Aufgaben:Exercise 3.7: Comparison of Two Convolutional Encoders - Revision history

Guenter at 17:09, 16 November 2022

2022-11-16T17:09:13Z

Guenter at 15:03, 14 November 2022

2022-11-14T15:03:48Z

Guenter at 14:50, 14 November 2022

2022-11-14T14:50:46Z

Noah at 14:01, 3 October 2022

2022-10-03T14:01:22Z

Noah at 14:00, 3 October 2022

2022-10-03T14:00:50Z

Guenter at 12:38, 2 October 2022

2022-10-02T12:38:07Z

Guenter: Guenter moved page Aufgaben:Aufgabe 3.7: Vergleich zweier Faltungscodierer to Aufgaben:Exercise 3.7: Comparison of Two Convolutional Encoders

2022-10-02T12:33:37Z

Guenter moved page Aufgabe 3.7: Vergleich zweier Faltungscodierer to Exercise 3.7: Comparison of Two Convolutional Encoders

Javier: Text replacement - "Category:Aufgaben zu Kanalcodierung" to "Category:Channel Coding: Exercises"

2021-03-23T12:48:43Z

Text replacement - "Category:Aufgaben zu Kanalcodierung" to "Category:Channel Coding: Exercises"

Javier: Text replacement - "[[Kanalcodierung" to "[[Channel_Coding"

2020-07-09T12:50:42Z

Text replacement - "[[Kanalcodierung" to "[[Channel_Coding"

Guenter at 14:10, 7 June 2019

2019-06-07T14:10:11Z

@@ Line 1: / Line 1: @@
 {{quiz-Header|Buchseite=Channel_Coding/Code_Description_with_State_and_Trellis_Diagram}}
-[[File:P_ID2672__KC_A_3_7.png|right|frame|Two convolutional encoders with parameters&nbsp; $n = 2, \ k = 1, \ m = 2$]]
+[[File:EN_KC_A_3_7_neu_v2.png|right|frame|Two convolutional encoders with parameters&nbsp; $n = 2, \ k = 1, \ m = 2$]]
 The graph shows two rate&nbsp; $1/2$&nbsp; convolutional encoders,&nbsp; each with memory&nbsp; $m = 2$:
 * The encoder &nbsp;$\rm A$&nbsp; has the transfer function matrix $\mathbf{G}(D) = (1 + D^2, \ 1 + D + D^2)$.

