Aufgaben:Exercise 2.4Z: Error Probabilities for the Octal System - Revision history

Hwang at 08:19, 24 May 2022

2022-05-24T08:19:08Z

Guenter at 13:16, 17 May 2022

2022-05-17T13:16:50Z

Guenter at 12:58, 17 May 2022

2022-05-17T12:58:47Z

Hwang at 15:48, 16 May 2022

2022-05-16T15:48:25Z

Guenter at 15:03, 9 May 2022

2022-05-09T15:03:50Z

Hwang at 13:32, 19 April 2022

2022-04-19T13:32:59Z

Guenter at 12:57, 4 April 2022

2022-04-04T12:57:10Z

Guenter: Guenter moved page Aufgaben:Aufgabe 2.4Z: Fehlerwahrscheinlichkeiten beim Oktalsystem to Aufgaben:Exercise 2.4Z: Error Probabilities for the Octal System

2022-04-04T12:53:52Z

Guenter moved page Aufgabe 2.4Z: Fehlerwahrscheinlichkeiten beim Oktalsystem to Exercise 2.4Z: Error Probabilities for the Octal System

Javier: Text replacement - "Category:Aufgaben zu Digitalsignalübertragung" to "Category:Digital Signal Transmission: Exercises"

2021-03-23T12:50:31Z

Text replacement - "Category:Aufgaben zu Digitalsignalübertragung" to "Category:Digital Signal Transmission: Exercises"

Javier: Text replacement - "[[Digitalsignalübertragung" to "[[Digital_Signal_Transmission"

2020-07-09T12:46:40Z

Text replacement - "[[Digitalsignalübertragung" to "[[Digital_Signal_Transmission"

← Older revision		Revision as of 08:19, 24 May 2022
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−	'''(2)'''  The outer coefficients  $(a_{1}$  and  $a_{8})$  are each ~~falsiied~~ with probability  $p = 1 \%$,  the  $M – 2 = 6$  inner ones with twice the probability  $(2p= 2 \%)$.  By averaging,  we obtain:	+	'''(2)'''  The outer coefficients  $(a_{1}$  and  $a_{8})$  are each falsified with probability  $p = 1 \%$,  the  $M – 2 = 6$  inner ones with twice the probability  $(2p= 2 \%)$.  By averaging,  we obtain:
	:$$p_{\rm S} = \frac{2 \cdot 1 + 6 \cdot 2} { 8} \cdot p\hspace{0.15cm}\underline { = 1.75 \,\%} \hspace{0.05cm}.$$		:$$p_{\rm S} = \frac{2 \cdot 1 + 6 \cdot 2} { 8} \cdot p\hspace{0.15cm}\underline { = 1.75 \,\%} \hspace{0.05cm}.$$

