatz} Eine Idee ist aus den Daten @@ -48,8 +55,8 @@ Dafür sind mehr übertragene Werte nötig. \begin{figure} \centering - %\includegraphics[width=0.5\textwidth]{papers/reedsolomon/images/polynom2} - \input{papers/reedsolomon/images/polynom2.tex} + \includegraphics[width=\textwidth]{papers/reedsolomon/figures/polynom2} + %\input{papers/reedsolomon/images/polynom2.tex} \caption{Polynom $p(x)$ \eqref{reedsolomon:equation1}} \label{fig:polynom} \end{figure} diff --git a/buch/papers/reedsolomon/images/codiert.txt b/buch/papers/reedsolomon/images/codiert.txt deleted file mode 100644 index 4a481d8..0000000 --- a/buch/papers/reedsolomon/images/codiert.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,284 -1,131.570790435043 -2,41.9840308053375 -3,12.1189172092243 -4,23.8408857476069 -5,69.1793197789512 -6,24.0186013379153 -7,37.3066577242559 -8,18.2010889773887 -9,12.3214904922455 -10,15.6627133315015 -11,24.5237955316204 -12,32.1114345314062 -13,44.9845039238714 -14,13.5324640263625 -15,10.1736266929292 -16,4.58257569495584 -17,23.217268502288 -18,16.5769107917917 -19,6.89948680823017 -20,4.84567134895776 -21,10.4219666223433 -22,43.6179140616243 -23,35.9073375743642 -24,15.0332963783729 -25,21.7594021268945 -26,23.2496572716993 -27,17.9815599423852 -28,11.3577742151117 -29,38.467599433197 -30,28.3035029562577 -31,9.54321919833388 -32,21.377558326432 -33,17.6292439561917 -34,12.6951848921471 -35,20.0667752354841 -36,22.9097309529208 -37,8.78894645948548 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-86,15.6627133315015 -87,12.3214904922455 -88,18.2010889773887 -89,37.3066577242559 -90,24.0186013379153 -91,69.1793197789512 -92,23.8408857476069 -93,12.1189172092243 -94,41.9840308053375 -95,131.570790435043 diff --git a/buch/papers/reedsolomon/images/decodiert.txt b/buch/papers/reedsolomon/images/decodiert.txt deleted file mode 100644 index f6221e6..0000000 --- a/buch/papers/reedsolomon/images/decodiert.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,6.05208333333333 -1,6.02602539785853 -2,0.0261327016093151 -3,5.98927158561317 -4,4.019445724874 -5,0.0247005083663722 -6,4.97798278395618 -7,1.95246440445439 -8,0.974000110512201 -9,2.00528527696027 -10,1.00071804528155 -11,1.97630907888264 -12,0.0232923747656228 -13,6.01302820392331 -14,3.03567381915226 -15,5.02435590137329 -16,7.00526061008995 -17,5.00739608089369 -18,5.02211514480064 -19,4.02175864806658 -20,1.00236543833726 -21,4.98147315261261 -22,8.97728828610336 -23,8.98481304394618 -24,2.98958333333333 -25,1.98491220960989 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-0,0 -1,0 -2,0 -3,0 -4,0 -5,0 -6,2 -7,0 -8,0 -9,0 -10,0 -11,0 -12,0 -13,0 -14,0 -15,0 -16,0 -17,0 -18,0 -19,0 -20,2 -21,0 -22,0 -23,0 -24,0 -25,0 -26,0 -27,0 -28,0 -29,0 -30,0 -31,0 -32,0 -33,0 -34,0 -35,0 -36,0 -37,0 -38,0 -39,0 -40,0 -41,0 -42,0 -43,0 -44,0 -45,0 -46,0 -47,0 -48,0 -49,0 -50,0 -51,0 -52,0 -53,0 -54,0 -55,0 -56,0 -57,0 -58,0 -59,0 -60,0 -61,0 -62,0 -63,0 -64,0 -65,0 -66,0 -67,0 -68,0 -69,0 -70,0 -71,0 -72,0 -73,0 -74,1 -75,0 -76,0 -77,0 -78,0 -79,0 -80,0 -81,0 -82,0 -83,0 -84,0 -85,0 -86,0 -87,0 -88,0 -89,0 -90,0 -91,0 -92,0 -93,0 -94,0 -95,0 diff --git a/buch/papers/reedsolomon/images/locator.txt b/buch/papers/reedsolomon/images/locator.txt deleted file mode 100644 index b28988c..0000000 --- a/buch/papers/reedsolomon/images/locator.