@@ Line 20: / Line 20: @@
+<u>Hints:</u>
 *This exercise belongs to the chapter&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram| "Code description with state and trellis diagram"]].
@@ Line 56: / Line 54: @@
 {{ML-Kopf}}
   [[File:P_ID2673__KC_A_3_7a_neu.png|right|frame|Calculation of the code sequence]]
-'''(1)'''&nbsp; The calculation is based on the equations.
+'''(1)'''&nbsp; The calculation is based on the equations
 :$$x_i^{(1)} = u_i + u_{i&ndash;2},$$
 :$$x_i^{(2)} = u_i + u_{i&ndash;1} + u_{i&ndash;2}.$$
-*Initially, the two memories ($u_{i&ndash;1}$ and $u_{i&ndash;2}$) are preallocated with zeros &nbsp;&#8658;&nbsp; $s_1 = S_0$.
+*Initially,&nbsp; the two memories&nbsp; $(u_{i&ndash;1}$&nbsp; and&nbsp; $u_{i&ndash;2})$&nbsp; are preallocated with zeros &nbsp; &#8658; &nbsp; $s_1 = S_0$.
 *With $u_1 = 0$, we get $\underline{x}_1 = (00)$ and $s_2 = S_0$.
-*With $u_2 = 1$ one obtains the output $\underline{x}_2 = (11)$ and the new state $s_3 = S_3$.
+*With&nbsp; $u_1 = 0$,&nbsp; we get&nbsp; $\underline{x}_1 = (00)$&nbsp; and&nbsp; $s_2 = S_0$.
-From the adjacent calculation scheme one recognizes the correctness of the <u>proposed solutions 1 and 4</u>.
+From the adjacent calculation scheme one recognizes the correctness of the&nbsp; <u>proposed solutions 1 and 4</u>.
 [[File:P_ID2674__KC_A_3_7b.png|right|frame|State transition diagram of encoder &nbsp;$\rm A$]]
-'''(2)'''&nbsp; <u>All proposed solutions</u> are correct:
+'''(2)'''&nbsp; <u>All proposed solutions</u>&nbsp; are correct:
-*This can be seen by evaluating the table at '''(1)'''.
+*This can be seen by evaluating the table at subtask&nbsp; '''(1)'''.
 *The results are shown in the adjacent graph.
 <br clear=all>
 [[File:P_ID2675__KC_A_3_7c.png|right|frame|State transition diagram of encoder &nbsp;$\rm B$]]
-'''(3)'''&nbsp; Correct is only <u>statement 3</u>:
+'''(3)'''&nbsp; Correct is only&nbsp; <u>statement 3</u>:
-*The state transition diagram of Coder &nbsp;$\rm B$&nbsp; is sketched on the right. For derivation and interpretation, see section [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#Representation_in_the_state_transition_diagram|"Representation in the state transition diagram"]].
+*The state transition diagram of encoder &nbsp;$\rm B$&nbsp; is sketched on the right.&nbsp; For derivation and interpretation,&nbsp; see section [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#Representation_in_the_state_transition_diagram|"Representation in the state transition diagram"]].
 *If we swap the two output bits $x_i^{(1)}$ and $x_i^{(2)}$, we get from the convolutional encoder &nbsp;$\rm A$&nbsp; to the convolutional encoder&nbsp; $\rm B$&nbsp; (and vice versa).

@@ Line 2: / Line 2: @@
 [[File:P_ID2672__KC_A_3_7.png|right|frame|Two convolutional encoders with parameters&nbsp; $n = 2, \ k = 1, \ m = 2$]]
-The graph shows two rate $1/2$ convolutional encoders, each with memory&nbsp; $m = 2$:
+The graph shows two rate&nbsp; $1/2$&nbsp; convolutional encoders,&nbsp; each with memory&nbsp; $m = 2$:
-* The coder &nbsp;$\rm A$&nbsp; has the transfer function matrix $\mathbf{G}(D) = (1 + D^2, \ 1 + D + D^2)$.
+* The encoder &nbsp;$\rm A$&nbsp; has the transfer function matrix $\mathbf{G}(D) = (1 + D^2, \ 1 + D + D^2)$.
-* In the coder &nbsp;$\rm B$&nbsp; the two filters (top and bottom) are interchanged, and it holds : $\mathbf{G}(D) = (1 + D + D^2, \ 1 + D^2)$.
 The lower encoder &nbsp;$\rm B$&nbsp; has already been treated in detail in the theory part.
-In the present exercise, you are to first determine the state transition diagram for coder &nbsp;$\rm A$&nbsp; and then work out the differences and the similarities between the two state diagrams.
+In the present exercise,&nbsp;
@@ Line 19: / Line 24: @@
 Hints:
 *This exercise belongs to the chapter&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram| "Code description with state and trellis diagram"]].
-*Reference is made in particular to the sections.
-**&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#State_definition_for_a_memory_register|"State definition for a memory register"]]&nbsp; and.
+*Reference is made in particular to the sections
-**&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#Representation_in_the_state_transition_diagram|"Representation in the state transition diagram"]].
+:*&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#State_definition_for_a_memory_register|"State definition for a memory register"]]&nbsp; and.
 ===Questions===
 <quiz display=simple>
-{&nbsp; $\underline{u} = (0, \, 1, \, 1, \, 1, \, 0, \, 1, \, 0, \, 0, \, \text{...}\hspace{0.05cm})$ holds. Which sequences does Coder &nbsp;$\rm A$ generate?
+{&nbsp; $\underline{u} = (0, \, 1, \, 1, \, 1, \, 0, \, 1, \, 0, \, 0, \, \text{...}\hspace{0.05cm})$&nbsp; holds.&nbsp; Which sequences does encoder &nbsp;$\rm A$ generate?
 |type="[]"}
 + $\underline{x}^{(1)} = (0, \, 1, \, 1, \, 0, \, 1, \, 0, \, 0, \, 1, \, \text{...}\hspace{0.05cm})$,
@@ Line 44: / Line 50: @@
 - Other state transitions are possible.
 - All eight transitions have different code sequences.
-+ Differences exist only for the code sequences&nbsp; $(01)$&nbsp; and&nbsp; $(10)$.
++ Differences exist only for the code sequences&nbsp; "$(01)$"&nbsp; and&nbsp; "$(10)$".
 </quiz>

