Aufgaben:Exercise 2.10: Shannon-Fano Coding - Revision history

Hwang at 15:05, 1 November 2022

2022-11-01T15:05:53Z

Guenter at 12:33, 12 August 2021

2021-08-12T12:33:03Z

Guenter at 12:20, 12 August 2021

2021-08-12T12:20:43Z

Guenter at 12:13, 12 August 2021

2021-08-12T12:13:57Z

Guenter at 12:10, 12 August 2021

2021-08-12T12:10:39Z

Guenter at 12:09, 12 August 2021

2021-08-12T12:09:33Z

Noah at 19:59, 6 August 2021

2021-08-06T19:59:08Z

Noah at 13:44, 6 August 2021

2021-08-06T13:44:34Z

Noah at 10:40, 6 August 2021

2021-08-06T10:40:17Z

Guenter at 13:03, 16 July 2021

2021-07-16T13:03:19Z

@@ Line 25: / Line 25: @@
 : &nbsp; &nbsp; &nbsp; $\rm A$ &nbsp; &#8594; &nbsp; <b>111</b>, &nbsp; &nbsp; $\rm B$ &nbsp; &#8594; &nbsp; <b>10</b>, &nbsp; &nbsp; $\rm C$ &nbsp; &#8594; &nbsp; <b>0</b>, &nbsp; &nbsp; $\rm D$ &nbsp; &#8594; &nbsp; <b>110</b>.
-This gives the following for the average codeword length:
+This gives the following for the average code word length:
 :$$L_{\rm M} = 0.4 \cdot 1 + 0.3 \cdot 2 + (0.2 + 0.1) \cdot 3 = 1.9\,\,{\rm bit/source\hspace{0.15cm}symbol}\hspace{0.05cm}.$$
@@ Line 65: / Line 65: @@
 <quiz display=simple>
-{What is the average codeword length&nbsp; $L_{\rm M}$&nbsp; for the&nbsp; <u>Huffman code</u>?
+{What is the average code word length&nbsp; $L_{\rm M}$&nbsp; for the&nbsp; <u>Huffman code</u>?
 |type="{}"}
 $L_{\rm M}\ = \ $ { 2.54 3% } $\ \rm bit/source\hspace{0.15cm}symbol$
@@ Line 84: / Line 84: @@
-{What is the average codeword length&nbsp; $L_{\rm M}$&nbsp; for&nbsp; <u>Shannon&ndash;Fano code</u>?
+{What is the average code word length&nbsp; $L_{\rm M}$&nbsp; for&nbsp; <u>Shannon&ndash;Fano code</u>?
 |type="{}"}
 $L_{\rm M}\ = \ $ { 2.58 3% } $\ \rm bit/source\hspace{0.15cm}symbol$

← Older revision		Revision as of 12:33, 12 August 2021
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−	{{quiz-Header\|Buchseite=~~Informationstheorie~~/~~Weitere Quellencodierverfahren~~	+	{{quiz-Header\|Buchseite=Information_Theory/Further_Source_Coding_Methods
	}}		}}

