diff options
Diffstat (limited to '')
| -rw-r--r-- | buch/papers/reedsolomon/experiments/codiert.txt | 96 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/experiments/decodiert.txt | 96 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/experiments/empfangen.txt | 96 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/experiments/f.m | 22 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/experiments/fehler.txt | 96 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/experiments/locator.txt | 96 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/experiments/signal.txt | 96 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/experiments/syndrom.txt | 96 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/idee.tex | 7 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/images/polynom2.tex | 32 | ||||
| -rw-r--r-- | buch/papers/reedsolomon/packages.tex | 2 |
11 files changed, 712 insertions, 23 deletions
diff --git a/buch/papers/reedsolomon/experiments/codiert.txt b/buch/papers/reedsolomon/experiments/codiert.txt new file mode 100644 index 0000000..a57fb3e --- /dev/null +++ b/buch/papers/reedsolomon/experiments/codiert.txt @@ -0,0 +1,96 @@ +305 +114.502535214877 +86.2532974498148 +10.2450106137816 +68.1373455525487 +12.2281691909479 +3.18633753309102 +20.0196562371296 +12.2767246322969 +11.7216140392957 +24.8752690882777 +16.2978466490127 +23.2518118214845 +16.5845482358975 +15.6140674930647 +33.396205039034 +20.7846096908265 +19.3528753492232 +16.3850575123207 +20.9502842499826 +17.064465004608 +11.7252100463969 +31.1005540675575 +29.4336965143315 +26.6270539113887 +18.0164813754079 +24.7444243500799 +7.51007272621331 +4.06984153366859 +27.215173252412 +17.2339815787965 +23.5539874432174 +22.2710574513201 +14.7961619823174 +25.5530773949688 +33.4185813747547 +11.5478676394508 +21.0691619228239 +28.7948800016184 +12.3795084046074 +17.0082930449459 +19.7473571196866 +18.4490385219626 +12.2195365467659 +7.58568158110485 +6.02300839250873 +14.565530706253 +3.78959213976527 +21 +3.78959213976527 +14.565530706253 +6.02300839250873 +7.58568158110485 +12.2195365467659 +18.4490385219626 +19.7473571196866 +17.0082930449459 +12.3795084046074 +28.7948800016184 +21.0691619228239 +11.5478676394508 +33.4185813747547 +25.5530773949688 +14.7961619823174 +22.2710574513201 +23.5539874432174 +17.2339815787965 +27.215173252412 +4.06984153366859 +7.51007272621331 +24.7444243500799 +18.0164813754079 +26.6270539113887 +29.4336965143315 +31.1005540675575 +11.7252100463969 +17.064465004608 +20.9502842499826 +16.3850575123207 +19.3528753492232 +20.7846096908265 +33.396205039034 +15.6140674930647 +16.5845482358975 +23.2518118214845 +16.2978466490127 +24.8752690882777 +11.7216140392957 +12.2767246322969 +20.0196562371296 +3.18633753309102 +12.2281691909479 +68.1373455525487 +10.2450106137816 +86.2532974498148 +114.502535214877 diff --git a/buch/papers/reedsolomon/experiments/decodiert.txt b/buch/papers/reedsolomon/experiments/decodiert.txt new file mode 100644 index 0000000..5295e2a --- /dev/null +++ b/buch/papers/reedsolomon/experiments/decodiert.txt @@ -0,0 +1,96 @@ +5.05208333333333 +4.02603841132848 +3.9866906905523 +2.98928833660435 +5.01944413899123 +5.01851886476838 +7.97795274966527 +7.9523893732277 +5.97396514457618 +4.00519657776884 +8.0006276895628 +4.97630831658918 +3.97918030102376 +9.01298821331865 +9.03553822210758 +6.02435577439403 +6.005269315244 +6.00739475784899 +2.02214193521707 +3.02175993431401 +5.00158984940366 +1.98176205240977 +7.97728830439693 +1.98491220960989 +1.98958333333333 +1.98491220960989 +1.97728880273589 +3.98152108172961 +3.00171929847136 +9.02175649397959 +4.02211963444795 +2.00740795901169 +9.00524899981178 +10.0243555198185 +4.03562322003676 +1.01362103081199 +2.97918487756672 +3.97630844288113 +6.00063199465927 +3.00522617023784 +5.97396514457618 +6.95239288504068 +1.97810392013073 +1.01862378300238 +3.0194483612015 +2.98928833660435 +3.9866906905523 +5.02603060999077 +1.05208333333333 +3.02605136876764 +7.9866590265379 +0.0177592928994289 +9.01944131204563 +7.01851125156932 +4.97798278395618 +5.95239757681758 +1.97397894668217 +5.00517880987882 +10.0006251063956 +4.97630831658918 +4.97917756274958 +2.01326692505463 +5.0355927170407 +6.02435577439403 +0.0275599094902566 +0.0115837187254189 +0.0258777610142382 +0.0224618032819705 +0.0441059468994403 +0.0474504002669344 +0.0227694695500614 +0.0271436638090525 +0.0104166666666661 +0.027143663809052 +0.0227694695500605 +0.0474504002669342 +0.04410594689944 +0.0224618032819704 +0.0258777610142386 +0.0115837187254188 +0.027559909490256 +0.0245124379481791 +0.0499782237195213 +0.0401432022864264 +0.023292374765623 +0.0237974288564093 +0.0143895905726623 +0.0271745729691686 +0.0275599094902561 +0.051550167218498 +0.0358255004834538 +0.0247005083663728 +0.0210194725405181 +0.0177592928994299 +0.0261327016093146 +0.0314909067039408 diff --git a/buch/papers/reedsolomon/experiments/empfangen.txt b/buch/papers/reedsolomon/experiments/empfangen.txt new file mode 100644 index 0000000..326dd83 --- /dev/null +++ b/buch/papers/reedsolomon/experiments/empfangen.txt @@ -0,0 +1,96 @@ +305 +114.502535214877 +86.2532974498148 +10.2450106137816 +68.1373455525487 +12.2281691909479 +4.75208293424194 +20.0196562371296 +12.2767246322969 +11.7216140392957 +24.8752690882777 +16.2978466490127 +23.2518118214845 +16.5845482358975 +15.6140674930647 +33.396205039034 +20.7846096908265 +19.3528753492232 +16.3850575123207 +20.9502842499826 +19.0535931901409 +11.7252100463969 +31.1005540675575 +29.4336965143315 +26.6270539113887 +18.0164813754079 +24.7444243500799 +7.51007272621331 +4.06984153366859 +27.215173252412 +17.2339815787965 +23.5539874432174 +22.2710574513201 +14.7961619823174 +25.5530773949688 +33.4185813747547 +11.5478676394508 +21.0691619228239 +28.7948800016184 +12.3795084046074 +17.0082930449459 +19.7473571196866 +18.4490385219626 +12.2195365467659 +7.58568158110485 +6.02300839250873 +14.565530706253 +3.78959213976527 +21 +3.78959213976527 +14.565530706253 +6.02300839250873 +7.58568158110485 +12.2195365467659 +18.4490385219626 +19.7473571196866 +17.0082930449459 +12.3795084046074 +28.7948800016184 +21.0691619228239 +11.5478676394508 +33.4185813747547 +25.5530773949688 +14.7961619823174 +22.2710574513201 +23.5539874432174 +17.2339815787965 +27.215173252412 +4.06984153366859 +7.51007272621331 +24.7444243500799 +18.0164813754079 +26.6270539113887 +29.4336965143315 +30.3915028428898 +11.7252100463969 +17.064465004608 +20.9502842499826 +16.3850575123207 +19.3528753492232 +20.7846096908265 +33.396205039034 +15.6140674930647 +16.5845482358975 +23.2518118214845 +16.2978466490127 +24.8752690882777 +11.7216140392957 +12.2767246322969 +20.0196562371296 +3.18633753309102 +12.2281691909479 +68.1373455525487 +10.2450106137816 +86.2532974498148 +114.502535214877 diff --git a/buch/papers/reedsolomon/experiments/f.m b/buch/papers/reedsolomon/experiments/f.m index 6bdc741..5e4da85 100644 --- a/buch/papers/reedsolomon/experiments/f.m +++ b/buch/papers/reedsolomon/experiments/f.m @@ -1,8 +1,8 @@ -# -# f.m -- Reed-Solomon-Visualisierung mit FFT -# -# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -# +% +% f.m -- Reed-Solomon-Visualisierung mit FFT +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + N = 64; b = 32; l = N + b; @@ -59,3 +59,15 @@ plot(locator); xlim([1, l]); title("Locator"); pause() + +writematrix(abs(signal), 