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#LyX 2.3 created this file. For more info see http://www.lyx.org/
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\begin_body
\begin_layout Title
\series bold
Zusammenfassung INCO
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\begin_layout Part
Informationstheorie
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\begin_layout Section
Formeln
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\begin_layout Description
Informationsgehalt:
\begin_inset Formula $I(X_{n})=\log_{2}\frac{1}{P(X_{n})}$
\end_inset
\end_layout
\begin_layout Description
Entropie
\begin_inset Formula $H(X)=\overset{N-1}{\underset{n=0}{\sum}}P(x_{n})\cdot\log_{2}\frac{1}{P(x_{n})}$
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\end_layout
\begin_layout Section
Glossar
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\begin_layout Description
\series bold
Discrete
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\end_inset
Memoryless
\begin_inset space ~
\end_inset
Source
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\end_inset
(DMS)
\series default
Quelle, welche einzelne, voneinander unabhängige, Ereignisse liefert.
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Binary
\begin_inset space ~
\end_inset
Memoryless
\begin_inset space ~
\end_inset
Source
\begin_inset space ~
\end_inset
(BMS) DMS, die nur zwei verschiedene ereignisse erzeugt.
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\begin_layout Part
Digitaltechnik
\end_layout
\begin_layout Section
Boolische Operationen
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\begin_layout Subsection
Operatoren
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\begin_layout Standard
\begin_inset Tabular
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Operator
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Zeichen
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NOT
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!A
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,¬A,A'
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AND
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&
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,∩,∧
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OR
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#
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,∪,∨
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$
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\end_layout
\begin_layout Subsection
Regeln
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\begin_layout Standard
\noindent
A & A = A
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\begin_layout Standard
\noindent
A # A = A
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\begin_layout Standard
\noindent
!(!(A)) = A
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\begin_layout Standard
\noindent
A & (A # B) = A
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\begin_layout Standard
\noindent
A # (A & B) = A
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\noindent
A & (!A # B) = A & B
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\begin_layout Standard
\noindent
A # (!A & B) = A # B
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\begin_layout Standard
\noindent
A # (B & C) = (A # B) & (A # C)
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\begin_layout Standard
\noindent
Umwandlung negierter Ausdrücke:
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\begin_layout Standard
\noindent
!(A & B) = !A # !B
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\begin_layout Standard
\noindent
!(A # B) = !A & !B
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\begin_layout Section
Glossar
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\begin_layout Description
Halbadierer Ein Addierer der nur ein Bit addiert.
Er kann keinen Übertrag addieren, es kann jedoch ein Übertrag enstehen.
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\end_layout
\begin_layout Description
Volladierer Ein Addierer der den Übertrag aus der vorher gehenden Stufe
addieren kann.
Er wird für alle Bits 0 < k ≤ N im N-Bit Addierer verwendet.
\end_layout
\begin_layout Description
D-Flip-Flop Ein Speicher, welcher ein Bit festhalten kann.
Das jeweils am Dateneingang anliegende Bit wird bei jeder ansteigenden
Flanke des Clock Signals an den Ausgang weitergegeben.
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\begin_layout Description
Schieberegister Eine Sequenzielle Schaltung aus Flip-Flops.
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\begin_layout Description
Disjunktive
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Normalform Mit OR zusammengefasste zutreffende Zeilen aus der Wahrheitstabelle
z.B.
(A&B) # (B&C) # (X&Y)
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Zahlensysteme
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Umwandlungen
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Zehner- zu Zweiersystem
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\noindent
6 : 2 = 3 Rest
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0
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| 3 : 2 = 1 Rest
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1
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| 1 : 2 = 0 Rest
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1
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\begin_layout Standard
\noindent
Ergebnis:
\series bold
110
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\begin_layout Subsection
\noindent
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Zehner- zu Sechszehnersystem
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\begin_layout Standard
\noindent
100 : 16 = 6 Rest
\series bold
4
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| 6 : 16 = 0 Rest
\series bold
6
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\begin_layout Standard
\noindent
Ergebnis:
\series bold
64
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\begin_layout Subsection
\noindent
\series bold
Dezimal- ins Zweiersystem
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\begin_layout Standard
\noindent
\begin_inset Formula $0.6875\cdot2=0.3750+\boldsymbol{1}$
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\begin_layout Standard
\noindent
\begin_inset Formula $0.3750\cdot2=0.7500+\boldsymbol{0}$
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\begin_layout Standard
\noindent
\begin_inset Formula $0.7500\cdot2=0.5000+\boldsymbol{1}$
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\begin_layout Standard
\noindent
\begin_inset Formula $0.5000\cdot2=0.0000+\boldsymbol{1}$
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\begin_layout Standard
\noindent
Ergebnis:
\series bold
0.1011
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\begin_layout Section
Darstellung von Zahlen
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\begin_layout Subsection
Negative Zahlen
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\begin_layout Standard
Um negative Zahlen darzustellen werden Komplemente gebildet.