@@ Line 102: / Line 102: @@
 {{ML-Kopf}}
 '''(1)'''&nbsp; For the given Huffman code one obtains:
-:$$L_{\rm M} = 0.4 \cdot 1 +  (0.17 + 0.14 + 0.10) \cdot 3  + 0.09 \cdot 4 + 0.05 \cdot 5 + (0.03 + 0.02) \cdot 6 =\underline{ 2.54 \,\,{\rm bit/source\:symbol}}\hspace{0.05cm}. $$
+:$$L_{\rm M} = 0.4 \cdot 1 +  (0.17 + 0.14 + 0.10) \cdot 3  + 0.09 \cdot 4 + 0.05 \cdot 5 + (0.03 + 0.02) \cdot 6 =\underline{ 2.54 \,\,{\rm bit/source\hspace{0.15cm}symbol}}\hspace{0.05cm}. $$
@@ Line 110: / Line 110: @@
 *All sorted characters must be divided into two groups in such a way that the group probabilities are as equal as possible. For the first step:
 :$${\rm Pr}(\boldsymbol{\rm BE})  = 0.57\hspace{0.05cm}, \hspace{0.2cm}{\rm Pr}(\boldsymbol{\rm DAHGFC})  = 0.43  \hspace{0.05cm}.$$
 *With the distribution according to solution suggestion 3, the equal distribution would be achieved even less:
 :$${\rm Pr}(\boldsymbol{\rm B})  = 0.40\hspace{0.05cm}, \hspace{0.2cm}{\rm Pr}(\boldsymbol{\rm EDAHGFC})  = 0.60  \hspace{0.05cm}.$$
@@ Line 127: / Line 125: @@
 '''(4)'''&nbsp; Using the result of sub-task&nbsp; '''(3)'''&nbsp;, we get:
-:$$L_{\rm M}= (0.40 + 0.17) \cdot 2  + (0.14 + 0.10 + 0.09) \cdot 3 + 0.05 \cdot 4 + (0.03 + 0.02) \cdot 5 =\underline{ 2.58 \,\,{\rm bit/source\:symbol}}\hspace{0.05cm}. $$
+:$$L_{\rm M}= (0.40 + 0.17) \cdot 2  + (0.14 + 0.10 + 0.09) \cdot 3 + 0.05 \cdot 4 + (0.03 + 0.02) \cdot 5 =\underline{ 2.58 \,\,{\rm bit/source\hspace{0.15cm}symbol}}\hspace{0.05cm}. $$
@@ Line 133: / Line 131: @@
 '''(5)'''&nbsp; <u>Statements 2 and 3</u> are correct:
 *In the present example, Shannon-Fano results in a less favourable value than Huffman.
-*In most cases &ndash; including the example on the information page &ndash; Huffman and Shannon-Fano result in an equivalent code and thus also the same average code word length.
+*In most cases &ndash; including the example on the information page &ndash;&nbsp; "Huffman"&nbsp; and&nbsp; "Shannon-Fano"&nbsp; result in an equivalent code and thus also to the same average code word length.
 *Shannon-Fano, on the other hand, never delivers a more effective code than Huffman.
 {{ML-Fuß}}

@@ Line 70: / Line 70: @@
-{What happens in the first step of&nbsp; <u>Shannon&ndash;Fano coding</u>?&nbsp; ''Hint'':&nbsp; All other symbols are grouped together in the second group.
+{What happens in the first step of&nbsp; <u>Shannon&ndash;Fano coding</u>?&nbsp; <u>Hint</u>:&nbsp; All other symbols are grouped together in the second group.
-|type="[]"}
+|type="()"}
 - &nbsp; $\rm A$&nbsp; and&nbsp; $\rm B$&nbsp; are combined into the first group.
 + &nbsp; $\rm B$&nbsp; and&nbsp; $\rm E$&nbsp; are combined into the first group.
@@ Line 79: / Line 79: @@
 {Which assignments result for the&nbsp; <u>Shannon&ndash;Fano algorithm</u>?
 |type="[]"}
-+ The character&nbsp; $\rm A$&nbsp; is binary coded with&nbsp; <b>010</b>&nbsp;.
++ The character&nbsp; $\rm A$&nbsp; is binary encoded with&nbsp; <b>010</b>&nbsp;.
-+ The character&nbsp; $\rm B$&nbsp; is binary coded with&nbsp; <b>11</b>&nbsp;.
++ The character&nbsp; $\rm B$&nbsp; is binary encoded with&nbsp; <b>11</b>&nbsp;.
-+ The character&nbsp; $\rm C$&nbsp; is binary coded with&nbsp; <b>00110</b>&nbsp;.
++ The character&nbsp; $\rm C$&nbsp; is binary encoded with&nbsp; <b>00110</b>&nbsp;.
@@ Line 91: / Line 91: @@
 {Which statements are true for arbitrary probabilities?
 |type="[]"}
-- $L_{\rm M}$&nbsp; could be smaller for "Shannon&ndash;Fano" than for "Huffman".
+- $L_{\rm M}$&nbsp; could be smaller for&nbsp; "Shannon&ndash;Fano"&nbsp; than for&nbsp; "Huffman".
-+ $L_{\rm M}$&nbsp; could be larger at "Shannon&ndash;Fano" than at "Huffman".
++ $L_{\rm M}$&nbsp; could be larger at&nbsp; "Shannon&ndash;Fano"&nbsp; than at&nbsp; "Huffman".
-+ $L_{\rm M}$&nbsp; could be the same for "Shannon&ndash;Fano" and "Huffman".
++ $L_{\rm M}$&nbsp; could be the same for&nbsp; "Shannon&ndash;Fano"&nbsp; and&nbsp; "Huffman".

