Aufgaben:Exercise 3.6Z: Transition Diagram at 3 States - Revision history

Guenter at 14:43, 14 November 2022

2022-11-14T14:43:05Z

Guenter at 14:25, 14 November 2022

2022-11-14T14:25:18Z

Noah at 13:52, 3 October 2022

2022-10-03T13:52:01Z

Noah at 13:40, 3 October 2022

2022-10-03T13:40:57Z

Guenter at 12:37, 2 October 2022

2022-10-02T12:37:38Z

Guenter: Guenter moved page Aufgaben:Aufgabe 3.6Z: Übergangsdiagramm bei 3 Zuständen to Aufgaben:Exercise 3.6Z: Transition Diagram at 3 States

2022-10-02T12:32:35Z

Guenter moved page Aufgabe 3.6Z: Übergangsdiagramm bei 3 Zuständen to Exercise 3.6Z: Transition Diagram at 3 States

Javier: Text replacement - "„" to """

2021-05-28T14:36:25Z

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Javier: Text replacement - "”" to """

2021-05-28T14:36:15Z

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

2021-03-23T12:51:03Z

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

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

2020-07-09T12:50:20Z

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

@@ Line 60: / Line 60: @@
 {To which state&nbsp; $S_{\mu}$&nbsp; does the second arrow in each case go?
 |type="{}"}
-${\rm From \ {\it S}_{\rm 1} \ to \ the state \ with \ index \ {\mu}} \ = \ ${ 3 }
+${\rm From \ {\it S}_{\rm 1} \ to \ the\ state \ with \ index \ {\mu}} \ = \ ${ 3 }
-${\rm From \ {\it S}_{\rm 3} \ to \ the state \ with \ index \ {\mu}} \ = \ ${ 6 }
+${\rm From \ {\it S}_{\rm 3} \ to \ the\ state \ with \ index \ {\mu}} \ = \ ${ 6 }
-${\rm From \ {\it S}_{\rm 5} \ to \ the state \ with \ index \ {\mu}} \ = \ ${ 2 }
+${\rm From \ {\it S}_{\rm 5} \ to \ the\ state \ with \ index \ {\mu}} \ = \ ${ 2 }
-${\rm From \ {\it S}_{\rm 7} \ to \ the state \ with \ index \ {\mu}} \ = \ ${ 6 }
+${\rm From \ {\it S}_{\rm 7} \ to \ the\ state \ with \ index \ {\mu}} \ = \ ${ 6 }
 </quiz>
@@ Line 69: / Line 69: @@
 {{ML-Kopf}}
 [[File:P_ID2668__KC_Z_3_6b_neu.png|right|frame|Relationship between placeholders and states]]
-'''(1)'''&nbsp; The placeholder $\mathbf{A}$ represents the state $S_0$ &nbsp;&#8658;&nbsp; $u_{i-1} = 0, \ u_{i-2} = 0, \ u_{i-3} = 0$.
+[[File:P_ID2669__KC_Z_3_6c.png|right|frame|State transition diagram with $2^3$ states]]
-*This is the only state $S_{\mu}$ where one remains in the same state $S_{\mu}$ by the infobit $u_i = 0$ (red arrow).
-*From the state $S_7$ &nbsp;&#8658;&nbsp; $u_{i-1} = 1, \ u_{i-2} = 1, \ u_{i-3} = 1$ one comes with $u_i = 1$ (blue arrow) also again to the state $S_7$.
+'''(1)'''&nbsp; The placeholder&nbsp; $\mathbf{A}$&nbsp; represents the state&nbsp; $S_0$ &nbsp; &#8658; &nbsp; $u_{i-1} = 0, \ u_{i-2} = 0, \ u_{i-3} = 0$.
 *Thus, for $\mathbf{A}$ the index $\underline{\mu = 0}$ and for $\mathbf{F}$ the index $\underline{\mu = 7}$ had to be entered.
-'''(2)'''&nbsp; Starting from the state $\mathbf{A} = S_0$, one arrives at the following states according to the initial graph in a clockwise direction with the red arrows $(u_i = 0)$ or the blue arrows $(u_i = 1)$:
+'''(2)'''&nbsp; Starting from the state&nbsp; $\mathbf{A} = S_0$,&nbsp; one arrives at the following states according to the initial graph in a clockwise direction with the red arrows&nbsp; $(u_i = 0)$&nbsp; or the blue arrows&nbsp; $(u_i = 1)$:
 :$$u_{i&ndash;3} = 0, \ u_{i&ndash;2} = 0, \ u_{i&ndash;1} = 0, \ u_i = 1 &#8658; s_{i+1} = \mathbf{B} = S_1,$$
 :$$u_{i&ndash;3} = 0, \ u_{i&ndash;2} = 0, \ u_{i&ndash;1} = 1, \ u_i = 0 &#8658; s_{i+1} = \mathbf{C} = S_2,$$
@@ Line 86: / Line 91: @@
 :$$u_{i&ndash;3} = 1, \ u_{i&ndash;2} = 0, \ u_{i&ndash;1} = 0, \ u_i = 0 &#8658; s_{i+1} = \mathbf{A} = S_0.$$
-*So the indices $\mu$ are to be entered in the <u>order 1, 2, 5, 3, 6, 4</u>.
+*So the indices&nbsp; $\mu$&nbsp; are to be entered in the&nbsp; <u>order 1,&nbsp; 2,&nbsp; 5,&nbsp; 3,&nbsp; 6,&nbsp; 4</u>.
 *The graphic shows the connection between the placeholders and the states $S_{\mu}$.
-[[File:P_ID2669__KC_Z_3_6c.png|right|frame|State transition diagram with $2^3$ states]]
+The adjacent graphic shows the state transition diagram with all transitions.&nbsp; From this it can be read:
-The adjacent graphic shows the state transition diagram with all transitions. From this it can be read:
+* From the state&nbsp; $S_7$&nbsp; one comes with&nbsp; $u_i = 0$&nbsp; to the state&nbsp; $S_6$.
-Thus, the indices are to be entered in the <u>order 3, 6, 2, 6</u>.
+Thus,&nbsp; the indices are to be entered in the <u>order 3,&nbsp; 6,&nbsp; 2,&nbsp; 6</u>.
 {{ML-Fuß}}