@@ Line 18: / Line 18: @@
 Hints:
-*This exercise belongs to the chapter&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram| "Code description with state&ndash; and trellis diagram"]].
+*This exercise belongs to the chapter&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram| "Code description with state and trellis diagram"]].
 *Reference is made in particular to the sections.
 **&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#State_definition_for_a_memory_register|"State definition for a memory register"]]&nbsp; and.

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Kanalcodierung/Codebeschreibung mit Zustands– und Trellisdiagramm}}
+{{quiz-Header|Buchseite=Channel_Coding/Code_Description_with_State_and_Trellis_Diagram}}
-[[File:P_ID2672__KC_A_3_7.png|right|frame|Zwei Faltungscodierer mit den Parametern&nbsp;  $n = 2, \ k = 1, \ m = 2$]]
+[[File:P_ID2672__KC_A_3_7.png|right|frame|Two convolutional encoders with parameters&nbsp; $n = 2, \ k = 1, \ m = 2$]]
-Die Grafik zeigt zwei Rate&ndash;$1/2$&ndash;Faltungscodierer, jeweils mit dem Gedächtnis&nbsp; $m = 2$:
+The graph shows two rate $1/2$ convolutional encoders, each with memory&nbsp; $m = 2$:
-* Der Coder &nbsp;$\rm A$&nbsp; weist die Übertragungsfunktionsmatrix $\mathbf{G}(D) = (1 + D^2, \ 1 + D + D^2)$ auf.
+* The coder &nbsp;$\rm A$&nbsp; has the transfer function matrix $\mathbf{G}(D) = (1 + D^2, \ 1 + D + D^2)$.
-* Beim Coder &nbsp;$\rm B$&nbsp; sind die beiden Filter (oben und unten) vertauscht, und es gilt : $\mathbf{G}(D) = (1 + D + D^2, \ 1 + D^2)$.
+* In the coder &nbsp;$\rm B$&nbsp; the two filters (top and bottom) are interchanged, and it holds : $\mathbf{G}(D) = (1 + D + D^2, \ 1 + D^2)$.
-Der untere Coder &nbsp;$\rm B$&nbsp; wurde im Theorieteil schon ausführlich behandelt.
+The lower encoder &nbsp;$\rm B$&nbsp; has already been treated in detail in the theory part.
-In der vorliegenden Aufgabe sollen Sie zunächst das Zustandsübergangsdiagramm für Coder &nbsp;$\rm A$&nbsp; ermitteln und anschließend die Unterschiede und die Gemeinsamkeiten zwischen den beiden Zustandsdiagrammen herausarbeiten.
+In the present exercise, you are to first determine the state transition diagram for coder &nbsp;$\rm A$&nbsp; and then work out the differences and the similarities between the two state diagrams.
@@ Line 17: / Line 17: @@
-''Hinweise:''
+Hints:
-* Die Aufgabe gehört zum Kapitel&nbsp; [[Channel_Coding/Codebeschreibung_mit_Zustands%E2%80%93_und_Trellisdiagramm| Codebeschreibung mit Zustands&ndash; und Trellisdiagramm]].
+*This exercise belongs to the chapter&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram| "Code description with state&ndash; and trellis diagram"]].
-*Bezug genommen wird insbesondere auf die Abschnitte
+*Reference is made in particular to the sections.