@@ Line 29: / Line 29: @@
 Notes:
 *The exercise belongs to the chapter&nbsp;  [[Digital_Signal_Transmission/Grundlagen_der_codierten_Übertragung|"Basics of Coded Transmission"]].
@@ Line 66: / Line 64: @@
 {{ML-Kopf}}
 '''(1)'''&nbsp;  According to the description on the specification page
-*"LHH" for the amplitude coefficient $a_{3}$  &nbsp; &rArr; &nbsp; $\underline{\mu =3}$.
+*$\rm LHH$&nbsp; for the amplitude coefficient&nbsp; $a_{3}$  &nbsp; &rArr; &nbsp; $\underline{\mu =3}$.
-*"HLL" for the amplitude coefficient $a_{8}$  &nbsp; &rArr; &nbsp; $\underline{\mu =8}$.
+*$\rm HLL$&nbsp; for the amplitude coefficient&nbsp; $a_{8}$  &nbsp; &rArr; &nbsp; $\underline{\mu =8}$.
-'''(2)'''&nbsp; The outer coefficients ($a_{1}$ and $a_{8}$) are each distorted with probability $p = 1 \%$, <br>the $M – 2 = 6$ inner ones with twice the probability $(2p= 2 \%)$. By averaging, we obtain:
+'''(2)'''&nbsp; The outer coefficients&nbsp; $(a_{1}$&nbsp; and&nbsp; $a_{8})$&nbsp; are each falsiied with probability&nbsp; $p = 1 \%$,&nbsp; the&nbsp; $M – 2 = 6$&nbsp; inner ones with twice the probability&nbsp; $(2p= 2 \%)$.&nbsp; By averaging,&nbsp; we obtain:
 :$$p_{\rm S} = \frac{2 \cdot 1 + 6 \cdot 2} { 8} \cdot p\hspace{0.15cm}\underline { = 1.75 \,\%} \hspace{0.05cm}.$$
-'''(3)'''&nbsp; Each transmission error (symbol error) results in exactly one bit error in gray code. However, since each octal symbol contains three binary characters, the following applies
 :$$p_{\rm B} ={p_{\rm S}}/ { 3}\hspace{0.15cm}\underline { = 0.583 \,\%} \hspace{0.05cm}.$$
 '''(4)'''&nbsp; Of the total of seven possible transitions (each in both directions) lead to
-*one error: &nbsp; &nbsp; '''HLH''' $\Leftrightarrow$ '''LLH''',
+'''(4)'''&nbsp; Of the total of seven possible transitions&nbsp; (each in both directions)&nbsp; lead to
-*two errors: &nbsp; &nbsp;&nbsp;  '''HLL''' $\Leftrightarrow$ '''HHH''', '''LLL''' $\Leftrightarrow$ '''LHH''', '''HHL''' $\Leftrightarrow$ '''HLH''', '''LLH''' $\Leftrightarrow$ '''LHL''',
+*one error: &nbsp; &nbsp; $\rm HLH \ \Leftrightarrow \ LLH$,
-*three errors: &nbsp; &nbsp; &nbsp; '''HHH''' $\Leftrightarrow$ '''LLL''', '''LHH''' $\Leftrightarrow$ '''HHL'''.
+*two errors: &nbsp; &nbsp;&nbsp; $\rm HLL \ \Leftrightarrow \ HHH$, &nbsp;  &nbsp; $\rm LLL \ \Leftrightarrow \ LHH$, &nbsp;   &nbsp; $\rm HHL \ \Leftrightarrow \ HLH$, &nbsp;  &nbsp; $\rm LLH \ \Leftrightarrow \ LHL$,