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,0.0301224340567056 -1,0.141653026854885 -2,0.138226631799377 -3,0.0339903276086929 -4,0.310585462557496 -5,0.551427312631385 -6,0.628514858396814 -7,0.51102386251559 -8,0.275861355940449 -9,0.0502396354182268 -10,0.090185502547573 -11,0.110759344849756 -12,0.0684618905063001 -13,0.0362855426992259 -14,0.0697096919781468 -15,0.109288539370248 -16,0.0923187999496653 -17,0.0512198536768088 -18,0.274192386987782 -19,0.51349614953654 -20,0.633154426602466 -21,0.553283743533942 -22,0.307840573214514 -23,0.0341664350328392 -24,0.140270857957 -25,0.138527177682831 -26,0.029637547736156 -27,0.0816962563186052 -28,0.0944383203811073 -29,0.0263932110686261 -30,0.0585881348402056 -31,0.0737117341599984 -32,0.0239973937701886 -33,0.0464215468420038 -34,0.0616218854220964 -35,0.0221963086695009 -36,0.0390764778127646 -37,0.0537637218396934 -38,0.0208333333333332 -39,0.0343107696069045 -40,0.0483441215964552 -41,0.0198077862118806 -42,0.0311207395968725 -43,0.0444955089373458 -44,0.0190533549944159 -45,0.0290049795038723 -46,0.0417536642697558 -47,0.0185261550443084 -48,0.0277059929762261 -49,0.0398606084144816 -50,0.0181978813094817 -51,0.0271098219177584 -52,0.0386836665079729 -53,0.0180518611046889 -54,0.0272138992557141 -55,0.0381891287148314 -56,0.0180809085252469 -57,0.0281418959420061 -58,0.0384596362516637 -59,0.0182864418432272 -60,0.0302250788423173 -61,0.0397874837986351 -62,0.0186786556701694 -63,0.0342489348284216 -64,0.0429932815348666 -65,0.0192777878591759 -66,0.0422808966931999 -67,0.0506815964680563 -68,0.0201167847752226 -69,0.0615048274405271 -70,0.0744953894508454 -71,0.021246054596492 -72,0.142602265816215 -73,0.273502052865436 -74,0.325309673287599 -75,0.272705389655349 -76,0.149074257381345 -77,0.0247199397628712 -78,0.0680137859566976 -79,0.075388270873485 -80,0.0273637831604903 -81,0.0407867704453274 -82,0.0632964886441949 -83,0.0309749128751093 -84,0.0315202035072035 -85,0.0627625211892184 -86,0.0360843918243497 -87,0.02794920551495 -88,0.0677921493367236 -89,0.0437167157553067 -90,0.0270640150996317 -91,0.0783380025231622 -92,0.0561293738314281 -93,0.0278742033265809 -94,0.0981443889498639 -95,0.0794543457386548 diff --git a/buch/papers/reedsolomon/images/plotfft.tex b/buch/papers/reedsolomon/images/plotfft.tex deleted file mode 100644 index 83a89eb..0000000 --- a/buch/papers/reedsolomon/images/plotfft.tex +++ /dev/null @@ -1,89 +0,0 @@ -% -% Plot der Übertrangungsabfolge ins FFT und zurück mit IFFT -% -\begin{tikzpicture}[] - -%--------------------------------------------------------------- - %Knote -\matrix[draw = none, column sep=25mm, row sep=2mm]{ - \node(signal) [] { - \begin{tikzpicture} - \begin{axis} - [title = {\Large {Signal}}, - xlabel={Anzahl Übertragene Zahlen}, - xtick={0,20,40,64,80,98},] - \addplot[blue] table[col sep=comma] {papers/reedsolomon/images/signal.txt}; - \end{axis} - \end{tikzpicture}}; & - - \node(codiert) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Codiert}}] - \addplot[] table[col sep=comma] {papers/reedsolomon/images/codiert.txt}; - \end{axis} - \end{tikzpicture}}; \\ - - &\node(fehler) [] { - \begin{tikzpicture} - \begin{axis}[scale=0.6, title = {\Large {Fehler}}, - xtick={7,21,75}] - \addplot[red] table[col sep=comma] {papers/reedsolomon/images/fehler.txt}; - \end{axis} - \end{tikzpicture}};\\ - - \node(decodiert) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Decodiert}}] - \addplot[blue] table[col sep=comma] {papers/reedsolomon/images/decodiert.txt}; - \end{axis} - \end{tikzpicture}}; & - - \node(empfangen) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Empfangen}}] - \addplot[] table[col sep=comma] {papers/reedsolomon/images/empfangen.txt}; - \end{axis} - \end{tikzpicture}};\\ - - \node(syndrom) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Syndrom}}] - \addplot[blue] table[col sep=comma] {papers/reedsolomon/images/syndrom.txt}; - \end{axis} - \end{tikzpicture}}; & - - \node(locator) [] { - \begin{tikzpicture} - \begin{axis}[title = {\Large {Locator}}] - \addplot[] table[col sep=comma] {papers/reedsolomon/images/locator.txt}; - \end{axis} - \end{tikzpicture}};\\ -}; -%------------------------------------------------------------- - %FFT & IFFT deskription - -\draw[thin,gray,dashed] (0,12) to (0,-12); -\node(IFFT) [scale=0.7] at (0,12.3) {IFFT}; -\draw[<-](IFFT.south west)--(IFFT.south east); -\node(FFT) [scale=0.7, above of=IFFT] {FFT}; -\draw[->](FFT.north west)--(FFT.north east); - -\draw[thick, ->,] (fehler.west)++(-1,0) +(0.05,0.5) -- +(-0.1,-0.1) -- +(0.1,0.1) -- +(0,-0.5); -%Arrows -\draw[ultra thick, ->] (signal.east) to (codiert.west); -\draw[ultra thick, ->] (codiert.south) to (fehler.north); -\draw[ultra thick, ->] (fehler.south) to (empfangen.north); -\draw[ultra thick, ->] (empfangen.west) to (decodiert.east); -\draw[ultra thick, ->] (syndrom.east) to (locator.west); -\draw(decodiert.south east)++(-1.8,1) ellipse (1.3cm and 0.8cm) ++(-1.3,0) coordinate(zoom) ; -\draw[ultra thick, ->] (zoom) to[out=180, in=90] (syndrom.north); - -%item -\node[circle, draw, fill =lightgray] at (signal.north west) {1}; -\node[circle, draw, fill =lightgray] at (codiert.north west) {2}; -\node[circle, draw, fill =lightgray] at (fehler.north west) {3}; -\node[circle, draw, fill =lightgray] at (empfangen.north west) {4}; -\node[circle, draw, fill =lightgray] at (decodiert.north west) {5}; -\node[circle, draw, fill =lightgray] at (syndrom.north west) {6}; -\node[circle, draw, fill =lightgray] at (locator.north west) {7}; -\end{tikzpicture} \ No