@@ Line 1: / Line 1: @@
 {{quiz-Header|Buchseite=Channel_Coding/Code_Description_with_State_and_Trellis_Diagram}}
-[[File:P_ID2667__KC_Z_3_6.png|right|frame|State transition diagram for&nbsp; $m = 3$&nbsp; (incomplete)]]
+[[File:P_ID2667__KC_Z_3_6.png|right|frame|State transition diagram for&nbsp; $m = 3$&nbsp; $($incomplete$)$]]
-In the state transition diagram of an encoder with memory&nbsp; $m$&nbsp; there are&nbsp; $2^m$&nbsp; states. Therefore, the diagram shown with eight states describes a convolutional encoder with memory&nbsp; $m = 3$.
+In the state transition diagram of an encoder with memory&nbsp; $m$&nbsp; there are&nbsp; $2^m$&nbsp; states.&nbsp; Therefore,&nbsp; the diagram shown with eight states describes a convolutional encoder with memory&nbsp; $m = 3$.
-Usually the states are denoted by&nbsp; $S_0, \ \text{...} \ , \ S_{\mu}, \ \text{...} \ , \ S_7$, where the index&nbsp; $\mu$&nbsp; is determined from the occupancy of the shift register (contents from left to right: &nbsp; $u_{i-1}, u_{i-2}, u_{i-3})$&nbsp;:
+Usually the states are denoted by&nbsp; $S_0, \ \text{...} \ , \ S_{\mu}, \ \text{...} \ , \ S_7$,&nbsp; where the index&nbsp; $\mu$&nbsp; is determined from the occupancy of the shift register&nbsp; $($contents from left to right: &nbsp; $u_{i-1}, u_{i-2}, u_{i-3})$&nbsp;:
 :$$\mu = \sum_{l = 1}^{m} \hspace{0.1cm}2\hspace{0.03cm}^{l-1} \cdot u_{i-l}
 \hspace{0.05cm}.$$
-The state&nbsp; $S_0$&nbsp; therefore results for the shift register content "$000$", the state&nbsp; $S_1$&nbsp; for "$100$" and the state&nbsp; $S_7$&nbsp; for "$111$".
+The state&nbsp; $S_0$&nbsp; therefore results for the shift register content&nbsp; "$000$",&nbsp; the state&nbsp; $S_1$&nbsp; for&nbsp; "$100$"&nbsp; and the state&nbsp; $S_7$&nbsp; for&nbsp; "$111$".
-However, in the above graphic, for the states&nbsp; $S_0, \, \text{...} \, , \, S_7$&nbsp; placeholder names&nbsp; $\mathbf{A}, \, \text{...} \, , \, \mathbf{H}$&nbsp; used. In the subtasks '''(1)''' and '''(2)''' you should clarify which placeholder stands for which state.
+However,&nbsp; in the above graphic,&nbsp; for the states&nbsp; $S_0, \, \text{...} \, , \, S_7$&nbsp; only placeholder names&nbsp; $\mathbf{A}, \, \text{...} \, , \, \mathbf{H}$&nbsp; are used.&nbsp; In the subtasks&nbsp; '''(1)'''&nbsp; and&nbsp; '''(2)'''&nbsp; you should clarify which placeholder stands for which state.
-For convolutional encoders of rate&nbsp; $1/n$, which will be exclusively considered here, two arrows depart from each state&nbsp; $S_{\mu}$&nbsp;,
+For convolutional encoders of rate&nbsp; $1/n$,&nbsp; which will be exclusively considered here,&nbsp; two arrows depart from each state&nbsp; $S_{\mu}$&nbsp;,
-*one red one for the current information bit&nbsp; $u_i = 0$&nbsp; and.
+*a red one for the current information bit&nbsp; $u_i = 0$&nbsp; and
 *a blue one for&nbsp; $u_i = 1$.
-This is another reason why the state transition diagram shown is not complete. It is to be mentioned furthermore:
+This is another reason why the state transition diagram shown is not complete.&nbsp; It is to be mentioned furthermore:
-* At each state also two arrows arrive, whereby these can be absolutely of the same color.
+* At each state also two arrows arrive,&nbsp; whereby these can be absolutely of the same color.
 * Next to the arrows there are usually the&nbsp; $n$&nbsp; code bits. This was also omitted here.
@@ Line 25: / Line 27: @@
 *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; as well as.
+:*[[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#State_definition_for_a_memory_register|"State definition for a memory register"]]&nbsp; as well as
-** [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#Representation_in_the_state_transition_diagram|"Representation in the state transition diagram"]].
+:* [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#Representation_in_the_state_transition_diagram|"Representation in the state transition diagram"]].
@@ Line 45: / Line 46: @@
 {For which states&nbsp; $S_{\mu}$&nbsp; do the placeholders&nbsp; $\mathbf{A}$&nbsp; and&nbsp; $\mathbf{F}$ stand?
 |type="{}"}
-${\rm Zustand} \ \mathbf{A} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 0. }
+${\rm state} \ \mathbf{A} \ &#8658; \ {\rm index} \ {\mu} \ = \ ${ 0. }
-${\rm Zustand} \ \mathbf{F} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 7 }
+${\rm state} \ \mathbf{F} \ &#8658; \ {\rm index} \ {\mu} \ = \ ${ 7 }
 {Also name the mappings of the other placeholders to the indexes.
 |type="{}"}
-${\rm Zustand} \ \mathbf{B} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 1 }
+${\rm state} \ \mathbf{B} \ &#8658; \ {\rm index} \ {\mu} \ = \ ${ 1 }
-${\rm Zustand} \ \mathbf{C} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 2 }
+${\rm state} \ \mathbf{C} \ &#8658; \ {\rm index} \ {\mu} \ = \ ${ 2 }
-${\rm Zustand} \ \mathbf{D} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 5 }
+${\rm state} \ \mathbf{D} \ &#8658; \ {\rm index} \ {\mu} \ = \ ${ 5 }
-${\rm Zustand} \ \mathbf{E} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 3 }
+${\rm state} \ \mathbf{E} \ &#8658; \ {\rm index} \ {\mu} \ = \ ${ 3 }
-${\rm Zustand} \ \mathbf{G} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 6 }
+${\rm state} \ \mathbf{G} \ &#8658; \ {\rm index} \ {\mu} \ = \ ${ 6 }
-${\rm Zustand} \ \mathbf{H} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 4 }
+${\rm state} \ \mathbf{H} \ &#8658; \ {\rm index} \ {\mu} \ = \ ${ 4 }
 {To which state&nbsp; $S_{\mu}$&nbsp; does the second arrow in each case go?
 |type="{}"}
-${\rm Von \ {\it S}_{\rm 1} \ zum \ Zustand \ mit \ Index \ {\mu}} \ = \ ${ 3 }
+${\rm From \ {\it S}_{\rm 1} \ to \ the state \ with \ index \ {\mu}} \ = \ ${ 3 }
-${\rm Von \ {\it S}_{\rm 3} \ zum \ Zustand \ mit \ Index \ {\mu}} \ = \ ${ 6 }
+${\rm From \ {\it S}_{\rm 3} \ to \ the state \ with \ index \ {\mu}} \ = \ ${ 6 }
-${\rm Von \ {\it S}_{\rm 5} \ zum \ Zustand \ mit \ Index \ {\mu}} \ = \ ${ 2 }
+${\rm From \ {\it S}_{\rm 5} \ to \ the state \ with \ index \ {\mu}} \ = \ ${ 2 }
-${\rm Von \ {\it S}_{\rm 7} \ zum \ Zustand \ mit \ Index \ {\mu}} \ = \ ${ 6 }
+${\rm From \ {\it S}_{\rm 7} \ to \ the state \ with \ index \ {\mu}} \ = \ ${ 6 }
 </quiz>

