Aufgaben:Exercise 5.7: McCullough and Gilbert-Elliott Parameters - Revision history

Guenter at 12:25, 19 October 2022

2022-10-19T12:25:30Z

2022-10-18T11:42:42Z

2022-09-20T06:31:26Z

2022-09-09T15:09:09Z

2022-09-09T15:04:40Z

2022-09-01T15:52:16Z

2021-05-28T14:34:29Z

Text replacement - "„" to """

2021-05-28T14:33:35Z

Text replacement - "”" to """

2021-03-23T12:48:00Z

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

2019-03-26T14:32:35Z

← Older revision		Revision as of 12:25, 19 October 2022
Line 18:		Line 18:


−	The parameters of the GE model   ⇒   $p_{\rm G}, \hspace{0.1cm} p_{\rm B}, \hspace{0.1cm} p({\rm B\hspace{0.05cm}\|\hspace{0.05cm}G}), \hspace{0.1cm} p({\rm G\hspace{0.05cm}\|\hspace{0.05cm}B})$   can be converted to the corresponding MC parameters  $q_{\rm G}, \hspace{0.1cm} q_{\rm B},\hspace{0.1cm} q({\rm B\hspace{0.05cm}\|\hspace{0.05cm}G})$  and  $q({\rm G\hspace{0.05cm}\|\hspace{0.05cm}B})$  in such a way that ~~a fault '''KORREKTUR:~~ error~~'''~~ sequence identical in its statistical properties to the GE model is produced, but not the identical sequence.	+	The parameters of the GE model   ⇒   $p_{\rm G}, \hspace{0.1cm} p_{\rm B}, \hspace{0.1cm} p({\rm B\hspace{0.05cm}\|\hspace{0.05cm}G}), \hspace{0.1cm} p({\rm G\hspace{0.05cm}\|\hspace{0.05cm}B})$   can be converted to the corresponding MC parameters  $q_{\rm G}, \hspace{0.1cm} q_{\rm B},\hspace{0.1cm} q({\rm B\hspace{0.05cm}\|\hspace{0.05cm}G})$  and  $q({\rm G\hspace{0.05cm}\|\hspace{0.05cm}B})$  in such a way that an error sequence identical in its statistical properties to the GE model is produced, but not the identical sequence.

	The conversion equations are:		The conversion equations are:

← Older revision		Revision as of 11:42, 18 October 2022
Line 18:		Line 18:


−	The parameters of the GE model   ⇒   $p_{\rm G}, \hspace{0.1cm} p_{\rm B}, \hspace{0.1cm} p({\rm B\hspace{0.05cm}\|\hspace{0.05cm}G}), \hspace{0.1cm} p({\rm G\hspace{0.05cm}\|\hspace{0.05cm}B})$   can be converted to the corresponding MC parameters  $q_{\rm G}, \hspace{0.1cm} q_{\rm B},\hspace{0.1cm} q({\rm B\hspace{0.05cm}\|\hspace{0.05cm}G})$  and  $q({\rm G\hspace{0.05cm}\|\hspace{0.05cm}B})$  in such a way that a fault sequence identical in its statistical properties to the GE model is produced, but not the identical sequence.	+	The parameters of the GE model   ⇒   $p_{\rm G}, \hspace{0.1cm} p_{\rm B}, \hspace{0.1cm} p({\rm B\hspace{0.05cm}\|\hspace{0.05cm}G}), \hspace{0.1cm} p({\rm G\hspace{0.05cm}\|\hspace{0.05cm}B})$   can be converted to the corresponding MC parameters  $q_{\rm G}, \hspace{0.1cm} q_{\rm B},\hspace{0.1cm} q({\rm B\hspace{0.05cm}\|\hspace{0.05cm}G})$  and  $q({\rm G\hspace{0.05cm}\|\hspace{0.05cm}B})$  in such a way that a fault '''KORREKTUR: error''' sequence identical in its statistical properties to the GE model is produced, but not the identical sequence.