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Dig_A_2_6.png|right|frame|Octal "random coding" and gray coding]]
+[[File:EN_Dig_A_2_6.png|right|frame|Octal&nbsp; "random coding"&nbsp; and&nbsp; Gray coding]]
-A digital system with &nbsp;$M = 8$&nbsp; amplitude levels (octal system) is considered, whose &nbsp;$M – 1 = 7$&nbsp; decision thresholds lie exactly at the respective interval centers.
+A digital system with &nbsp;$M = 8$&nbsp; amplitude levels&nbsp; ("octal system")&nbsp; is considered,&nbsp; whose &nbsp;$M – 1 = 7$&nbsp; decision thresholds lie exactly at the respective interval centers.
-Each of the equally probable amplitude coefficients &nbsp;$a_{\mu}$&nbsp; with &nbsp;$1 ≤ \mu ≤ 8$&nbsp; can be distorted only into the immediate neighbor coefficients &nbsp;$a_{\mu–1}$&nbsp; and &nbsp;$a_{\mu+1}$,&nbsp; respectively, and in both directions with the same probability &nbsp;$p = 0.01$. Here are some examples:
+Each of the equally probable amplitude coefficients &nbsp;$a_{\mu}$&nbsp; with &nbsp;$1 ≤ \mu ≤ 8$&nbsp; can be falsified only into the immediate neighbor coefficients &nbsp;$a_{\mu–1}$&nbsp; and &nbsp;$a_{\mu+1}$,&nbsp; respectively,&nbsp; and in both directions with the same probability &nbsp;$p = 0.01$.&nbsp; Here are some examples:
 *$a_5$&nbsp; passes into coefficient $a_4$ with probability &nbsp;$p = 0.01$&nbsp; and into coefficient &nbsp;$a_6$ with the same probability &nbsp;$p = 0.01$.&nbsp;
-*$a_8$&nbsp; is distorted with probability &nbsp;$p = 0.01$&nbsp; into coefficient &nbsp;$a_7$.&nbsp; No distortion is possible in the other direction.
 The mapping of each three binary source symbols into an octal amplitude coefficient happens alternatively according to
-*the second column in the given table, which was generated "randomly" - without strategy,
+*the second column in the given table,&nbsp; which was generated&nbsp; "randomly"&nbsp; - without strategy,
-*the gray coding, which is only incompletely indicated in column 3 and is still to be supplemented.
-The gray code is given for &nbsp;$M = 4$. For &nbsp;$M = 8$&nbsp; the last two binary characters are to be mirrored at the dashed line. For the first four amplitude coefficients a '''L''' is to be added at the first place, for &nbsp;$a_{5}, ..., a_{8}$&nbsp; the binary symbol '''H'''.
+The Gray code is given for &nbsp;$M = 4$.&nbsp; For &nbsp;$M = 8$&nbsp; the last two binary characters are to be mirrored at the dashed line.&nbsp; For the first four amplitude coefficients a&nbsp; $\rm L$&nbsp; is to be added at the first place,&nbsp; for &nbsp;$a_{5}, ..., a_{8}$&nbsp; the binary symbol&nbsp; $\rm H$.
-For the two mappings "Random" and "Gray" are to be calculated:
+For the two mappings&nbsp; "Random"&nbsp; and&nbsp; "Gray"&nbsp; are to be calculated:
-*the ''symbol error probability'' &nbsp;$p_{\rm S}$, which is the same in both cases; $p_{\rm S}$&nbsp; indicates the average distortion probability of an amplitude coefficient &nbsp;$a_{\mu}$;&nbsp;
+*the&nbsp; "symbol error probability" &nbsp;$p_{\rm S}$,&nbsp; which is the same in both cases;&nbsp; $p_{\rm S}$&nbsp; indicates the average falsifcation probability of an amplitude coefficient &nbsp;$a_{\mu}$;&nbsp;
-*the ''bit error probability'' &nbsp;$p_{\rm B}$&nbsp; related to the (decoded) binary symbols.
@@ Line 30: / Line 33: @@
 ''Notes:''
 *The exercise belongs to the chapter&nbsp;  [[Digital_Signal_Transmission/Grundlagen_der_codierten_Übertragung|"Basics of Coded Transmission"]].
 *Reference is also made to the chapter&nbsp; [[Digital_Signal_Transmission/Redundanzfreie_Codierung|"Redundancy-Free Coding"]] .
@@ Line 39: / Line 43: @@
 <quiz display=simple>
-{To which amplitude coefficient &nbsp;$a_{ \mu}$&nbsp; do the binary sequences &nbsp;$\rm {LHH}$&nbsp; and &nbsp;$\rm {HLL}$ correspond in the gray code? <br>Please enter index &nbsp;$ \mu$&nbsp;  &nbsp;$(1 <  \mu < 8)$.
+{To which amplitude coefficient &nbsp;$a_{ \mu}$&nbsp; do the binary sequences &nbsp;$\rm {LHH}$&nbsp; and &nbsp;$\rm {HLL}$ correspond in the Gray code? <br>Please enter index &nbsp;$ \mu$&nbsp;  &nbsp;$(1 <  \mu < 8)$.
 |type="{}"}
 $ \rm {LHH}\text{:}\hspace{0.4cm}  \mu  \ = \ $ { 3 3% }
@@ Line 48: / Line 52: @@
 $p_{\rm S} \ = \ $ { 1.75 3% } $\ \%$
-{Calculate the bit error probability &nbsp;$p_{\rm B}$&nbsp; for the <u>gray code</u>.
+{Calculate the bit error probability &nbsp;$p_{\rm B}$&nbsp; for the&nbsp; <u>Gray code</u>.
 |type="{}"}
 $p_{\rm B} \ = \ $ { 0.583 3% } $\ \%$
-{Calculate the bit error probability &nbsp;$p_{\rm B}$&nbsp; for the <u>random code</u>.
+{Calculate the bit error probability &nbsp;$p_{\rm B}$&nbsp; for the&nbsp; <u>random code</u>.
 |type="{}"}
 $p_{\rm B} \ = \ $ { 0.714 3% } $\ \%$

@@ Line 29: / Line 29: @@
 ''Notes:''
-*The exercise belongs to the chapter&nbsp;  [[Digital_Signal_Transmission/Grundlagen_der_codierten_Übertragung|Basics of Coded Transmission]].
+*The exercise belongs to the chapter&nbsp;  [[Digital_Signal_Transmission/Grundlagen_der_codierten_Übertragung|"Basics of Coded Transmission"]].
-*Reference is also made to the chapter&nbsp; [[Digital_Signal_Transmission/Redundanzfreie_Codierung|Redundancy-Free Coding]] .
+*Reference is also made to the chapter&nbsp; [[Digital_Signal_Transmission/Redundanzfreie_Codierung|"Redundancy-Free Coding"]] .