@@ Line 43: / Line 43: @@
 ===Questions===
 <quiz display=simple>
-{Für welche Zustände&nbsp; $S_{\mu}$&nbsp; stehen die Platzhalter&nbsp; $\mathbf{A}$&nbsp; und&nbsp; $\mathbf{F}$?
+{For which states&nbsp; $S_{\mu}$&nbsp; do the placeholders&nbsp; $\mathbf{A}$&nbsp; and&nbsp; $\mathbf{F}$ stand?
 |type="{}"}
 ${\rm Zustand} \ \mathbf{A} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 0. }
 ${\rm Zustand} \ \mathbf{F} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 7 }
-{Nennen Sie auch die Zuordnungen der anderen Platzhalter zu den Indizes.
+{Also name the mappings of the other placeholders to the indexes.
 |type="{}"}
 ${\rm Zustand} \ \mathbf{B} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 1 }
@@ Line 57: / Line 57: @@
 ${\rm Zustand} \ \mathbf{H} \ &#8658; \ {\rm Index} \ {\mu} \ = \ ${ 4 }
-{Zu welchem Zustand&nbsp; $S_{\mu}$&nbsp; geht der jeweils zweite Pfeil?
+{To which state&nbsp; $S_{\mu}$&nbsp; does the second arrow in each case go?
 |type="{}"}
 ${\rm Von \ {\it S}_{\rm 1} \ zum \ Zustand \ mit \ Index \ {\mu}} \ = \ ${ 3 }
@@ Line 65: / Line 65: @@
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-[[File:P_ID2668__KC_Z_3_6b_neu.png|right|frame|Zusammenhang zwischen Platzhalter und Zuständen]]
+[[File:P_ID2668__KC_Z_3_6b_neu.png|right|frame|Relationship between placeholders and states]]
-'''(1)'''&nbsp; Der Platzhalter $\mathbf{A}$ steht für den Zustand $S_0$ &nbsp;&#8658;&nbsp; $u_{i-1} = 0, \ u_{i-2} = 0, \ u_{i-3} = 0$.
+'''(1)'''&nbsp; The placeholder $\mathbf{A}$ represents the state $S_0$ &nbsp;&#8658;&nbsp; $u_{i-1} = 0, \ u_{i-2} = 0, \ u_{i-3} = 0$.
-*Dies ist der einzige Zustand $S_{\mu}$, bei dem man durch das Infobit $u_i = 0$ (roter Pfeil) im gleichen Zustand $S_{\mu}$ bleibt.
+*This is the only state $S_{\mu}$ where one remains in the same state $S_{\mu}$ by the infobit $u_i = 0$ (red arrow).
-*Vom Zustand $S_7$ &nbsp;&#8658;&nbsp; $u_{i-1} = 1, \ u_{i-2} = 1, \ u_{i-3} = 1$ kommt man mit $u_i = 1$ (blauer Pfeil) auch wieder zum Zustand $S_7$.
+*From the state $S_7$ &nbsp;&#8658;&nbsp; $u_{i-1} = 1, \ u_{i-2} = 1, \ u_{i-3} = 1$ one comes with $u_i = 1$ (blue arrow) also again to the state $S_7$.
-*Einzugeben waren also für $\mathbf{A}$ der Index $\underline{\mu = 0}$ und für $\mathbf{F}$ der Index $\underline{\mu = 7}$.
+*Thus, for $\mathbf{A}$ the index $\underline{\mu = 0}$ and for $\mathbf{F}$ the index $\underline{\mu = 7}$ had to be entered.
-'''(2)'''&nbsp; Ausgehend vom Zustand $\mathbf{A} = S_0$ kommt man entsprechend der Ausgangsgrafik im Uhrzeigersinn mit den roten Pfeilen $(u_i = 0)$ bzw. den blauen Pfeilen $(u_i = 1)$ zu folgenden Zuständen:
+'''(2)'''&nbsp; Starting from the state $\mathbf{A} = S_0$, one arrives at the following states according to the initial graph in a clockwise direction with the red arrows $(u_i = 0)$ or the blue arrows $(u_i = 1)$:
 :$$u_{i&ndash;3} = 0, \ u_{i&ndash;2} = 0, \ u_{i&ndash;1} = 0, \ u_i = 1 &#8658; s_{i+1} = \mathbf{B} = S_1,$$
 :$$u_{i&ndash;3} = 0, \ u_{i&ndash;2} = 0, \ u_{i&ndash;1} = 1, \ u_i = 0 &#8658; s_{i+1} = \mathbf{C} = S_2,$$
@@ Line 85: / Line 85: @@
 :$$u_{i&ndash;3} = 1, \ u_{i&ndash;2} = 0, \ u_{i&ndash;1} = 0, \ u_i = 0 &#8658; s_{i+1} = \mathbf{A} = S_0.$$
-*Einzugeben sind also die Indizes $\mu$ in der <u>Reihenfolge 1, 2, 5, 3, 6, 4</u>.
+*So the indices $\mu$ are to be entered in the <u>order 1, 2, 5, 3, 6, 4</u>.
-*Die Grafik zeigt den Zusammenhang zwischen den Platzhaltern und den Zuständen $S_{\mu}$.
+*The graphic shows the connection between the placeholders and the states $S_{\mu}$.
-'''(3)'''&nbsp; Vom Zustand $S_1$ &#8658; $u_{i&ndash;1} = 1, \ u_{i&ndash;2} = 0, \ u_{i&ndash;3} = 0$ kommt man mit $u_i = 0$ (roter Pfeil) zum Zustand $S_2$. Dagegen landet man mit $u_i = 1$ (blauer Pfeil) beim Zustand $S_3$ &#8658; $u_{i&ndash;1} = 1, \ u_{i&ndash;2} = 1, \ u_{i&ndash;3} = 0$.
+'''(3)'''&nbsp; From state $S_1$ &#8658; $u_{i&ndash;1} = 1, \ u_{i&ndash;2} = 0, \ u_{i&ndash;3} = 0$ one arrives with $u_i = 0$ (red arrow) at state $S_2$. On the other hand, with $u_i = 1$ (blue arrow) one ends up at the state $S_3$ &#8658; $u_{i&ndash;1} = 1, \ u_{i&ndash;2} = 1, \ u_{i&ndash;3} = 0$.
-[[File:P_ID2669__KC_Z_3_6c.png|right|frame|Zustandsübergangsdiagramm mit $2^3$ Zuständen]]
+[[File:P_ID2669__KC_Z_3_6c.png|right|frame|State transition diagram with $2^3$ states]]
-Nebenstehende Grafik zeigt das Zustandsübergangsdiagramm mit allen Übergängen. Aus diesem kann abgelesen werden:
+The adjacent graphic shows the state transition diagram with all transitions. From this it can be read:
-* Vom Zustand $S_3$ kommt man mit $u_i = 0$ zum Zustand $S_6$.
+* From state $S_3$ one comes with $u_i = 0$ to state $S_6$.
-* Vom Zustand $S_5$ kommt man mit $u_i = 0$ zum Zustand $S_2$.
+* From the state $S_5$ one comes with $u_i = 0$ to the state $S_2$.
-* Vom Zustand $S_7$ kommt man mit $u_i = 0$ zum Zustand $S_6$.
+* From the state $S_7$ one comes with $u_i = 0$ to the state $S_6$.
-Einzugeben sind also die Indizes in der <u>Reihenfolge 3, 6, 2, 6</u>.
+Thus, the indices are to be entered in the <u>order 3, 6, 2, 6</u>.
 {{ML-Fuß}}