Beim 10-er System wird zuerst das
\series bold
9-er Komplement
\series default
gebildet.
Durch das hinzufügen von
\series bold
eins
\series default
an der letzten Stelle wird das
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10-er Komplement
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gebildet.
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...
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9 9 9 9 9 8
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9
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Im Binärsystem wird zuerst das 1-er Komplement gebildet und anschliessend
ein Bit an der letzten Stelle hinzugefügt um das 2-er Komplement zu erhalten.
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\begin_inset Formula $5.25_{d}$
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.
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\begin_layout Standard
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0 1
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...
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1 0
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2-er Komplement
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1 1 1 0 1 0.1
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1
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Darstellbare Zahlen
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status open
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\backslash
label{zahlentabelle}
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Maximal darstellbare Zahl
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8 Bit
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16 Bit
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32 Bit
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64 Bit
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128 Bit
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\begin_layout Section
Rechnen
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Addition
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0111
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
7
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0011
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1000
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
8
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0100
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1001
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
9
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Subsection
Darstellung
\end_layout
\begin_layout Standard
\begin_inset Graphics
filename Images/BCD.png
lyxscale 60
scale 40
\end_inset
\end_layout
\begin_layout Section
Codes
\end_layout
\begin_layout Subsection
Ascii Tabelle
\end_layout
\begin_layout Standard
\begin_inset Graphics
filename Images/Ascii_Table.png
lyxscale 50
scale 40
\end_inset
\end_layout
\begin_layout Subsection
UTF-8 Codierung
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="3">
<features tabularvalignment="middle">
<column alignment="left" valignment="top" width="0pt">
<column alignment="left" valignment="top" width="0pt">
<column alignment="left" valignment="top" width="0pt">
<row>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
Unicode-Bereich (hex)
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
UTF-8 Codierung
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
Code-Bits
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
0000’0000 - 0000’007F
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
0xxxxxxx
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
7
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
0000’0080 - 0000’07FF
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
110xxxxx 10xxxxxx
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
11 (5 + 1*6)
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
0000’0800 - 0000’FFFF
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
1110xxxx 10xxxxxx 10xxxxxx
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
11 (5 + 1*6)
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
0001’0000 - 0010’FFFF
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
11110xxx 10xxxxxx 10xxxxxx 10xxxxxx
\end_layout
\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\size tiny
21 (3 + 3*6)
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Section
Definitionen
\end_layout
\begin_layout Description
Gray
\begin_inset space ~
\end_inset
Code Benachbarte Codeworte unterscheiden sich nur in einem Bit.
\end_layout
\begin_layout Description
ASCII
\begin_inset space ~
\end_inset
Code Älterer 7 Bit (heute 8 Bit) langer Zeichencode.
Es gibt mehrere Zeichensätze.
\end_layout
\begin_layout Description
Unicode Moderner Zeichensatz, welcher alle bekannten Zeichen zusammenfasst.
\end_layout
\begin_layout Description
UTF-8 Ein Code mit variabler Breite, es werden 1 bis 4 Bytes verwendet,
um die Code Points zu codieren.
Für ASCII-Zeichen (die untersten 128 Code Points, von 0 bis 127) wird ein
Byte verwendet.
Für alle anderen Code Points sind mehrere Bytes nötig.
\end_layout
\begin_layout Description
UTF-16 für die Codierung entweder 2 oder 4 Bytes verwendet.
Für die Zeichen der BMP mit den Code Points von 0000h bis FFFF h genügen
2 Bytes.
\end_layout
\begin_layout Description
Endianness Little-endian heisst, dass das niederstwertige Byte zuerst geschriebe
n (oder übertragen) wird, das “kleine” Ende wird also vorangeschickt.
Die andere Variante heisst big-endian, hier wird das höchstwertige Byte
zuerst gespeichert (also an die niedrigste Adresse).
\end_layout
\begin_layout Description
Überlauf Überläufe passieren, wenn bei einer Verrechnung von zwei Zahlen
die obere oder untere maximal darstellbare Zahl (siehe
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
ref{zahlentabelle}
\end_layout
\end_inset
) überschritten wird.
Der Prozessor setzt in diesem Fall ein Borrow (Unterläuf) oder Carry (Überläuf)
Flag.
\end_layout
\begin_layout Part
Quellencodierung
\end_layout
\begin_layout Section
Definitionen
\end_layout
\begin_layout Description
Codewortlänge Die Codewortlänge
\begin_inset Formula $\boldsymbol{\ell}_{\boldsymbol{n}}$
\end_inset
bezieht sich auf das Codewort
\begin_inset Formula $\boldsymbol{c}_{\boldsymbol{n}}$
\end_inset
eines bestimmten Symbols
\begin_inset Formula $\boldsymbol{x}_{\boldsymbol{n}}$
\end_inset
und gibt an,
\series bold
aus wievielen Bits das Codewort besteht.