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1326__Dig_Z_2_4.png|right|frame|Octal "random coding" and gray coding]]
+[[File:EN_Dig_A_2_6.png|right|frame|Octal "random coding" and gray coding]]
 A digital system with &nbsp;$M = 8$&nbsp; amplitude levels (octal system) is considered, whose &nbsp;$M – 1 = 7$&nbsp; decision thresholds lie exactly at the respective interval centers.

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Digitalsignalübertragung/Redundanzfreie Codierung
+{{quiz-Header|Buchseite=Digital_Signal_Transmission/Redundancy-Free_Coding
 }}
-[[File:P_ID1326__Dig_Z_2_4.png|right|frame|Oktale „Zufallscodierung” und Graycodierung]]
+[[File:P_ID1326__Dig_Z_2_4.png|right|frame|Octal "random coding" and gray coding]]
-Es wird ein Digitalsystem mit &nbsp;$M = 8$&nbsp; Amplitudenstufen (Oktalsystem) betrachtet, dessen &nbsp;$M – 1 = 7$&nbsp; Entscheiderschwellen genau bei den jeweiligen Intervallmitten liegen.
+A digital system with &nbsp;$M = 8$&nbsp; amplitude levels (octal system) is considered, whose &nbsp;$M – 1 = 7$&nbsp; decision thresholds lie exactly at the respective interval centers.
-Ein jeder der gleichwahrscheinlichen Amplitudenkoeffizienten &nbsp;$a_{\mu}$&nbsp; mit &nbsp;$1 ≤ \mu ≤ 8$&nbsp; kann nur in die unmittelbaren Nachbarkoeffizienten &nbsp;$a_{\mu–1}$&nbsp; bzw. &nbsp;$a_{\mu+1}$&nbsp; verfälscht werden und zwar in beiden Richtungen mit der gleichen Wahrscheinlichkeit &nbsp;$p = 0.01$. Hierzu einige Beispiele:
+Each of the equally probable amplitude coefficients &nbsp;$a_{\mu}$&nbsp; with &nbsp;$1 ≤ \mu ≤ 8$&nbsp; can be distorted only into the immediate neighbor coefficients &nbsp;$a_{\mu–1}$&nbsp; and &nbsp;$a_{\mu+1}$,&nbsp; respectively, and in both directions with the same probability &nbsp;$p = 0.01$. Here are some examples:
-*$a_5$&nbsp; geht mit der Wahrscheinlichkeit &nbsp;$p = 0.01$&nbsp; in den Koeffizienten $a_4$ über und mit der gleichen Wahrscheinlichkeit &nbsp;$p = 0.01$&nbsp; in den Koeffizienten &nbsp;$a_6$.
+*$a_5$&nbsp; passes into coefficient $a_4$ with probability &nbsp;$p = 0.01$&nbsp; and into coefficient &nbsp;$a_6$ with the same probability &nbsp;$p = 0.01$.&nbsp;
-*$a_8$&nbsp; wird mit der Wahrscheinlichkeit &nbsp;$p = 0.01$&nbsp; in den Koeffizienten &nbsp;$a_7$&nbsp; verfälscht. In die andere Richtung ist keine Verfälschung möglich.
+*$a_8$&nbsp; is distorted with probability &nbsp;$p = 0.01$&nbsp; into coefficient &nbsp;$a_7$.&nbsp; No distortion is possible in the other direction.
-Die Zuordnung von jeweils drei binären Quellensymbolen in einen oktalen Amplitudenkoeffizienten geschieht alternativ entsprechend
+The mapping of each three binary source symbols into an octal amplitude coefficient happens alternatively according to
-*der zweiten Spalte in der angegebenen Tabelle, die „zufällig” – ohne Strategie – generiert wurde,
+*the second column in the given table, which was generated "randomly" - without strategy,
-*der Graycodierung, die in Spalte 3 nur unvollständig angegeben ist und noch ergänzt werden soll.
+*the gray coding, which is only incompletely indicated in column 3 and is still to be supplemented.
