Aufgaben:Exercise 3.11: Erasure Channel - Revision history

Guenter at 11:56, 24 September 2021

2021-09-24T11:56:06Z

Guenter at 09:53, 24 September 2021

2021-09-24T09:53:58Z

Guenter at 09:43, 24 September 2021

2021-09-24T09:43:57Z

Noah at 08:24, 24 September 2021

2021-09-24T08:24:22Z

Noah at 12:10, 23 September 2021

2021-09-23T12:10:38Z

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Guenter at 11:35, 22 September 2021

2021-09-22T11:35:42Z

Noah at 11:30, 14 September 2021

2021-09-14T11:30:35Z

Guenter: Guenter moved page Aufgaben:Exercise 3.11: Erasure channel to Aufgaben:Exercise 3.11: Erasure Channel

2021-07-22T15:14:23Z

Guenter moved page Exercise 3.11: Erasure channel to Exercise 3.11: Erasure Channel

Guenter: Guenter moved page Aufgaben:Aufgabe 3.11: Auslöschungskanal to Aufgaben:Exercise 3.11: Erasure channel

2021-07-22T14:52:31Z

Guenter moved page Aufgabe 3.11: Auslöschungskanal to Exercise 3.11: Erasure channel

Javier: Text replacement - "Category:Aufgaben zu Informationstheorie" to "Category:Information Theory: Exercises"

2021-03-23T12:46:12Z

Text replacement - "Category:Aufgaben zu Informationstheorie" to "Category:Information Theory: Exercises"

← Older revision		Revision as of 11:56, 24 September 2021
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−	[[Category:Information Theory: Exercises\|^3.3 ~~Anwendung auf DSÜ-Kanäle~~^]]	+	[[Category:Information Theory: Exercises\|^3.3 Application to Digital Signal Transmission^]]

@@ Line 83: / Line 83: @@
-'''(2)'''&nbsp;  Correct is the <u>proposed solution 3</u>, i.e. exactly&nbsp; $2M$&nbsp; connections.&nbsp; There:
+'''(2)'''&nbsp;  Correct is the <u>proposed solution 3</u>, i.e. exactly&nbsp; $2M$&nbsp; connections.&nbsp; Because:
 *From each source symbol&nbsp; $X = μ$&nbsp; one gets to the sink symbol&nbsp; $Y = μ$&nbsp; as well as to the erasure&nbsp; $Y = \text{E}$.
@@ Line 125: / Line 125: @@
-'''(6)'''&nbsp;  The&nbsp; ''Binary Erasure Channel''&nbsp; $\rm (BEC)$&nbsp; is a special case of the general model considered here with&nbsp; $M = 2$:
+'''(6)'''&nbsp;  The&nbsp; "Binary Erasure Channel"&nbsp; $\rm (BEC)$&nbsp; is a special case of the general model considered here with&nbsp; $M = 2$:
 :$$C_{\rm BEC} = 1-\lambda \hspace{0.05cm}.$$
 *Thus, the correct <u>solution proposal 1</u>.
-*The second proposed solution, on the other hand, applies to the&nbsp; ''Binary Symmetric Channel''&nbsp; $\rm (BSC)$&nbsp; with distortion probability&nbsp; $λ$.
+*The second proposed solution, on the other hand, applies to the&nbsp; "Binary Symmetric Channel"&nbsp; $\rm (BSC)$&nbsp; with distortion probability&nbsp; $λ$.
 {{ML-Fuß}}

@@ Line 29: / Line 29: @@
 *The exercise belongs to the chapter&nbsp; [[Information_Theory/Anwendung_auf_die_Digitalsignalübertragung|Application to Digital Signal Transmission]].
 *Reference is made in particular to the page&nbsp;    [[Information_Theory/Anwendung_auf_die_Digitalsignalübertragung#Information-theoretical_model_of_digital_signal_transmission|Information-theoretical model of digital signal transmission]].
-*In the above diagram, cancellations&nbsp; $($with probability&nbsp; $λ)$&nbsp; are drawn in blue.
+*In the above diagram,&nbsp; "erasures"&nbsp; $($with probability&nbsp; $λ)$&nbsp; are drawn in blue.
 * "Correct transmission paths"&nbsp; $($i.e., from&nbsp; $X = μ$&nbsp; to&nbsp; $Y = μ)$&nbsp; are shown in red &nbsp;($1 ≤ μ ≤ M$).
@@ Line 38: / Line 38: @@
 <quiz display=simple>
-{ What&nbsp; $P_X(X)$&nbsp; should be generally applied for channel capacity calculation?
+{ What&nbsp; $P_X(X)$&nbsp; should be generally applied for the channel capacity calculation?
 |type="[]"}
 - $P_X(X) = (0.5, \  0.5),$

← Older revision		Revision as of 08:24, 24 September 2021
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−	{{quiz-Header\|Buchseite=~~Informationstheorie~~/~~Anwendung auf die Digitalsignalübertragung~~	+	{{quiz-Header\|Buchseite=Information_Theory/Application_to_Digital_Signal_Transmission
	}}		}}