@@ Line 55: / Line 55: @@
 Hints:
-*The assignment belongs to the chapter&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren|Other source coding methods]].
+*The assignment belongs to the chapter&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren|Further source coding methods]].
 *In particular, reference is made to the page&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren#The_Shannon-Fano_algorithm|The Shannon-Fano algorithm]].
 *To check your results, please refer to the (German language) SWF module&nbsp; [[Applets:Huffman_Shannon_Fano|Coding according to Huffman and Shannon/Fano]].

@@ Line 4: / Line 4: @@
 [[File:P_ID2465__Inf_A_2_10.png |right|frame|Tree diagram of the <br>Shannon-Fano coding]]
-Another algorithm for entropy coding was given in 1949 by&nbsp; [https://en.wikipedia.org/wiki/Claude_Shannon Claude Elwood Shannon]&nbsp; and&nbsp; [https://en.wikipedia.org/wiki/Robert_Fano Robert Fano]&nbsp;, which is described in the theory section.
+Another algorithm for entropy coding was given in 1949 by&nbsp; [https://en.wikipedia.org/wiki/Claude_Shannon Claude Elwood Shannon]&nbsp; and&nbsp; [https://en.wikipedia.org/wiki/Robert_Fano Robert Fano],&nbsp; which is described in the theory section.
-This special type of source coding will be described here using a simple example for the symbol range&nbsp; $M = 4$&nbsp; and the following symbol probabilities:
+This special type of source coding will be described here using a simple example for the symbol set size&nbsp; $M = 4$&nbsp; and the following symbol probabilities:
 :$$p_{\rm A} = 0.2 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm B}= 0.3 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm C}= 0.4 \hspace{0.05cm},\hspace{0.4cm}
@@ Line 17: / Line 17: @@
 :2. Divide the symbols into two groups of approximately equal probability, here&nbsp; $\rm C$&nbsp; and&nbsp; $\rm BAD$.
-:3. The binary symbol&nbsp; <b>0</b>is assigned to the less probable group,&nbsp; <b>1</b>&nbsp;  to the other group.
+:3. The binary symbol&nbsp; <b>0</b>&nbsp; is assigned to the less probable group,&nbsp; <b>1</b>&nbsp;  to the other group.
 :4. If there is more than one symbol in a group, the algorithm is to be applied recursively.
-For this example, the following code assignment results (in the tree diagram, a red connection marks a&nbsp; <b>1</b>&nbsp; and a blue one a&nbsp; <b>0</b>:
+For this example, the following code assignment results&nbsp; (in the tree diagram, a red connection marks a&nbsp; <b>1</b>&nbsp; and a blue one a&nbsp; <b>0</b>):
 : &nbsp; &nbsp; &nbsp; $\rm A$ &nbsp; &#8594; &nbsp; <b>111</b>, &nbsp; &nbsp; $\rm B$ &nbsp; &#8594; &nbsp; <b>10</b>, &nbsp; &nbsp; $\rm C$ &nbsp; &#8594; &nbsp; <b>0</b>, &nbsp; &nbsp; $\rm D$ &nbsp; &#8594; &nbsp; <b>110</b>.
-This gives the following for the mean codeword length:
+This gives the following for the average codeword length:
-:$$L_{\rm M} = 0.4 \cdot 1 + 0.3 \cdot 2 + (0.2 + 0.1) \cdot 3 = 1.9\,\,{\rm bit/source\:symbol}\hspace{0.05cm}.$$