-Angegeben ist der Graycode für &nbsp;$M = 4$. Bei &nbsp;$M = 8$&nbsp; sind die beiden letzten Binärzeichen an der gestrichelt eingezeichneten Linie zu spiegeln. Für die ersten vier Amplitudenkoeffizienten ist an der ersten Stelle ein '''L''' zu ergänzen, für &nbsp;$a_{5}, ..., a_{8}$&nbsp; das Binärsymbol '''H'''.
+The gray code is given for &nbsp;$M = 4$. For &nbsp;$M = 8$&nbsp; the last two binary characters are to be mirrored at the dashed line. For the first four amplitude coefficients a '''L''' is to be added at the first place, for &nbsp;$a_{5}, ..., a_{8}$&nbsp; the binary symbol '''H'''.
-Für die beiden Zuordnungen „Zufall” und „Gray” sollen berechnet werden:
+For the two mappings "Random" and "Gray" are to be calculated:
-*die ''Symbolfehlerwahrscheinlichkeit'' &nbsp;$p_{\rm S}$, die in beiden Fällen gleich ist; $p_{\rm S}$&nbsp; gibt die mittlere Verfälschungswahrscheinlichkeit eines Amplitudenkoeffizienten &nbsp;$a_{\mu}$&nbsp; an;
+*the ''symbol error probability'' &nbsp;$p_{\rm S}$, which is the same in both cases; $p_{\rm S}$&nbsp; indicates the average distortion probability of an amplitude coefficient &nbsp;$a_{\mu}$;&nbsp;
-*die ''Bitfehlerwahrscheinlichkeit'' &nbsp;$p_{\rm B}$&nbsp; bezogen auf die (decodierten) Binärsymbole.
+*the ''bit error probability'' &nbsp;$p_{\rm B}$&nbsp; related to the (decoded) binary symbols.
@@ Line 28: / Line 28: @@
-''Hinweise:''
+''Notes:''
-*Die Aufgabe gehört zum  Kapitel&nbsp;  [[Digital_Signal_Transmission/Grundlagen_der_codierten_Übertragung|Grundlagen der codierten Übertragung]].
+*The exercise belongs to the chapter&nbsp;  [[Digital_Signal_Transmission/Grundlagen_der_codierten_Übertragung|Basics of Coded Transmission]].
-*Bezug genommen wird auch auf das Kapitel&nbsp; [[Digital_Signal_Transmission/Redundanzfreie_Codierung|Redundanzfreie Codierung]] .
+*Reference is also made to the chapter&nbsp; [[Digital_Signal_Transmission/Redundanzfreie_Codierung|Redundancy-Free Coding]] .
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Welchem Amplitudenkoeffizienten &nbsp;$a_{ \mu}$&nbsp; entsprechen beim Graycode die binären Folgen &nbsp;$\rm {LHH}$&nbsp; bzw. &nbsp;$\rm {HLL}$? <br>Bitte Index &nbsp;$ \mu$&nbsp;  eingeben &nbsp;$(1 <  \mu < 8)$.
+{To which amplitude coefficient &nbsp;$a_{ \mu}$&nbsp; do the binary sequences &nbsp;$\rm {LHH}$&nbsp; and &nbsp;$\rm {HLL}$ correspond in the gray code? <br>Please enter index &nbsp;$ \mu$&nbsp;  &nbsp;$(1 <  \mu < 8)$.
 |type="{}"}
 $ \rm {LHH}\text{:}\hspace{0.4cm}  \mu  \ = \ $ { 3 3% }
 $ \rm {HLL}\text{:}\hspace{0.45cm}   \mu  \ = \ $ { 8 3% }
-{Berechnen Sie die Symbolfehlerwahrscheinlichkeit &nbsp;$p_{\rm S}$.
+{Calculate the symbol error probability &nbsp;$p_{\rm S}$.
 |type="{}"}
 $p_{\rm S} \ = \ $ { 1.75 3% } $\ \%$
-{Berechnen Sie die Bitfehlerwahrscheinlichkeit &nbsp;$p_{\rm B}$&nbsp; für den <u>Graycode</u>.
+{Calculate the bit error probability &nbsp;$p_{\rm B}$&nbsp; for the <u>gray code</u>.
 |type="{}"}
 $p_{\rm B} \ = \ $ { 0.583 3% } $\ \%$
-{Berechnen Sie die Bitfehlerwahrscheinlichkeit &nbsp;$p_{\rm B}$&nbsp; für den <u>Zufallscode</u>.
+{Calculate the bit error probability &nbsp;$p_{\rm B}$&nbsp; for the <u>random code</u>.
 |type="{}"}
 $p_{\rm B} \ = \ $ { 0.714 3% } $\ \%$
@@ Line 59: / Line 59: @@
