Aufgaben:Exercise 4.08Z: Basics about Interleaving - Revision history

Guenter at 12:53, 14 December 2022

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Guenter at 12:42, 14 December 2022

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Guenter at 12:40, 14 December 2022

2022-12-14T12:40:59Z

Noah at 18:01, 29 November 2022

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Noah at 17:24, 29 November 2022

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Noah at 18:44, 28 November 2022

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Noah at 21:31, 26 November 2022

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Guenter at 17:00, 31 October 2022

2022-10-31T17:00:44Z

Guenter: Guenter moved page Aufgaben:Aufgabe 4.08Z: Grundlegendes zum Interleaving to Aufgaben:Exercise 4.08Z: Basics about Interleaving

2022-10-31T16:56:47Z

Guenter moved page Aufgabe 4.08Z: Grundlegendes zum Interleaving to Exercise 4.08Z: Basics about Interleaving

Javier: Text replacement - "„" to """

2021-05-28T14:36:04Z

Text replacement - "„" to """

@@ Line 63: / Line 63: @@
 ===Solution===
 {{ML-Kopf}}
-[[File:P_ID3041__KC_Z_4_8b_v2.png|right|frame|4×3 Interleaver Matrix]]
+[[File:P_ID3041__KC_Z_4_8b_v2.png|right|frame|$4×3$&nbsp; interleaver matrix]]
-'''(1)'''&nbsp; From the regular structure of the function $I_{\rm Out}(I_{\rm In})$ one can see that it is a block interleaver &nbsp;&#8658;&nbsp; <u>Response 1</u>.
+'''(1)'''&nbsp; From the regular structure of the function&nbsp; $I_{\rm Out}(I_{\rm In})$&nbsp; one can see that it is a block interleaver &nbsp; &#8658; &nbsp; <u>Response 1</u>.
-'''(2)'''&nbsp; The index "1" is output as the first character. Further applies:
+'''(2)'''&nbsp; The index&nbsp; "1"&nbsp; is output as the first character.&nbsp; Further applies:
-* The index 5 is output as the second character &nbsp;&#8658;&nbsp; $\underline{Z = 4}$.
+* The index 5 is output as the second character &nbsp; &#8658; &nbsp; $\underline{N_{\rm R} = 4}$.
 The upper graph shows for the 4×3 interleaver matrix:
-* the column by column write (red),
+The upper graph shows for the&nbsp; $4×3$&nbsp; interleaver matrix:
-* the row by row readout (green).
+* the column-by-column write&nbsp; $($red$)$,
 [[File:P_ID3042__KC_Z_4_8c_v3.png|right|frame|Interleaving]]
-'''(3)'''&nbsp; Correct is <u>the proposed solution 2</u>:
+'''(3)'''&nbsp; Correct is&nbsp; <u>the proposed solution 2</u>:
-*The matrix is written column by column and read row by row.
+*The matrix is written column-by-column and read row-by-row.
-*After 12 bits, the matrix is cleared and the procedure starts over.
-*The graphic shows that now the solution suggestion 2 is correct.
+*After&nbsp; $12$&nbsp; bits,&nbsp; the matrix is cleared and the procedure starts again.
 <br clear=all>
-[[File:P_ID3043__KC_Z_4_8d_v1.png|right|frame|Zum De–Interleaving]]
+[[File:P_ID3043__KC_Z_4_8d_v1.png|right|frame|De–interleaving]]
-'''(4)'''&nbsp; Correct is <u>the proposed solution 1</u>:
+'''(4)'''&nbsp; Correct is&nbsp; <u>the proposed solution 1</u>:
-*In deinterleaving, the matrix is written row by row and read column by column.
+*In de-interleaving,&nbsp; the matrix is written row-by-row and read column-by-column.
 *The graphic shows that here the solution suggestion 1 is correct.

@@ Line 31: / Line 31: @@
 *But other&nbsp; $\rm LNTwww$&nbsp; books also discuss interleaving,&nbsp; including the book&nbsp; "Examples of Communication Systems"&nbsp; with reference to the
 :* standard digital subscriber line</i> $\rm (DSL)$ &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Methods_to_Reduce_the_Bit_Error_Rate_in_DSL#Interleaving_und_De.E2.80.93Interleaving| "Interleaving and Deinterleaving"]],
-:* 2G mobile communication system&nbsp; $\rm GSM$ &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Entire_GSM_Transmission_System#Komponenten_der_Sprach.E2.80.93_und_Daten.C3.BCbertragung| "Components of voice&ndash; and data transmission"]],
+:* 2G mobile communication system&nbsp; $\rm GSM$ &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Entire_GSM_Transmission_System#Komponenten_der_Sprach.E2.80.93_und_Daten.C3.BCbertragung| "Components of voice and data transmission"]],
 :* 3G mobile communication system&nbsp; $\rm UMTS$ &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Telecommunications_Aspects_of_UMTS#Kanalcodierung_bei_UMTS| "Channel Coding"]],
 :* 4G mobile communication system&nbsp; $\rm LTE$ &nbsp; &#8658; &nbsp; [[Mobile_Communications/The_Application_of_OFDMA_and_SC-FDMA_in_LTE#Functionality_of_SC-FDMA| "Functionality of SC-FDMA"]]&nbsp; $($in the boo&nbsp; "Mobile Communications"$)$.