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID2791__Inf_A_3_10.png|right|frame|Erasure channel with four inputs and five outputs]]
+[[File:P_ID2791__Inf_A_3_10.png|right|frame|Erasure channel with <br>four inputs and five outputs]]
-A cancellation channel is considered with
+An erasure channel is considered with
 * the&nbsp; $M$&nbsp; inputs&nbsp; $x ∈ X = \{1,\ 2, \ \text{...} \  ,\ M\}$,&nbsp; and
 * the&nbsp; $M + 1$&nbsp; outputs&nbsp; $y ∈ Y = \{1,\ 2,\ \ \text{...} \  ,\ M,\ \text{E}\}.$
@@ Line 15: / Line 15: @@
 :$${\rm Pr}(Y \hspace{-0.05cm} = {\rm E}\hspace{-0.05cm}\mid \hspace{-0.05cm} X \hspace{-0.05cm}= \mu) = \lambda \hspace{0.05cm}.$$
 We are looking for:
-* the capacity &nbsp;$C_{M\rm –EC}$&nbsp; of this ''M–ary Erasure Channels'',
+* the capacity &nbsp;$C_{M\rm –EC}$&nbsp; of this M–ary Erasure Channel,
 * the capacity &nbsp;$C_{\rm BEC}$&nbsp; of the&nbsp; [[Channel_Coding/Kanalmodelle_und_Entscheiderstrukturen#Binary_Erasure_Channel_.E2.80.93_BEC|Binary Erasure Channels]]&nbsp; as a special case of the above model.

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID2791__Inf_A_3_10.png|right|frame|Auslöschungskanal mit vier Eingängen und fünf Ausgängen]]
+[[File:P_ID2791__Inf_A_3_10.png|right|frame|Erasure channel with four inputs and five outputs]]
-Betrachtet wird ein Auslöschungskanal mit
+A cancellation channel is considered with
-* den&nbsp; $M$&nbsp; Eingängen&nbsp; $x ∈ X = \{1,\ 2, \ \text{...} \  ,\ M\}$,&nbsp; und
+* the&nbsp; $M$&nbsp; inputs&nbsp; $x ∈ X = \{1,\ 2, \ \text{...} \  ,\ M\}$,&nbsp; and
-* den&nbsp; $M + 1$&nbsp; Ausgängen&nbsp; $y ∈ Y = \{1,\ 2,\ \ \text{...} \  ,\ M,\ \text{E}\}.$
+* the&nbsp; $M + 1$&nbsp; outputs&nbsp; $y ∈ Y = \{1,\ 2,\ \ \text{...} \  ,\ M,\ \text{E}\}.$
-Die Grafik zeigt das Modell für den Sonderfall&nbsp; $M = 4$.&nbsp; Das Sinkensymbol&nbsp; $y = \text{E}$&nbsp; berücksichtigt eine&nbsp; ''Auslöschung''&nbsp; (englisch:&nbsp; ''Erasure''&nbsp;)&nbsp; für den Fall, dass der Empfänger keine hinreichend gesicherte Entscheidung treffen kann.
+The graph shows the model for the special case&nbsp; $M = 4$.&nbsp; The sink symbol&nbsp; $y = \text{E}$&nbsp; takes into account an erasure for the case that the receiver cannot make a sufficiently certain decision.
-Die Übergangswahrscheinlichkeiten sind für&nbsp; $1 ≤ μ ≤ M$&nbsp; wie folgt gegeben:
+The transition probabilities are given for&nbsp; $1 ≤ μ ≤ M$&nbsp; as follows:
 :$${\rm Pr}(Y \hspace{-0.05cm} = \mu\hspace{-0.05cm}\mid \hspace{-0.05cm} X \hspace{-0.05cm}= \mu) = 1-\lambda \hspace{0.05cm},$$
 :$${\rm Pr}(Y \hspace{-0.05cm} = {\rm E}\hspace{-0.05cm}\mid \hspace{-0.05cm} X \hspace{-0.05cm}= \mu) = \lambda \hspace{0.05cm}.$$
-Gesucht werden:
+We are looking for:
-* die Kapazität &nbsp;$C_{M\rm –EC}$&nbsp; dieses ''M–ary Erasure Channels'',
+* the capacity &nbsp;$C_{M\rm –EC}$&nbsp; of this ''M–ary Erasure Channels'',
-* die Kapazität &nbsp;$C_{\rm BEC}$&nbsp; des&nbsp; [[Channel_Coding/Kanalmodelle_und_Entscheiderstrukturen#Binary_Erasure_Channel_.E2.80.93_BEC|Binary Erasure Channels]]&nbsp; als Sonderfall des obigen Modells.
+* the capacity &nbsp;$C_{\rm BEC}$&nbsp; of the&nbsp; [[Channel_Coding/Kanalmodelle_und_Entscheiderstrukturen#Binary_Erasure_Channel_.E2.80.93_BEC|Binary Erasure Channels]]&nbsp; as a special case of the above model.

← Older revision	Revision as of 15:14, 22 July 2021
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← Older revision	Revision as of 14:52, 22 July 2021
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← Older revision		Revision as of 12:46, 23 March 2021
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−	[[Category:~~Aufgaben zu Informationstheorie~~\|^3.3 Anwendung auf DSÜ-Kanäle^]]	+	[[Category:Information Theory: Exercises\|^3.3 Anwendung auf DSÜ-Kanäle^]]