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;  Entsprechend der Beschreibung auf der Angabenseite steht
+'''(1)'''&nbsp;  According to the description on the specification page
-*„LHH” für den Amplitudenkoeffizienten $a_{3}$  &nbsp; &rArr; &nbsp; $\underline{\mu =3}$.
+*"LHH" for the amplitude coefficient $a_{3}$  &nbsp; &rArr; &nbsp; $\underline{\mu =3}$.
-* „HLL” für für den Amplitudenkoeffizienten $a_{8}$  &nbsp; &rArr; &nbsp; $\underline{\mu =8}$.
+*"HLL" for the amplitude coefficient $a_{8}$  &nbsp; &rArr; &nbsp; $\underline{\mu =8}$.
-'''(2)'''&nbsp; Die äußeren Koeffizienten ($a_{1}$ und $a_{8}$) werden jeweils mit der Wahrscheinlichkeit $p = 1 \%$ verfälscht, <br>die $M – 2 = 6$ inneren mit der doppelten Wahrscheinlichkeit $(2p= 2 \%)$. Durch Mittelung erhält man:
+'''(2)'''&nbsp; The outer coefficients ($a_{1}$ and $a_{8}$) are each distorted with probability $p = 1 \%$, <br>the $M – 2 = 6$ inner ones with twice the probability $(2p= 2 \%)$. By averaging, we obtain:
 :$$p_{\rm S} = \frac{2 \cdot 1 + 6 \cdot 2} { 8} \cdot p\hspace{0.15cm}\underline { = 1.75 \,\%} \hspace{0.05cm}.$$
-'''(3)'''&nbsp; Jeder Übertragungsfehler (Symbolfehler) hat beim Graycode genau einen Bitfehler zur Folge. Da jedoch jedes Oktalsymbol drei Binärzeichen beinhaltet, gilt
+'''(3)'''&nbsp; Each transmission error (symbol error) results in exactly one bit error in gray code. However, since each octal symbol contains three binary characters, the following applies
 :$$p_{\rm B} ={p_{\rm S}}/ { 3}\hspace{0.15cm}\underline { = 0.583 \,\%} \hspace{0.05cm}.$$
-'''(4)'''&nbsp; Von den insgesamt sieben möglichen Übergängen (jeweils in beiden Richtungen) führen zu
+'''(4)'''&nbsp; Of the total of seven possible transitions (each in both directions) lead to
-*einem Fehler: &nbsp; &nbsp; '''HLH''' $\Leftrightarrow$ '''LLH''',
+*one error: &nbsp; &nbsp; '''HLH''' $\Leftrightarrow$ '''LLH''',
-*zwei Fehlern: &nbsp; &nbsp;&nbsp;  '''HLL''' $\Leftrightarrow$ '''HHH''', '''LLL''' $\Leftrightarrow$ '''LHH''', '''HHL''' $\Leftrightarrow$ '''HLH''', '''LLH''' $\Leftrightarrow$ '''LHL''',
+*two errors: &nbsp; &nbsp;&nbsp;  '''HLL''' $\Leftrightarrow$ '''HHH''', '''LLL''' $\Leftrightarrow$ '''LHH''', '''HHL''' $\Leftrightarrow$ '''HLH''', '''LLH''' $\Leftrightarrow$ '''LHL''',
-*drei Fehlern: &nbsp; &nbsp; &nbsp; '''HHH''' $\Leftrightarrow$ '''LLL''', '''LHH''' $\Leftrightarrow$ '''HHL'''.
+*three errors: &nbsp; &nbsp; &nbsp; '''HHH''' $\Leftrightarrow$ '''LLL''', '''LHH''' $\Leftrightarrow$ '''HHL'''.
-Daraus folgt:
+It follows that:
 :$$p_{\rm B} = \frac{p} { 3} \cdot \frac{1 + 4 \cdot 2 + 2 \cdot 3} { 7} = \frac{15} { 21} \cdot p \hspace{0.15cm}\underline { = 0.714 \,\%} \hspace{0.05cm}.$$

← Older revision		Revision as of 12:57, 4 April 2022
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−	[[Category:Digital Signal Transmission: Exercises\|^2.2 ~~Redundanzfreie Codierung~~^]]	+	[[Category:Digital Signal Transmission: Exercises\|^2.2 Redundancy-Free Coding^]]

← Older revision		Revision as of 12:50, 23 March 2021
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−	[[Category:~~Aufgaben zu Digitalsignalübertragung~~\|^2.2 Redundanzfreie Codierung^]]	+	[[Category:Digital Signal Transmission: Exercises\|^2.2 Redundanzfreie Codierung^]]