@@ 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_ID2667__KC_Z_3_6.png|right|frame|Zustandsübergangsdiagramm für&nbsp; $m = 3$&nbsp; (unvollständig)]]
+[[File:P_ID2667__KC_Z_3_6.png|right|frame|State transition diagram for&nbsp; $m = 3$&nbsp; (incomplete)]]
-Im Zustandsübergangsdiagramm eines Codierers mit Gedächtnis&nbsp; $m$&nbsp; gibt es&nbsp; $2^m$&nbsp; Zustände. Das dargestellte Diagramm mit acht Zuständen beschreibt deshalb einen Faltungscoder mit dem Gedächtnis&nbsp; $m = 3$.
+In the state transition diagram of an encoder with memory&nbsp; $m$&nbsp; there are&nbsp; $2^m$&nbsp; states. Therefore, the diagram shown with eight states describes a convolutional encoder with memory&nbsp; $m = 3$.
-Normalerweise bezeichnet man die Zustände mit&nbsp; $S_0, \ \text{...} \ , \ S_{\mu}, \ \text{...} \ , \ S_7$, wobei der Index&nbsp; $\mu$&nbsp; aus der Belegung des Schieberegisters (Inhalt von links nach rechts: &nbsp; $u_{i-1}, u_{i-2}, u_{i-3})$&nbsp; festgelegt ist:
+Usually the states are denoted by&nbsp; $S_0, \ \text{...} \ , \ S_{\mu}, \ \text{...} \ , \ S_7$, where the index&nbsp; $\mu$&nbsp; is determined from the occupancy of the shift register (contents from left to right: &nbsp; $u_{i-1}, u_{i-2}, u_{i-3})$&nbsp;:
 :$$\mu = \sum_{l = 1}^{m} \hspace{0.1cm}2\hspace{0.03cm}^{l-1} \cdot u_{i-l}
 \hspace{0.05cm}.$$
-Der Zustand&nbsp; $S_0$&nbsp; ergibt sich deshalb für den Schieberegisterinhalt "$000$", der Zustand&nbsp; $S_1$&nbsp; für "$100$" und der Zustand&nbsp; $S_7$&nbsp; für "$111$".
+The state&nbsp; $S_0$&nbsp; therefore results for the shift register content "$000$", the state&nbsp; $S_1$&nbsp; for "$100$" and the state&nbsp; $S_7$&nbsp; for "$111$".
-In obiger Grafik sind allerdings für die Zustände&nbsp; $S_0, \, \text{...} \, , \, S_7$&nbsp; Platzhalter names&nbsp; $\mathbf{A}, \, \text{...} \, , \, \mathbf{H}$&nbsp; verwendet. In den Teilaufgaben '''(1)''' und '''(2)''' sollen Sie klären, welcher Platzhalter für welchen Zustand steht.
+However, in the above graphic, for the states&nbsp; $S_0, \, \text{...} \, , \, S_7$&nbsp; placeholder names&nbsp; $\mathbf{A}, \, \text{...} \, , \, \mathbf{H}$&nbsp; used. In the subtasks '''(1)''' and '''(2)''' you should clarify which placeholder stands for which state.
-Bei Faltungscodierer der Rate&nbsp; $1/n$, die hier ausschließlich betrachtet werden sollen, gehen von jedem Zustand&nbsp; $S_{\mu}$&nbsp; zwei Pfeile ab,
+For convolutional encoders of rate&nbsp; $1/n$, which will be exclusively considered here, two arrows depart from each state&nbsp; $S_{\mu}$&nbsp;,
-*ein roter für das aktuelle Informationsbit&nbsp; $u_i = 0$&nbsp; und
+*one red one for the current information bit&nbsp; $u_i = 0$&nbsp; and.
-*ein blauer für&nbsp; $u_i = 1$.
+*a blue one for&nbsp; $u_i = 1$.
-Auch deshalb ist das gezeigte Zustandsübergangsdiagramm nicht vollständig. Zu erwähnen ist weiterhin:
+This is another reason why the state transition diagram shown is not complete. It is to be mentioned furthermore:
-* Bei jedem Zustand kommen auch zwei Pfeile an, wobei diese durchaus gleichfarbig sein können.
+* At each state also two arrows arrive, whereby these can be absolutely of the same color.
-* Neben den Pfeilen stehen üblicherweise noch die&nbsp; $n$&nbsp; Codebits. Auch hierauf wurde hier verzichtet.
+* Next to the arrows there are usually the&nbsp; $n$&nbsp; code bits. This was also omitted here.
@@ Line 28: / Line 28: @@
-''Hinweise:''
+Hints:
-* Die Aufgabe gehört zum Kapitel&nbsp; [[Channel_Coding/Codebeschreibung_mit_Zustands%E2%80%93_und_Trellisdiagramm| Codebeschreibung mit Zustands&ndash; und Trellisdiagramm]].
+* The exercise belongs to the chapter&nbsp; [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram| "Code Description with State and Trellis Diagram"]].
-* In&nbsp; [[Aufgaben:Aufgabe_3.7Z:_Welcher_Code_ist_katastrophal%3F| Aufgabe 3.7Z]]&nbsp; werden zwei Faltungscodes mit Gedächtnis&nbsp; $m = 3$&nbsp; untersucht, die beide durch das hier analysierte Übergangsdiagramm beschrieben werden können.
+*In&nbsp; [[Aufgaben:Exercise_3.7Z:_Which_Code_is_Catastrophic%3F| "Exercise 3.7Z"]]&nbsp; two convolutional codes with memory&nbsp; $m = 3$&nbsp; are examined, both of which can be described by the transition diagram analyzed here.
-*Bitte bei allen Fragen den ensprechenden ''Index'' &nbsp;$\mu$&nbsp; eingeben.
+*Please include the appropriate ''index'' &nbsp;$\mu$&nbsp; for all questions.
-*Bezug genommen wird insbesondere auf die Abschnitte&nbsp;
+*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
+**[[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#State_definition_for_a_memory_register|"State definition for a memory register"]]&nbsp; as well as.
-** [[Channel_Coding/Codebeschreibung_mit_Zustands–_und_Trellisdiagramm#Darstellung im_Zustands.C3.BCbergangsdiagramm|Darstellung im Zustandsübergangsdiagramm]].
+** [[Channel_Coding/Code_Description_with_State_and_Trellis_Diagram#Representation_in_the_state_transition_diagram|"Representation in the state transition diagram"]].
-===Fragebogen===
 <quiz display=simple>
 {Für welche Zustände&nbsp; $S_{\mu}$&nbsp; stehen die Platzhalter&nbsp; $\mathbf{A}$&nbsp; und&nbsp; $\mathbf{F}$?