'signal.txt') +writematrix(abs(codiert), 'codiert.txt') +writematrix(fehler, 'fehler.txt') +writematrix(abs(empfangen), 'empfangen.txt') +writematrix(abs(decodiert), 'decodiert.txt') +writematrix(abs(syndrom), 'syndrom.txt') +writematrix(locator, 'locator.txt') + + + + diff --git a/buch/papers/reedsolomon/experiments/fehler.txt b/buch/papers/reedsolomon/experiments/fehler.txt new file mode 100644 index 0000000..b8f9afb --- /dev/null +++ b/buch/papers/reedsolomon/experiments/fehler.txt @@ -0,0 +1,96 @@ +0 +0 +0 +0 +0 +0 +2 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +2 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +1 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 diff --git a/buch/papers/reedsolomon/experiments/locator.txt b/buch/papers/reedsolomon/experiments/locator.txt new file mode 100644 index 0000000..421d36e --- /dev/null +++ b/buch/papers/reedsolomon/experiments/locator.txt @@ -0,0 +1,96 @@ +0.0301224340566959 +0.141653026854878 +0.138226631799375 +0.0339903276086926 +0.310585462557496 +0.551427312631386 +0.628514858396816 +0.511023862515591 +0.275861355940448 +0.0502396354182231 +0.0901855025475772 +0.110759344849757 +0.0684618905062958 +0.0362855426992255 +0.0697096919781522 +0.109288539370249 +0.0923187999496619 +0.0512198536768151 +0.274192386987786 +0.513496149536541 +0.633154426602464 +0.553283743533939 +0.307840573214511 +0.0341664350328389 +0.140270857956999 +0.138527177682829 +0.0296375477361526 +0.0816962563186064 +0.0944383203811072 +0.0263932110686224 +0.058588134840207 +0.0737117341600011 +0.0239973937701886 +0.0464215468420024 +0.0616218854220982 +0.0221963086695035 +0.0390764778127614 +0.0537637218396927 +0.0208333333333355 +0.0343107696069015 +0.0483441215964522 +0.0198077862118787 +0.0311207395968709 +0.0444955089373439 +0.0190533549944134 +0.0290049795038704 +0.0417536642697542 +0.0185261550443044 +0.0277059929762204 +0.0398606084144781 +0.0181978813094801 +0.0271098219177536 +0.0386836665079658 +0.018051861104682 +0.0272138992557153 +0.0381891287148298 +0.0180809085252426 +0.0281418959420076 +0.0384596362516644 +0.0182864418432244 +0.0302250788423177 +0.0397874837986374 +0.0186786556701704 +0.0342489348284176 +0.0429932815348636 +0.0192777878591794 +0.0422808966932026 +0.0506815964680558 +0.0201167847752232 +0.0615048274405276 +0.074495389450843 +0.0212460545964937 +0.142602265816219 +0.273502052865438 +0.325309673287598 +0.272705389655347 +0.149074257381343 +0.0247199397628717 +0.0680137859566989 +0.0753882708734869 +0.0273637831604916 +0.0407867704453288 +0.0632964886441987 +0.0309749128751131 +0.0315202035072016 +0.0627625211892194 +0.0360843918243526 +0.0279492055149482 +0.0677921493367224 +0.0437167157553051 +0.0270640150996341 +0.0783380025231665 +0.0561293738314322 +0.0278742033265804 +0.0981443889498686 +0.0794543457386637 diff --git a/buch/papers/reedsolomon/experiments/signal.txt b/buch/papers/reedsolomon/experiments/signal.txt new file mode 100644 index 0000000..202dd02 --- /dev/null +++ b/buch/papers/reedsolomon/experiments/signal.txt @@ -0,0 +1,96 @@ +5 +4 +4 +3 +5 +5 +8 +8 +6 +4 +8 +5 +4 +9 +9 +6 +6 +6 +2 +3 +5 +2 +8 +2 +2 +2 +2 +4 +3 +9 +4 +2 +9 +10 +4 +1 +3 +4 +6 +3 +6 +7 +2 +1 +3 +3 +4 +5 +1 +3 +8 +0 +9 +7 +5 +6 +2 +5 +10 +5 +5 +2 +5 +6 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 diff --git a/buch/papers/reedsolomon/experiments/syndrom.txt b/buch/papers/reedsolomon/experiments/syndrom.txt new file mode 100644 index 0000000..59b9dc4 --- /dev/null +++ b/buch/papers/reedsolomon/experiments/syndrom.txt @@ -0,0 +1,96 @@ +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0.0275599094902566 +0.0115837187254189 +0.0258777610142382 +0.0224618032819705 +0.0441059468994403 +0.0474504002669344 +0.0227694695500614 +0.0271436638090525 +0.0104166666666661 +0.027143663809052 +0.0227694695500605 +0.0474504002669342 +0.04410594689944 +0.0224618032819704 +0.0258777610142386 +0.0115837187254188 +0.027559909490256 +0.0245124379481791 +0.0499782237195213 +0.0401432022864264 +0.023292374765623 +0.0237974288564093 +0.0143895905726623 +0.0271745729691686 +0.0275599094902561 +0.051550167218498 +0.0358255004834538 +0.0247005083663728 +0.0210194725405181 +0.0177592928994299 +0.0261327016093146 +0.0314909067039408 diff --git a/buch/papers/reedsolomon/idee.tex b/buch/papers/reedsolomon/idee.tex index 28b65bd..5e91559 100644 --- a/buch/papers/reedsolomon/idee.tex +++ b/buch/papers/reedsolomon/idee.tex @@ -31,7 +31,8 @@ Der Leser/Empfänger weiss, den Grad des Polynoms und dessen Werte übermittelt \begin{figure} \centering - \includegraphics[width=0.5\textwidth]{papers/reedsolomon/images/polynom2.pdf} + %\includegraphics[width=0.5\textwidth]{papers/reedsolomon/images/polynom2} + %\input{papers/reedsolomon/images/polynom2.tex} \caption{Polynom \eqref{reedsolomon:equation1}} \label{fig:polynom} \end{figure} @@ -43,7 +44,7 @@ Hat es Fehler in der Übertragunge gegeben, kann man diese erkennen, da alle Punkte, die korrekt sind, auf dem Polynom liegen müssen. Ab wie vielen Fehler ist das Polynom nicht mehr erkennbar beim Übertragen von 7 Punkten? Bei 2 Fehlern kann man noch eindeutig bestimmen, dass das Polynom mit 4 Punkten, -gegenüber dem mit 5 Punkten falsch liegt. +gegenüber dem mit 5 Punkten falsch liegt.\ref{fig:polynom} Werden es mehr Fehler kann nur erkennt werden, dass das Polynom nicht stimmt. Das orginale Polynom kann aber nicht mehr gefunden werden. Dafür sind mehr übertragene Werte nötig. @@ -58,6 +59,7 @@ die Entschlüsselt werden sollen, brauchen die gleiche Anzahl an Polynomgraden, Für die Anzahl an Übertragungspunkte, muss bestimmt werden wieviel Fehler erkennt und korrigiert werden sollen. Mit Hilfe der Tabelle, sieht man das es bei $t$ Fehlern und $k$ Nutzlast Zahlen, $k+2t$ Punkte übertragen werden müssen. + \begin{center} \begin{tabular}{ c c c } \hline @@ -71,6 +73,7 @@ $k+2t$ Punkte übertragen werden müssen. \hline \end{tabular} \end{center} + Ein toller Nebeneffekt ist das dadurch auch $2t$ Fehler erkannt werden. Um zurück auf unser Beispiel zu kommen, können von den 7 Übertragungspunkten bis zu $2t = 2\cdot2 = 4 $ Punkten falsch liegen diff --git a/buch/papers/reedsolomon/images/polynom2.tex b/buch/papers/reedsolomon/images/polynom2.tex index be9a65e..4fdfc81 100644 --- a/buch/papers/reedsolomon/images/polynom2.tex +++ b/buch/papers/reedsolomon/images/polynom2.tex @@ -1,21 +1,21 @@ % polynome2 %------------------- -\documentclass[tikz]{standalone} -\usepackage{amsmath} -\usepackage{times} -\usepackage{txfonts} -\usepackage{pgfplots} -\usepackage{csvsimple} -\usetikzlibrary{arrows,intersections,math} +%\documentclass[tikz]{standalone} +%\usepackage{amsmath} +%\usepackage{times} +%\usepackage{txfonts} +%\usepackage{pgfplots} +%\usepackage{csvsimple} +%\usetikzlibrary{arrows,intersections,math} \newcommand{\teiler}{40} -\begin{document} -% 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})$ +%\begin{document} + 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})$ \begin{tikzpicture}[>=latex,thick] @@ -48,4 +48,4 @@ \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} +%\end{document} diff --git a/buch/papers/reedsolomon/packages.tex b/buch/papers/reedsolomon/packages.tex index 3643731..4b1ee68 100644 --- a/buch/papers/reedsolomon/packages.tex +++ b/buch/papers/reedsolomon/packages.tex @@ -8,3 +8,5 @@ % following example %\usepackage{packagename} +\usepackage{pgfplots} + |