\end_layout
\begin_layout Description
Redundanz Solange die Redundanz R eines Codes grösser als null ist, kann
noch verlustfrei komprimiert werden.
Falls R ≤ 0, so kann nur noch verlustbehaftet komprimiert werden.
\end_layout
\begin_layout Description
Lempel
\begin_inset space ~
\end_inset
Ziv
\begin_inset space ~
\end_inset
Codes Jede Sequenz von Quellensymbolen wird durch einen Index in ein Wörterbuch
ersetzt.
\end_layout
\begin_layout Description
Präfixfrei Ein Code ist Präfixfrei, wenn die Codeworte in einem Bitstrom
immer eindeutig identifiziert werden können (z.B.
Hoffman-Code)
\end_layout
\begin_layout Section
Formeln
\end_layout
\begin_layout Description
Mittlere
\begin_inset space ~
\end_inset
Codewortlänge
\begin_inset Formula $L=\underset{n=0}{\overset{n-1}{\sum}}p(x_{n})\cdot\ell_{n}$
\end_inset
in
\begin_inset Formula $\frac{Bit}{Symbol}$
\end_inset
\end_layout
\begin_layout Description
Redundanz
\begin_inset Formula $R=L-H$
\end_inset
in
\begin_inset Formula $\frac{Bit}{Symbol}$
\end_inset
\end_layout
\begin_layout Section
Codierungen
\end_layout
\begin_layout Subsection
Lauflängencodierung
\end_layout
\begin_layout Standard
Ketten von identischen Zeichen werden zusammengefasst.
Für die Kompressionsrate gilt
\begin_inset Formula $\frac{Komprimierte\,Bits}{Originale\,Bits}$
\end_inset
\begin_inset Newline newline
\end_inset
\end_layout
\begin_layout Standard
...TERRRRRRRRRMAUIIIIIIIIIIIIIIIIIWQCSSSSSSSSSSL...
\end_layout
\begin_layout Standard
...TE
\series bold
(9xR)
\series default
MAU
\series bold
(17xI)
\series default
WQC
\series bold
(10xS)
\series default
L...
\begin_inset Newline newline
\end_inset
\end_layout
\begin_layout Standard
Um noch effizienter zu sein verwendet man einen Marker, welcher bereits
im Zeichensatz vorhanden ist, in folgendem Beispiel ist das A.
\end_layout
\begin_layout Standard
...TE
\series bold
A09R
\series default
M
\series bold
A01A
\series default
U
\series bold
A17I
\series default
WQC
\series bold
A10S
\series default
L...
\begin_inset Newline newline
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Graphics
filename Images/Bild_Lauflaengencodierung.png
scale 35
\end_inset
\end_layout
\begin_layout Standard
(
\series bold
24
\series default
,
\series bold
11
\series default
, 65, 1, 23, 2, 8, 17, 7, 18, 6, 17, 21, 2, 22, 1, 54 )
\begin_inset Newline newline
\end_inset
\end_layout
\begin_layout Standard
Für die Lauflängencodierung eines Bildes wird folgendermassen vorgegangen:
\end_layout
\begin_layout Enumerate
Definiere vorgängig die Bitbreite des Pixelzählers.
\end_layout
\begin_layout Enumerate
Definiere vorgängig die Pixelfarbe mit der begonnen wird.
\end_layout
\begin_layout Enumerate
Serialisierung des Bildes.
• Falls der erste Pixel nicht die vordefinierte Farbe hat, setze die erste
Pixelzahl auf null.
\end_layout
\begin_layout Enumerate
Zähle jeweils alle Pixel gleicher Farbe bis zum nächsten Farbwechsel.
\end_layout
\begin_layout Enumerate
Sollte eine Pixelzahl grösser werden als das Maximum des Zählers, so teile
die Zahl auf, wie oben gezeigt.
\end_layout
\begin_layout Standard
Soll das Bild zeilenweise codiert werden, muss das Zeilenende jeweils mit
einem reservierten Wert signalisiert werden (normalerweise der max.
Wert).
\end_layout
\begin_layout Subsection
Huffman Codes
\end_layout
\begin_layout Standard
Häufige Symbole erhalten kurze Codes, seltene Symbole erhalten lange Codes.
\end_layout
\begin_layout Standard
\begin_inset Graphics
filename Images/Huffman-Baum.png
scale 40
\end_inset
\end_layout
\begin_layout Standard
Bei einer kleinen Anzahl Codes kann es Sinn machen, Doppelsymbole zu bilden
um die Redundanz zu verringern.