-**&nbsp; [[Channel_Coding/Codebeschreibung_mit_Zustands–_und_Trellisdiagramm#Zustandsdefinition_f.C3.BCr_ein_Speicherregister|Zustandsdefinition für ein Speicherregister]]&nbsp; sowie
+**&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#State_definition_for_a_memory_register|"State definition for a memory register"]]&nbsp; and.
-**&nbsp; [[Channel_Coding/Codebeschreibung_mit_Zustands–_und_Trellisdiagramm#Darstellung im_Zustands.C3.BCbergangsdiagramm|Darstellung im Zustandsübergangsdiagramm]].
+**&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#Representation_in_the_state_transition_diagram|"Representation in the state transition diagram"]].
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Es gelte&nbsp; $\underline{u} = (0, \, 1, \, 1, \, 1, \, 0, \, 1, \, 0, \, 0, \, \text{...}\hspace{0.05cm})$. Welche Sequenzen erzeugt Coder &nbsp;$\rm A$?
+{&nbsp; $\underline{u} = (0, \, 1, \, 1, \, 1, \, 0, \, 1, \, 0, \, 0, \, \text{...}\hspace{0.05cm})$ holds. Which sequences does Coder &nbsp;$\rm A$ generate?
 |type="[]"}
 + $\underline{x}^{(1)} = (0, \, 1, \, 1, \, 0, \, 1, \, 0, \, 0, \, 1, \, \text{...}\hspace{0.05cm})$,
@@ Line 33: / Line 33: @@
 + $\underline{x}^{(2)} = (0, \, 1, \, 0, \, 1, \, 0, \, 0, \, 1, \, 1, \, \text{...}\hspace{0.05cm})$.
-{Welche der genannten Zustandsübergänge gibt es bei Coder &nbsp;$\rm A$?
+{Which of the above state transitions exist in encoder &nbsp;$\rm A$?
 |type="[]"}
 + $s_i = S_0, \ u_i = 0 \ &#8658; \ s_{i+1} = S_0; \hspace{1cm} s_i = S_0, \ u_i = 1 \ &#8658; \ s_{i+1} = S_1$.
@@ Line 40: / Line 40: @@
 + $s_i = S_3, \ u_i = 0 \ &#8658; \ s_{i+1} = S_2; \hspace{1cm} s_i = S_3, \ u_i = 1 \ &#8658; \ s_{i+1} = S_3$.
-{Wie unterscheiden sich die beiden Zustandsübergangsdiagramme?
+{How do the two state transition diagrams differ?
 |type="[]"}
-- Es sind andere Zustandsübergänge möglich.
+- Other state transitions are possible.
-- Bei allen acht Übergängen stehen andere Codesequenzen.
+- All eight transitions have different code sequences.
-+ Unterschiede gibt es nur für die Codesequenzen&nbsp; $(01)$&nbsp; und&nbsp; $(10)$.
++ Differences exist only for the code sequences&nbsp; $(01)$&nbsp; and&nbsp; $(10)$.
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-  [[File:P_ID2673__KC_A_3_7a_neu.png|right|frame|Berechnung der Codesequenz]]
+  [[File:P_ID2673__KC_A_3_7a_neu.png|right|frame|Calculation of the code sequence]]
-'''(1)'''&nbsp; Die Berechnung basiert auf den Gleichungen
+'''(1)'''&nbsp; The calculation is based on the equations.
 :$$x_i^{(1)} = u_i + u_{i&ndash;2},$$
 :$$x_i^{(2)} = u_i + u_{i&ndash;1} + u_{i&ndash;2}.$$
-*Zu Beginn sind die beiden Speicher ($u_{i&ndash;1}$ und $u_{i&ndash;2}$) mit Nullen vorbelegt &nbsp;&#8658;&nbsp; $s_1 = S_0$.
+*Initially, the two memories ($u_{i&ndash;1}$ and $u_{i&ndash;2}$) are preallocated with zeros &nbsp;&#8658;&nbsp; $s_1 = S_0$.
-*Mit $u_1 = 0$ ergibt sich $\underline{x}_1 = (00)$ und $s_2 = S_0$.