@@ Line 2: / Line 2: @@
 [[File:P_ID3032__KC_Z_4_8_v3.png|right|frame|Interleaver description]]
-Interleaving is required, for example, for a channel with burst error characteristics in order to distribute the errors within the burst over a sufficiently large area so that they can subsequently be largely corrected (or at least detected).
+Interleaving is required,&nbsp;  for example,&nbsp;  for a channel with burst error characteristics in order to distribute the errors within the burst over a sufficiently large area so that they can subsequently be largely corrected&nbsp;  $($or at least detected$)$.
-For turbo codes based on so-called &nbsp;'''RSC encoder'''&nbsp; (<i>Recursive Systematic Convolutional Encoder</i>)&nbsp; &ndash; and only such make sense &ndash; <i>interleaving</i> is essential also with the AWGN channel, because then there are also always (some) input sequences, which deliver only zeros in the output sequence after quite a few ones, and that to infinity &nbsp; &#8658; &nbsp; there are output sequences with very small Hamming weight.
+For turbo codes based on so-called &nbsp;'''RSC encoder'''&nbsp; $($"Recursive Systematic Convolutional Encoder"$)$&nbsp; &ndash; and only such make sense &ndash; interleaving is essential also with the AWGN channel,&nbsp; because then there are also always $($some$)$ input sequences,&nbsp; which deliver only&nbsp; "zeros"&nbsp; in the output sequence after quite a few&nbsp; "ones",&nbsp; and that to infinity &nbsp; &#8658; &nbsp; there are output sequences with very small Hamming weight.
-If the bits of such input sequences are distributed over a wide range in the second coder, the problem can be (largely) eliminated by the interaction of both component decoders in the case of iterative symbol-wise decoding.
+If the bits of such input sequences are distributed over a wide range in the second encoder,&nbsp; the problem can be largely eliminated by the interaction of both component decoders in the case of iterative symbol-wise decoding.
 A general distinction is made between
-* '''Block interleaver''' and
+* '''block interleaver''' and
-On the right, two interleavers are indicated and in graphical form by the assignment&nbsp; $I_{\rm Out}(I_{\rm In})$. These quantities represent the "index of the output sequence" and the "index of the input sequence", respectively. It holds:
+In block interleaving&nbsp; one fills a matrix with&nbsp; $N_{\rm C}$&nbsp; columns and&nbsp; $N_{\rm R}$&nbsp; rows column-by-column and reads the matrix row-by-row.&nbsp; This deterministically scrambles a block of information with&nbsp; $I_{\rm max} = N_{\rm C} \cdot N_{\rm R}$&nbsp; bits.
-In the subtask&nbsp; '''(1)'''&nbsp; it is asked whether this is&nbsp; <i>block interleaving</i>&nbsp; or&nbsp; <i>random interleaving</i> &nbsp;. The latter are discussed in the&nbsp; [[Channel_Coding/The_Basics_of_Turbo_Codes#Second_requirement_for_turbo_codes:_Interleaving|"theory section"]]&nbsp; but only very briefly.
+On the right,&nbsp; two interleavers are indicated and in graphical form by the assignment&nbsp; $I_{\rm Out}(I_{\rm In})$.&nbsp; These quantities represent the&nbsp; "output sequence index"&nbsp; and the&nbsp; "input sequence index",&nbsp; respectively.&nbsp; It holds:
-*But other $\rm LNTww$&ndash;books also discuss interleaving, including the book "Examples of Message Systems" with reference to the
+<u>Hints:</u>
-:* Standard&nbsp; <i>Digital Subscriber Line</i> (DSL) &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Methods_to_Reduce_the_Bit_Error_Rate_in_DSL#Interleaving_und_De.E2.80.93Interleaving| "Interleaving and Deinterleaving"]],
+* The exercise refers to the chapter&nbsp; [[Channel_Coding/The_Basics_of_Turbo_Codes| "Basics of Turbo Codes"]].
 :* 2G mobile communication system&nbsp; GSM &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Entire_GSM_Transmission_System#Komponenten_der_Sprach.E2.80.93_und_Daten.C3.BCbertragung| "Components of voice&ndash; and data transmission"]],
-:* 3G mobile communication system&nbsp; UMTS &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Telecommunications_Aspects_of_UMTS#Kanalcodierung_bei_UMTS| "Channel Coding"]],
+*But other&nbsp; $\rm LNTwww$&nbsp; books also discuss interleaving,&nbsp; including the book&nbsp; "Examples of Communication Systems"&nbsp; with reference to the
-:* 4G mobile communication system LTE &nbsp; &#8658; &nbsp; [[Mobile_Communications/The_Application_of_OFDMA_and_SC-FDMA_in_LTE#Functionality_of_SC-FDMA| "Funktionsweise von SC&ndash;FDMA"]]&nbsp; (in the book "Mobile Communications").
+:* standard digital subscriber line</i> $\rm (DSL)$ &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Methods_to_Reduce_the_Bit_Error_Rate_in_DSL#Interleaving_und_De.E2.80.93Interleaving| "Interleaving and Deinterleaving"]],
@@ Line 39: / Line 40: @@
 ===Questions===
 <quiz display=simple>
-{What interleaver&ndash;type is shown in the graphic on the details page?
+{What interleaver type is shown in the graphic on the details page?
 |type="()"}
 + Block interleaving,
 - Random interleaving.
-{How many rows&nbsp; ($Z$)&nbsp; and columns&nbsp; ($S$)&nbsp; does the upper "Interleaver matrix 1" have?
+{How many rows&nbsp; ($N_{\rm R}$)&nbsp; and columns&nbsp; ($N_{\rm C}$)&nbsp; does the upper "Interleaver matrix 1" have?
 |type="{}"}
-$Z \ = \ ${ 4 }
+$N_{\rm R} \ = \ ${ 4 }
-$S \ = \ ${ 3 }
+$N_{\rm C} \ = \ ${ 3 }
-{It holds&nbsp; $\underline{u} = (1001'0001'1101'1101'0010'0111)$. How does the scrambled sequence begin&nbsp; $\underline{u}_{\pi}$? <br>&nbsp; &nbsp; Note: &nbsp; The quotation marks serve only as a reading aid.
+{It holds &nbsp; $\underline{u} = (1001'0001'1101'1101'0010'0111)$.&nbsp; How does the scrambled sequence&nbsp; $\underline{u}_{\pi}$ begin?&nbsp; &nbsp; Note: &nbsp; The quotation marks serve only as a reading aid.
 |type="()"}
 - $\underline{u}_{\pi} = (110'100'100'011'111'110'010'001' \text{...}\ )$,
 + $\underline{u}_{\pi} = (101'001'000'111'100'101'011'101'\text{...}\ )$.
-{The scrambled sequence be&nbsp; $\underline{u}_{\pi} = (100'100'011'101'110'100'100'111)$. What is the sequence after deinterleaving?
+{The scrambled sequence be&nbsp; $\underline{u}_{\pi} = (100'100'011'101'110'100'100'111)$.&nbsp; What is the sequence after de-interleaving?
 |type="()"}
 + $\underline{u} = (1101'0010'0011'1111'1001'0001'\text{...}\ )$,