Bei doppelsymbolen rechnet man mit
\begin_inset Formula $\frac{Bit}{\boldsymbol{2\,Symbole}}$
\end_inset
\end_layout
\begin_layout Enumerate
Ordne alle Symbole nach aufsteigenen Auftretenswahrscheinlichkeiten auf
einer Zeile.
Dies sind die Blätter des Huffman-Baums.
Gibt es Symbole mit gleichen Wahrscheinlichkeiten, so spielt die Reihenfolge
unter ihnen keine Rolle.
\end_layout
\begin_layout Enumerate
Notiere unter jedes Blatt seine Wahrscheinlichkeit.
\end_layout
\begin_layout Enumerate
Schliesse die beiden Blätter mit der kleinsten Wahrscheinlichkeit an einer
gemeinsamen Astga- bel an.
Ordne dem Ast die Summe der Wahrscheinlichkeiten der beiden Blätter zu.
Gibt es mehrere mögliche Kombinationen von Blättern mit den kleinsten Wahrschei
nlichkeiten, so spielt es keine Rolle, welche man davon auswählt.
\end_layout
\begin_layout Enumerate
Wiederhole Punkt 3 mit Blättern und Ästen so lange, bis nur noch der Stamm
des Baums übrig bleibt.
\end_layout
\begin_layout Enumerate
Nun wird festgelegt, ob bei jeder Astgabel der linke Zweig eine 0 oder eine
1 erhält.
Der rechte Zweig erhält dann das Komplement.
\end_layout
\begin_layout Enumerate
Nun werden auf dem Pfad vom Stamm zu jedem Blatt die Nullen und Einsen ausgelese
n und von links nach rechts nebeneinander geschrieben.
Dies sind die Huffman-Codeworte.
\end_layout
\begin_layout Subsubsection
LZ77
\end_layout
\begin_layout Standard
Bei LZ77 werden Tokens in der Form (Offset, Länge, Zeichen) verwendet.
\begin_inset Newline newline
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Graphics
filename Images/LZ77.png
scale 50
\end_inset
\end_layout
\begin_layout Standard
(0, 0, A) (0, 0, M) (2, 2, M) (4, 2, A) (6, 4, T)
\begin_inset Newline newline
\end_inset
\end_layout
\begin_layout Standard
Nehmen wir an, es handle sich um Zeichen, die
\series bold
je 1 Byte
\series default
belegen .
Die ursprünglichen
\series bold
13 Zeichen
\series default
belegen demnach total
\series bold
13 · 8 = 104 Bit
\series default
.
Im Token kommt ebenfalls ein derartiges Zeichen vor.
Zusätzlich muss der Offset gross genug sein, damit der
\series bold
jede Position (1 bis 10) im Such-Buffer
\series default
bezeichnen kann.
Hierfür sind
\series bold
4 Bit
\series default
nötig.
Die Längenangabe muss den gesamten Vorschau-Buffer abdecken können, ohne
das letzte Zeichen, das bestenfalls die Funktion eines zusätzlichen Zeichens
haben kann.
Man muss also bis
\series bold
4 Zählen
\series default
können, wozu
\series bold
3 Bit
\series default
nötig sind.
Ein Token besteht demnach aus total
\series bold
4 + 3 + 8 = 15 Bit.
\series default
Die fünf Token umfassen gesamthaft 5 · 15 = 75 Bit.
\end_layout
\begin_layout Standard
Der Decoder empfängt die oben genannten Token und decodiert diese mithilfe
des Suchbuffers.
\end_layout
\begin_layout Subsubsection
LZ78
\end_layout
\begin_layout Standard
Der LZ78 baut ein eigenes Wörterbuch auf.
Die Token bestehen aus (Index, Zeichen).
\begin_inset Newline newline
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Tabular
<lyxtabular version="3" rows="6" columns="6">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Index
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
String
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Token
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Index
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
String
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Token
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
-
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
5
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
AA
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(1, A)
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
A
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(0, A)
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
6
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
AMM
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(3, M)
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
M
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(0, M)
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
7
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
MT
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(2, T)
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
AM
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(1, M)
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
8
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
AAT
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(5, T)
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
MM
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
(2, M)
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
9
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
...
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
...
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Subsection
LZW
\end_layout
\begin_layout Standard
Das LZW-Verfahren16 ist eine Weiterentwicklung von LZ78 mit dem Ziel, den
Token zu verkleinern.
Der LZW-Token besteht in der Folge nur noch aus einem Wörterbuch-Index.
Das Wörterbuch von LZW ist vorinitialisiert mit allen Zeichencodes von
0 bis 255 (einschliesslich den ASCII-Zeichen im Bereich 0 bis 127).
\begin_inset Newline newline
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Graphics
filename Images/LZW.png
scale 60
\end_inset
\end_layout
\end_body
\end_document
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