	The conversion equations are:		The conversion equations are:

← Older revision		Revision as of 15:09, 9 September 2022
Line 186:		Line 186:


−	[[Category:Digital Signal Transmission: Exercises\|^5.3 ~~Bündelfehlerkanäle~~^]]	+	[[Category:Digital Signal Transmission: Exercises\|^5.3 Burst Error Channels^]]

@@ Line 2: / Line 2: @@
 {{quiz-Header|Buchseite=Digitalsignalübertragung/Bündelfehlerkanäle}}
-[[File:P_ID1844__Dig_A_5_7.png|right|frame|Gilbert-Elliott– und McCullough–Modell]]
+[[File:EN Dig A 5 7.png|right|frame|Gilbert-Elliott– und McCullough–Modell]]
 In&nbsp; [[Aufgaben:5.6:_Fehlerkorrelationsdauer| Aufgabe 5.6]]&nbsp; und&nbsp; [[Aufgaben:Aufgabe_5.6Z:_GE-Modelleigenschaften| Aufgabe 5.6Z]]&nbsp; wurden jeweils das GE&ndash;Modell mit den Parameterwerten
 :$$p_{\rm G} \hspace{-0.1cm} \ = \ \hspace{-0.1cm} 0.001,

@@ Line 62: / Line 62: @@
 \hspace{0.2cm}\alpha_{\rm B} = 1-\alpha_{\rm G}\hspace{0.05cm}.$$
-$w_{\rm G}$&nbsp; und &nbsp;$w_{\rm B}$&nbsp; sind die Zustandswahrscheinlichkeiten für &bdquo;GOOD" und &bdquo;BAD" des GE&ndash;Modells. In der&nbsp;  [[Aufgaben:5.6Z_GE-Modelleigenschaften| Aufgabe 5.6Z]]&nbsp; wurden diese wie folgt berechnet:
+$w_{\rm G}$&nbsp; und &nbsp;$w_{\rm B}$&nbsp; sind die Zustandswahrscheinlichkeiten für "GOOD" und "BAD" des GE&ndash;Modells. In der&nbsp;  [[Aufgaben:5.6Z_GE-Modelleigenschaften| Aufgabe 5.6Z]]&nbsp; wurden diese wie folgt berechnet:
 :$$w_{\rm G} = {10}/{11}\hspace{0.05cm}, \hspace{0.2cm}w_{\rm B}
 = {1}/{11}\hspace{0.05cm}.$$

← Older revision	Revision as of 15:04, 9 September 2022
(No difference)

← Older revision		Revision as of 12:48, 23 March 2021
Line 186:		Line 186:


−	[[Category:~~Aufgaben zu Digitalsignalübertragung~~\|^5.3 Bündelfehlerkanäle^]]	+	[[Category:Digital Signal Transmission: Exercises\|^5.3 Bündelfehlerkanäle^]]

@@ Line 131: / Line 131: @@
 \cdot (1 -0.1) \hspace{0.15cm}\underline {\approx 0.81}\hspace{0.05cm}.$$
-Daraus folgt für die $\beta$&ndash;Hilfsgrößen:
+*Daraus folgt für die $\beta$&ndash;Hilfsgrößen:
 :$$\beta_{\rm G} =\frac{u_{\rm GG} + u_{\rm BB} + \sqrt{(u_{\rm GG} -
 u_{\rm BB})^2 + 4 \cdot u_{\rm GB}\cdot u_{\rm BG}}}{2}
@@ Line 145: / Line 145: @@
 \hspace{0.15cm}\underline {= 0.8051} \hspace{0.05cm}.$$
 '''(2)'''&nbsp; Mit dem Ergebnis der Teilaufgabe (1) erhält man:
 :$$q_{\rm G} = 1-\beta_{\rm G} =
 - 0.9939 \hspace{0.15cm}\underline {= 0.0061}\hspace{0.05cm}, \hspace{0.3cm}q_{\rm B} = 1-\beta_{\rm B}= 1 - 0.8051 \hspace{0.15cm}\underline {=
 .1949}\hspace{0.05cm}.$$