+:$$L_{\rm M} = 0.4 \cdot 1 + 0.3 \cdot 2 + (0.2 + 0.1) \cdot 3 = 1.9\,\,{\rm bit/source\hspace{0.15cm}symbol}\hspace{0.05cm}.$$
 The Huffman algorithm would produce a slightly different code here, but even in this case&nbsp;
-*$\rm C$&nbsp; is coded with one bit,&nbsp;
+*$\rm C$&nbsp; is encoded with one bit,&nbsp;
 *$\rm B$&nbsp; with two bits and &nbsp;
 *$\rm A$ and&nbsp; $\rm D$&nbsp; with three bits each.&nbsp;
-&nbsp; This would also result in&nbsp; $L_{\rm M} = 1.9 \ \rm bit/source\:symbol$.
+&nbsp; This would also result in&nbsp; $L_{\rm M} = 1.9 \ \rm bit/source\hspace{0.15cm}symbol$.
 In this task you are to calculate the Shannon-Fano code for&nbsp; $M = 8$&nbsp; and the probabilities
 :$$p_{\rm A} = 0.10 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm B}= 0.40 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm C}= 0.02 \hspace{0.05cm},\hspace{0.4cm} p_{\rm D}= 0.14 \hspace{0.05cm},\hspace{0.4cm}
-p_{\rm E} = 0.17 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm F}= 0.03 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm G}= 0.05 \hspace{0.05cm},\hspace{0.4cm}p_{\rm H}= 0.09$$
+p_{\rm E} = 0.17 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm F}= 0.03 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm G}= 0.05 \hspace{0.05cm},\hspace{0.4cm}p_{\rm H}= 0.09.$$
-determine.&nbsp; You will see that with these probabilities "Shannon-Fano" will also differ from "Huffman" in terms of efficiency.&nbsp;
+You will see that with these probabilities&nbsp; "Shannon-Fano"&nbsp; will also differ from&nbsp; "Huffman"&nbsp; in terms of efficiency.&nbsp;
 With the Huffman code, the following assignment results with the probabilities at hand:
@@ Line 57: / Line 57: @@
 *The assignment belongs to the chapter&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren|Other source coding methods]].
 *In particular, reference is made to the page&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren#The_Shannon-Fano_algorithm|The Shannon-Fano algorithm]].
-*To check your results, please refer to the interactive applet&nbsp; [[Applets:Huffman-_und_Shannon-Fano-Codierung|Huffman and Shannon-Fano coding]].
+*To check your results, please refer to the (German language) SWF module&nbsp; [[Applets:Huffman_Shannon_Fano|Coding according to Huffman and Shannon/Fano]].
@@ Line 65: / Line 65: @@
 <quiz display=simple>
-{What is the mean codeword length&nbsp; $L_{\rm M}$&nbsp; for the&nbsp; <u>Huffman code</u>?
+{What is the average codeword length&nbsp; $L_{\rm M}$&nbsp; for the&nbsp; <u>Huffman code</u>?
 |type="{}"}
-$L_{\rm M}\ = \ $ { 2.54 3% } $\ \rm bit/source\:symbol$
+$L_{\rm M}\ = \ $ { 2.54 3% } $\ \rm bit/source\hspace{0.15cm}symbol$
@@ Line 86: / Line 86: @@
 {What is the average codeword length&nbsp; $L_{\rm M}$&nbsp; for&nbsp; <u>Shannon&ndash;Fano code</u>?
 |type="{}"}
-$L_{\rm M}\ = \ $ { 2.58 3% } $\ \rm bit/source\:symbol$
+$L_{\rm M}\ = \ $ { 2.58 3% } $\ \rm bit/source\hspace{0.15cm}symbol$