+*With $u_1 = 0$, we get $\underline{x}_1 = (00)$ and $s_2 = S_0$.
-*Mit $u_2 = 1$ erhält man die Ausgabe $\underline{x}_2 = (11)$ und den neuen Zustand $s_3 = S_3$.
+*With $u_2 = 1$ one obtains the output $\underline{x}_2 = (11)$ and the new state $s_3 = S_3$.
-Aus nebenstehendem Berechnungsschema erkennt man die Richtigkeit der <u>Lösungsvorschläge 1 und 4</u>.
+From the adjacent calculation scheme one recognizes the correctness of the <u>proposed solutions 1 and 4</u>.
+[[File:P_ID2674__KC_A_3_7b.png|right|frame|State transition diagram of encoder &nbsp;$\rm A$]]
-[[File:P_ID2674__KC_A_3_7b.png|right|frame|Zustandsübergangsdiagramm von Coder &nbsp;$\rm A$]]
+'''(2)'''&nbsp; <u>All proposed solutions</u> are correct:
-'''(2)'''&nbsp; <u>Alle Lösungsvorschläge</u> sind richtig:
+*This can be seen by evaluating the table at '''(1)'''.
-*Dies erkennt man durch Auswertung der Tabelle bei '''(1)'''.
+*The results are shown in the adjacent graph.
 <br clear=all>
-[[File:P_ID2675__KC_A_3_7c.png|right|frame|Zustandsübergangsdiagramm von Coder &nbsp;$\rm B$]]
+[[File:P_ID2675__KC_A_3_7c.png|right|frame|State transition diagram of encoder &nbsp;$\rm B$]]
-'''(3)'''&nbsp; Richtig ist nur die <u>Aussage 3</u>:
+'''(3)'''&nbsp; Correct is only <u>statement 3</u>:
-*Rechts ist das Zustandsübergangsdiagramm von Coder &nbsp;$\rm B$&nbsp; skizziert. Herleitung und Tnterpretation siehe Abschnitt [[Channel_Coding/Codebeschreibung_mit_Zustands–_und_Trellisdiagramm#Darstellung im_Zustands.C3.BCbergangsdiagramm|Darstellung im Zustandsübergangsdiagramm]].
+*The state transition diagram of Coder &nbsp;$\rm B$&nbsp; is sketched on the right. For derivation and interpretation, see section [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#Representation_in_the_state_transition_diagram|"Representation in the state transition diagram"]].
-*Vertauscht man die beiden Ausgabebits $x_i^{(1)}$ und $x_i^{(2)}$, so kommt man vom Faltungscodierer &nbsp;$\rm A$&nbsp; zum Faltungscodierer&nbsp; $\rm B$&nbsp; (und umgekehrt).
+*If we swap the two output bits $x_i^{(1)}$ and $x_i^{(2)}$, we get from the convolutional encoder &nbsp;$\rm A$&nbsp; to the convolutional encoder&nbsp; $\rm B$&nbsp; (and vice versa).

← Older revision		Revision as of 12:38, 2 October 2022
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−	[[Category:Channel Coding: Exercises\|^3.3 ~~Zustands– und Trellisdiagramm~~^]]	+	[[Category:Channel Coding: Exercises\|^3.3 State and Trellis Diagram^]]

← Older revision	Revision as of 12:33, 2 October 2022
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← Older revision		Revision as of 12:48, 23 March 2021
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−	[[Category:~~Aufgaben zu Kanalcodierung~~\|^3.3 Zustands– und Trellisdiagramm^]]	+	[[Category:Channel Coding: Exercises\|^3.3 Zustands– und Trellisdiagramm^]]