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−	[[Category:Channel Coding: Exercises\|^3.3 ~~Zustands– und Trellisdiagramm~~^]]	+	[[Category:Channel Coding: Exercises\|^3.3 State and Trellis Diagram^]]

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 \hspace{0.05cm}.$$
-Der Zustand&nbsp; $S_0$&nbsp; ergibt sich deshalb für den Schieberegisterinhalt &bdquo;$000$&rdquo;, der Zustand&nbsp; $S_1$&nbsp; für &bdquo;$100$&rdquo; und der Zustand&nbsp; $S_7$&nbsp; für &bdquo;$111$&rdquo;.
+Der Zustand&nbsp; $S_0$&nbsp; ergibt sich deshalb für den Schieberegisterinhalt &bdquo;$000$", der Zustand&nbsp; $S_1$&nbsp; für &bdquo;$100$" und der Zustand&nbsp; $S_7$&nbsp; für &bdquo;$111$".
 In obiger Grafik sind allerdings für die Zustände&nbsp; $S_0, \, \text{...} \, , \, S_7$&nbsp; Platzhalter names&nbsp; $\mathbf{A}, \, \text{...} \, , \, \mathbf{H}$&nbsp; verwendet. In den Teilaufgaben '''(1)''' und '''(2)''' sollen Sie klären, welcher Platzhalter für welchen Zustand steht.

← Older revision		Revision as of 12:51, 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^]]