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID2465__Inf_A_2_10.png |right|frame|Baumdiagramm der <br>Shannon–Fano–Codierung]]
+[[File:P_ID2465__Inf_A_2_10.png |right|frame|Baumdiagramm der <br>Shannon-Fano coding]]
-Ein weiterer Algorithmus zur Entropiecodierung wurde 1949 von&nbsp; [https://de.wikipedia.org/wiki/Claude_Shannon Claude Elwood Shannon]&nbsp; und&nbsp; [https://de.wikipedia.org/wiki/Robert_Fano Robert Fano]&nbsp; angegeben, der im Theorieteil beschrieben ist.
+Another algorithm for entropy coding was given in 1949 by&nbsp; [https://en.wikipedia.org/wiki/Claude_Shannon Claude Elwood Shannon]&nbsp; and&nbsp; [https://en.wikipedia.org/wiki/Robert_Fano Robert Fano]&nbsp;, which is described in the theory section.
-Diese spezielle Art von Quellencodierung soll hier an einem einfachen Beispiel für den Symbolumfang&nbsp; $M = 4$&nbsp; und die folgenden Symbolwahrscheinlichkeiten beschrieben werden:
+This special type of source coding will be described here using a simple example for the symbol range&nbsp; $M = 4$&nbsp; and the following symbol probabilities:
 :$$p_{\rm A} = 0.2 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm B}= 0.3 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm C}= 0.4 \hspace{0.05cm},\hspace{0.4cm}
 p_{\rm D}= 0.1 \hspace{0.05cm}. $$
-Die Grafik zeigt das dazugehörige Baumdiagramm.&nbsp; Man geht folgendermaßen vor:
+The graph shows the corresponding tree diagram.&nbsp; Proceed as follows:
-:1. Man ordnet die Symbole nach fallender Auftrittswahrscheinlichkeit, hier&nbsp; $\rm C$ &ndash; $\rm B$ &ndash; $\rm A$ &ndash; $\rm D$.
+:1. Order the symbols according to decreasing probability of occurrence, here&nbsp; $\rm C$ &ndash; $\rm B$ &ndash; $\rm A$ &ndash; $\rm D$.
-:2. Man teilt die Symbole in zwei etwa gleichwahrscheinliche Gruppen ein, hier&nbsp; $\rm C$&nbsp; und&nbsp; $\rm BAD$.
+:2. Divide the symbols into two groups of approximately equal probability, here&nbsp; $\rm C$&nbsp; and&nbsp; $\rm BAD$.
-:3. Der unwahrscheinlicheren Gruppe wird das Binärsymbol&nbsp; <b>0</b>, der anderen Gruppe  die&nbsp; <b>1</b>&nbsp; zugeordnet.
+:3. The binary symbol&nbsp; <b>0</b>is assigned to the less probable group,&nbsp; <b>1</b>&nbsp;  to the other group.
-:4. Sind in einer Gruppe mehr als ein Zeichen, so ist der Algorithmus rekursiv anzuwenden.
+:4. If there is more than one symbol in a group, the algorithm is to be applied recursively.
-Für dieses Beispiel ergibt sich die folgende Codezuordnung (im Baumdiagramm markiert eine rote Verbindung eine&nbsp; <b>1</b>&nbsp; und eine blaue eine&nbsp; <b>0</b>:
+For this example, the following code assignment results (in the tree diagram, a red connection marks a&nbsp; <b>1</b>&nbsp; and a blue one a&nbsp; <b>0</b>:
 : &nbsp; &nbsp; &nbsp; $\rm A$ &nbsp; &#8594; &nbsp; <b>111</b>, &nbsp; &nbsp; $\rm B$ &nbsp; &#8594; &nbsp; <b>10</b>, &nbsp; &nbsp; $\rm C$ &nbsp; &#8594; &nbsp; <b>0</b>, &nbsp; &nbsp; $\rm D$ &nbsp; &#8594; &nbsp; <b>110</b>.
-Damit ergibt sich für die mittlere Codewortlänge:
+This gives the following for the mean codeword length:
-:$$L_{\rm M} = 0.4 \cdot 1 + 0.3 \cdot 2 + (0.2 + 0.1) \cdot 3 = 1.9\,\,{\rm bit/Quellensymbol}\hspace{0.05cm}.$$
+:$$L_{\rm M} = 0.4 \cdot 1 + 0.3 \cdot 2 + (0.2 + 0.1) \cdot 3 = 1.9\,\,{\rm bit/source\:symbol}\hspace{0.05cm}.$$
-Der Huffman-Algorithmus würde hier zwar einen geringfügig anderen Code erzeugen, aber auch bei diesem würde&nbsp;