newline at end of file diff --git a/buch/papers/reedsolomon/images/polynom2.tex b/buch/papers/reedsolomon/images/polynom2.tex deleted file mode 100644 index 288b51c..0000000 --- a/buch/papers/reedsolomon/images/polynom2.tex +++ /dev/null @@ -1,49 +0,0 @@ -% polynome -%------------------- -% Teiler für das Skalieren der Grafik /40 -\newcommand{\teiler}{40} - - -%////////////////////////////////////// - -\begin{tikzpicture}[>=latex,thick] - \draw[color=blue, line width=1.4pt] - plot[domain=0:8, samples=100] - ({\x},{(2*\x^2+1*\x+5)/\teiler}); - - \draw[->] (-0.2,0) -- (8,0) coordinate[label={$x$}]; - \draw[->] (0,-0.2) -- (0,150/\teiler) coordinate[label={right:$p(x)$}]; - - \def\punkt#1{ - \fill[color=green] #1 circle[radius=0.08]; - \draw #1 circle[radius=0.07]; - } - - \def\hellpunkt#1{ - \fill[color=lightgray] #1 circle[radius=0.08]; - \draw #1 circle[radius=0.07]; - } - - \punkt{(1,8/\teiler)} - \hellpunkt{(2,15/\teiler)} - \hellpunkt{(3,26/\teiler)} - \punkt{(4,41/\teiler)} - \punkt{(5,60/\teiler)} - \punkt{(6,83/\teiler)} - \punkt{(7,110/\teiler)} - - \draw[color=gray,line width=1pt,dashed] - plot[domain=0.5:7, samples=100] - ({\x},{(7.832*\x^2-51.5*\x+121.668)/\teiler}); - - \def\erpunkt#1{ - \fill[color=red] #1 circle[radius=0.08]; - \draw #1 circle[radius=0.07]; - } - \erpunkt{(2,50/\teiler)} - \erpunkt{(3,37.66/\teiler)} - - \draw(0,100/\teiler) -- (-0.1,100/\teiler) coordinate[label={left:$100$}]; - \draw(1,0) -- (1,-0.1) coordinate[label={below:$1$}]; -\end{tikzpicture} -%\end{document} diff --git a/buch/papers/reedsolomon/images/signal.txt b/buch/papers/reedsolomon/images/signal.txt deleted file mode 100644 index c4fa5f8..0000000 --- a/buch/papers/reedsolomon/images/signal.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,6 -1,6 -2,0 -3,6 -4,4 -5,0 -6,5 -7,2 -8,1 -9,2 -10,1 -11,2 -12,0 -13,6 -14,3 -15,5 -16,7 -17,5 -18,5 -19,4 -20,1 -21,5 -22,9 -23,9 -24,3 -25,2 -26,6 -27,6 -28,4 -29,2 -30,9 -31,1 -32,1 -33,1 -34,2 -35,6 -36,6 -37,1 -38,9 -39,7 -40,7 -41,1 -42,9 -43,9 -44,10 -45,9 -46,8 -47,5 -48,2 -49,4 -50,1 -51,0 -52,9 -53,3 -54,3 -55,3 -56,5 -57,6 -58,0 -59,8 -60,6 -61,9 -62,3 -63,4 -64,0 -65,0 -66,0 -67,0 -68,0 -69,0 -70,0 -71,0 -72,0 -73,0 -74,0 -75,0 -76,0 -77,0 -78,0 -79,0 -80,0 -81,0 -82,0 -83,0 -84,0 -85,0 -86,0 -87,0 -88,0 -89,0 -90,0 -91,0 -92,0 -93,0 -94,0 -95,0 diff --git a/buch/papers/reedsolomon/images/syndrom.txt b/buch/papers/reedsolomon/images/syndrom.txt deleted file mode 100644 index 8ca9eed..0000000 --- a/buch/papers/reedsolomon/images/syndrom.txt +++ /dev/null @@ -1,96 +0,0 @@ -0,0 -1,0 -2,0 -3,0 -4,0 -5,0 -6,0 -7,0 -8,0 -9,0 -10,0 -11,0 -12,0 -13,0 -14,0 -15,0 -16,0 -17,0 -18,0 -19,0 -20,0 -21,0 -22,0 -23,0 -24,0 -25,0 -26,0 -27,0 -28,0 -29,0 -30,0 -31,0 -32,0 -33,0 -34,0 -35,0 -36,0 -37,0 -38,0 -39,0 -40,0 -41,0 -42,0 -43,0 -44,0 -45,0 -46,0 -47,0 -48,0 -49,0 -50,0 -51,0 -52,0 -53,0 -54,0 -55,0 -56,0 -57,0 -58,0 -59,0 -60,0 -61,0 -62,0 -63,0 -64,0.0275599094902563 -65,0.0115837187254191 -66,0.025877761014238 -67,0.0224618032819697 -68,0.04410594689944 -69,0.0474504002669341 -70,0.0227694695500626 -71,0.0271436638090525 -72,0.0104166666666667 -73,0.0271436638090523 -74,0.0227694695500608 -75,0.0474504002669343 -76,0.0441059468994397 -77,0.0224618032819701 -78,0.0258777610142379 -79,0.0115837187254183 -80,0.027559909490256 -81,0.0245124379481793 -82,0.0499782237195209 -83,0.0401432022864265 -84,0.0232923747656228 -85,0.0237974288564099 -86,0.0143895905726624 -87,0.0271745729691685 -88,0.0275599094902567 -89,0.0515501672184983 -90,0.0358255004834542 -91,0.024700508366373 -92,0.0210194725405171 -93,0.0177592928994296 -94,0.0261327016093158 -95,0.0314909067039411 diff --git a/buch/papers/reedsolomon/main.tex b/buch/papers/reedsolomon/main.tex index e68b947..327d01a 100644 --- a/buch/papers/reedsolomon/main.tex +++ b/buch/papers/reedsolomon/main.tex @@ -8,29 +8,9 @@ \begin{refsection} \chapterauthor{Joshua Bär und Michael Steiner} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} - % Joshua \input{papers/reedsolomon/einleitung.tex} \input{papers/reedsolomon/idee.tex} -%\input{papers/reedsolomon/teil2.tex} \input{papers/reedsolomon/dtf.tex} % Michael diff --git a/buch/papers/reedsolomon/standalone.tex b/buch/papers/reedsolomon/standalone.tex new file mode 100644 index 0000000..c850d1f --- /dev/null +++ b/buch/papers/reedsolomon/standalone.tex @@ -0,0 +1,30 @@ +\documentclass{book} + +\input{common/packages.tex} + +% additional packages used by the individual papers, add a line for +% each paper +\input{papers/common/addpackages.tex} + +% workaround for biblatex bug +\makeatletter +\def\blx@maxline{77} +\makeatother +\addbibresource{chapters/references.bib} + +% Bibresources for each article +\input{papers/common/addbibresources.tex} + +% make sure the last index starts on an odd page +\AtEndDocument{\clearpage\ifodd\value{page}\else\null\clearpage\fi} +\makeindex + +%\pgfplotsset{compat=1.12} +\setlength{\headheight}{15pt} % fix headheight warning +\DeclareGraphicsRule{*}{mps}{*}{} + +\begin{document} + \input{common/macros.tex} + \def\chapterauthor#1{{\large #1}\bigskip\bigskip} + \input{papers/reedsolomon/main.tex} +\end{document} diff --git a/buch/papers/reedsolomon/standalone/standalone.pdf b/buch/papers/reedsolomon/standalone/standalone.pdf new file mode 100644 index 0000000..80af280 Binary files /dev/null and b/buch/papers/reedsolomon/standalone/standalone.pdf differ diff --git a/buch/papers/reedsolomon/tikz/codiert.txt b/buch/papers/reedsolomon/tikz/codiert.txt new file mode 100644 index 0000000..4a481d8 --- /dev/null +++ b/buch/papers/reedsolomon/tikz/codiert.txt @@ -0,0 +1,96 @@ +0,284 +1,131.570790435043 +2,41.9840308053375 +3,12.1189172092243 +4,23.8408857476069 +5,69.1793197789512 +6,24.0186013379153 +7,37.3066577242559 +8,18.2010889773887 +9,12.3214904922455 +10,15.6627133315015 +11,24.5237955316204 +12,32.1114345314062 +13,44.9845039238714 +14,13.5324640263625 +15,10.1736266929292 +16,4.58257569495584 +17,23.217268502288 +18,16.5769107917917 +19,6.89948680823017 +20,4.84567134895776 +21,10.4219666223433 +22,43.6179140616243 +23,35.9073375743642 +24,15.0332963783729 +25,21.7594021268945 +26,23.2496572716993 +27,17.9815599423852 +28,11.3577742151117 +29,38.467599433197 +30,28.3035029562577 +31,9.54321919833388 +32,21.377558326432 +33,17.6292439561917 +34,12.6951848921471 +35,20.0667752354841 +36,22.9097309529208 +37,8.78894645948548 +38,13.360682005498 +39,25.1757616314718 +40,38.0357773686457 +41,18.4633287776253 +42,19.0584505869806 +43,10.8631093309173 +44,12.6147770818983 +45,12.5398140021274 +46,34.901983501949 +47,22.3480442021702 +48,6 +49,22.3480442021702 +50,34.901983501949 +51,12.5398140021274 +52,12.6147770818983 +53,10.8631093309173 +54,19.0584505869806 +55,18.4633287776253 +56,38.0357773686457 +57,25.1757616314718 +58,13.360682005498 +59,8.78894645948548 +60,22.9097309529208 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%--------------------------------------------------------------- + %Knote + \matrix[draw = none, column sep=25mm, row sep=2mm]{ + \node(signal) [] { + \begin{tikzpicture} + \begin{axis} + [title = {\Large {Signal}}, + xtick={0,20,40,64,80,98},] + \addplot[blue] table[col sep=comma] {tikz/signal.txt}; + \end{axis} + \end{tikzpicture}}; & + + \node(codiert) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Codiert}}] + \addplot[] table[col sep=comma] {tikz/codiert.txt}; + \end{axis} + \end{tikzpicture}}; \\ + + &\node(fehler) [] { + \begin{tikzpicture} + \begin{axis}[scale=0.6, title = {\Large {Fehler}}, + xtick={7,21,75}] + \addplot[red] table[col sep=comma] {tikz/fehler.txt}; + \end{axis} + \end{tikzpicture}};\\ + + \node(decodiert) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Decodiert}}] + \addplot[blue] table[col sep=comma] {tikz/decodiert.txt}; + \end{axis} + \end{tikzpicture}}; & + + \node(empfangen) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Empfangen}}] + \addplot[] table[col sep=comma] {tikz/empfangen.txt}; + \end{axis} + \end{tikzpicture}};\\ + + \node(syndrom) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Syndrom}}] + \addplot[blue] table[col sep=comma] {tikz/syndrom.txt}; + \end{axis} + \end{tikzpicture}}; & + + \node(locator) [] { + \begin{tikzpicture} + \begin{axis}[title = {\Large {Locator}}] + \addplot[] table[col sep=comma] {tikz/locator.txt}; + \end{axis} + \end{tikzpicture}};\\ + }; + %------------------------------------------------------------- + %FFT & IFFT deskription + + \draw[thin,gray,dashed] (0,12) to (0,-12); + \node(IFFT) [scale=0.7] at (0,12.3) {IFFT}; + \draw[<-](IFFT.south west)--(IFFT.south east); + \node(FFT) [scale=0.7, above of=IFFT] {FFT}; + \draw[->](FFT.north west)--(FFT.north east); + + \draw[thick, ->,] (fehler.west)++(-1,0) +(0.05,0.5) -- +(-0.1,-0.1) -- +(0.1,0.1) -- +(0,-0.5); + %Arrows + \draw[ultra thick, ->] (signal.east) to (codiert.west); + \draw[ultra thick, ->] (codiert.south) to (fehler.north); + \draw[ultra thick, ->] (fehler.south) to (empfangen.north); + \draw[ultra thick, ->] (empfangen.west) to (decodiert.east); + \draw[ultra thick, ->] (syndrom.east) to (locator.west); + \draw(decodiert.south east)++(-1.8,1) ellipse (1.3cm and 0.8cm) ++(-1.3,0) coordinate(zoom) ; + \draw[ultra thick, ->] (zoom) to[out=180, in=90] (syndrom.north); + + %item + \node[circle, draw, fill =lightgray] at (signal.north west) {1}; + \node[circle, draw, fill =lightgray] at (codiert.north west) {2}; + \node[circle, draw, fill =lightgray] at (fehler.north west) {3}; + \node[circle, draw, fill =lightgray] at (empfangen.north west) {4}; + \node[circle, draw, fill =lightgray] at (decodiert.north west) {5}; + \node[circle, draw, fill =lightgray] at (syndrom.north west) {6}; + \node[circle, draw, fill =lightgray] at (locator.north west) {7}; +\end{tikzpicture} +\end{document} \ No newline at end of file diff --git a/buch/papers/reedsolomon/tikz/polynom2.tex b/buch/papers/reedsolomon/tikz/polynom2.tex new file mode 100644 index 0000000..456e067 --- /dev/null +++ b/buch/papers/reedsolomon/tikz/polynom2.tex @@ -0,0 +1,57 @@ +% polynome +%------------------- + +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{pgfplots} + + +\begin{document} +% Teiler für das Skalieren der Grafik /40 +\newcommand{\teiler}{40} + + +%////////////////////////////////////// + +\begin{tikzpicture}[>=latex,thick] + \draw[color=blue, line width=1.4pt] + plot[domain=0:8, samples=100] + ({\x},{(2*\x^2+1*\x+5)/\teiler}); + + \draw[->] (-0.2,0) -- (8,0) coordinate[label={$x$}]; + \draw[->] (0,-0.2) -- (0,150/\teiler) coordinate[label={right:$p(x)$}]; + + \def\punkt#1{ + \fill[color=green] #1 circle[radius=0.08]; + \draw #1 circle[radius=0.07]; + } + + \def\hellpunkt#1{ + \fill[color=lightgray] #1 circle[radius=0.08]; + \draw #1 circle[radius=0.07]; + } + + \punkt{(1,8/\teiler)} + \hellpunkt{(2,15/\teiler)} + \hellpunkt{(3,26/\teiler)} + \punkt{(4,41/\teiler)} + \punkt{(5,60/\teiler)} + \punkt{(6,83/\teiler)} + \punkt{(7,110/\teiler)} + + \draw[color=gray,line width=1pt,dashed] + plot[domain=0.5:7, samples=100] + ({\x},{(7.832*\x^2-51.5*\x+121.668)/\teiler}); + + \def\erpunkt#1{ + \fill[color=red] #1 circle[radius=0.08]; + \draw #1 circle[radius=0.07]; + } + \erpunkt{(2,50/\teiler)} + \erpunkt{(3,37.66/\teiler)} + + \draw(0,100/\teiler) -- (-0.1,100/\teiler) coordinate[label={left:$100$}]; + \draw(1,0) -- (1,-0.1) coordinate[label={below:$1$}]; +\end{tikzpicture} +\end{document} diff --git a/buch/papers/reedsolomon/tikz/signal.txt b/buch/papers/reedsolomon/tikz/signal.txt new file mode 100644 index 0000000..c4fa5f8 --- /dev/null +++ b/buch/papers/reedsolomon/tikz/signal.txt @@ -0,0 +1,96 @@ +0,6 +1,6 +2,0 +3,6 +4,4 +5,0 +6,5 +7,2 +8,1 +9,2 +10,1 +11,2 +12,0 +13,6 +14,3 +15,5 +16,7 +17,5 +18,5 +19,4 +20,1 +21,5 +22,9 +23,9 +24,3 +25,2 +26,6 +27,6 +28,4 +29,2 +30,9 +31,1 +32,1 +33,1 +34,2 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