+The Huffman algorithm would produce a slightly different code here, but even in this case&nbsp;
-*$\rm C$&nbsp; mit einem Bit,&nbsp;
+*$\rm C$&nbsp; is coded with one bit,&nbsp;
-*$\rm B$&nbsp; mit zwei Bit und&nbsp;
+*$\rm B$&nbsp; with two bits and &nbsp;
-*$\rm A$ und&nbsp; $\rm D$&nbsp; mit jeweils drei Bit&nbsp;
+*$\rm A$ and&nbsp; $\rm D$&nbsp; with three bits each.&nbsp;
-codiert.&nbsp; Damit ergäbe sich ebenfalls&nbsp; $L_{\rm M} = 1.9 \ \rm bit/Quellensymbol$.
+&nbsp; This would also result in&nbsp; $L_{\rm M} = 1.9 \ \rm bit/source\:symbol$.
-In dieser Aufgabe sollen Sie den Shannon&ndash;Fano&ndash;Code für&nbsp; $M = 8$&nbsp; und die Wahrscheinlichkeiten
+In this task you are to calculate the Shannon-Fano code for&nbsp; $M = 8$&nbsp; and the probabilities
 :$$p_{\rm A} = 0.10 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm B}= 0.40 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm C}= 0.02 \hspace{0.05cm},\hspace{0.4cm} p_{\rm D}= 0.14 \hspace{0.05cm},\hspace{0.4cm}
 p_{\rm E} = 0.17 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm F}= 0.03 \hspace{0.05cm}, \hspace{0.4cm}p_{\rm G}= 0.05 \hspace{0.05cm},\hspace{0.4cm}p_{\rm H}= 0.09$$
-ermitteln.&nbsp; Sie werden erkennen, dass sich mit diesen Wahrscheinlichkeiten "Shannon&ndash;Fano" auch hinsichtlich der Effizienz von "Huffman" unterscheiden wird.&nbsp;
+determine.&nbsp; You will see that with these probabilities "Shannon-Fano" will also differ from "Huffman" in terms of efficiency.&nbsp;
-Beim Huffman&ndash;Code ergibt sich mit den vorliegenden Wahrscheinlichkeiten die folgende Zuordnung:
+With the Huffman code, the following assignment results with the probabilities at hand:
 : &nbsp; &nbsp; &nbsp; $\rm A$ &nbsp; &#8594; &nbsp; <b>100</b>, &nbsp; &nbsp;  $\rm B$ &nbsp; &#8594; &nbsp; <b>0</b>, &nbsp; &nbsp;  $\rm C$ &nbsp; &#8594; &nbsp; <b>111100</b>, &nbsp; &nbsp; $\rm D$ &nbsp; &#8594; &nbsp; <b>101</b>, &nbsp; &nbsp; $\rm E$ &nbsp; &#8594; &nbsp; <b>110</b>,  &nbsp; &nbsp; $\rm F$ &nbsp; &#8594; &nbsp; <b>111101</b>, &nbsp; &nbsp; $\rm G$ &nbsp; &#8594; &nbsp; <b>11111</b>, &nbsp; &nbsp; $\rm H$ &nbsp; &#8594; &nbsp; <b>1110</b>.
@@ Line 54: / Line 54: @@
-''Hinweise:''
+''Hints:''
-*Die Aufgabe gehört zum  Kapitel&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren|Weitere Quellencodierverfahren]].
+*The assignment belongs to the chapter&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren|Other source coding methods]].
-*Insbesondere wird  Bezug genommen auf die Seite&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren#Der_Shannon.E2.80.93Fano.E2.80.93Algorithmus|Der Shannon-Fano-Algorithmus]].
+*In particular, reference is made to the page&nbsp; [[Information_Theory/Weitere_Quellencodierverfahren#The_Shannon-Fano_algorithm|The Shannon-Fano algorithm]].
-*Zur Kontrolle Ihrer Ergebnisse verweisen wir auf das interaktive Applet&nbsp; [[Applets:Huffman-_und_Shannon-Fano-Codierung|Huffman&ndash; und Shannon&ndash;Fano&ndash;Codierung]].
+*To check your results, please refer to the interactive applet&nbsp; [[Applets:Huffman-_und_Shannon-Fano-Codierung|Huffman and Shannon-Fano coding]].
-===Fragebogen===
+===Questions===
 <quiz display=simple>

← Older revision		Revision as of 13:03, 16 July 2021
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−	[[Category:Information Theory: Exercises\|^2.4 ~~Weitere Quellencodierverfahren~~^]]	+	[[Category:Information Theory: Exercises\|^2.4 Further Source Coding Methods^]]