@@ Line 28: / Line 28: @@
 * Die Aufgabe bezieht sich auf das Kapitel&nbsp; [[Channel_Coding/The_Basics_of_Turbo_Codes| "The Basics of Turbo Codes"]].
-*Aber auch in anderen $\rm LNTwww$&ndash;Büchern wird Interleaving behandelt, unter anderem im Buch "Beispiele von Nachrichtensystemen" mit Bezug zum
+*But other $\rm LNTww$&ndash;books also discuss interleaving, including the book "Examples of Message Systems" with reference to the
-:* Standard&nbsp; <i>Digital Subscriber Line</i> (DSL) &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Methods_to_Reduce_the_Bit_Error_Rate_in_DSL#Interleaving_und_De.E2.80.93Interleaving| "Interleaving und De&ndash;Interleaving"]],
+:* Standard&nbsp; <i>Digital Subscriber Line</i> (DSL) &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Methods_to_Reduce_the_Bit_Error_Rate_in_DSL#Interleaving_und_De.E2.80.93Interleaving| "Interleaving and Deinterleaving"]],
-:* 2G&ndash;Mobilfunksystem&nbsp; GSM &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Entire_GSM_Transmission_System#Komponenten_der_Sprach.E2.80.93_und_Daten.C3.BCbertragung| "Komponenten der Sprach&ndash; und Datenübertragung"]],
+:* 2G mobile communication system&nbsp; GSM &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Entire_GSM_Transmission_System#Komponenten_der_Sprach.E2.80.93_und_Daten.C3.BCbertragung| "Components of voice&ndash; and data transmission"]],
-:* 3G&ndash;Mobilfunksystem&nbsp; UMTS &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Telecommunications_Aspects_of_UMTS#Kanalcodierung_bei_UMTS| "Kanalcodierung"]],
+:* 3G mobile communication system&nbsp; UMTS &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Telecommunications_Aspects_of_UMTS#Kanalcodierung_bei_UMTS| "Channel Coding"]],
-:* 4G&ndash;Mobilfunksystem&nbsp; LTE &nbsp; &#8658; &nbsp; [[Mobile_Communications/The_Application_of_OFDMA_and_SC-FDMA_in_LTE#Functionality_of_SC-FDMA| "Funktionsweise von SC&ndash;FDMA"]]&nbsp; (im Buch "Mobile Kommunikation").
+:* 4G mobile communication system LTE &nbsp; &#8658; &nbsp; [[Mobile_Communications/The_Application_of_OFDMA_and_SC-FDMA_in_LTE#Functionality_of_SC-FDMA| "Funktionsweise von SC&ndash;FDMA"]]&nbsp; (in the book "Mobile Communications").
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Welche Interleaver&ndash;Art ist in der Grafik auf der Angabenseite dargestellt?
+{What interleaver&ndash;type is shown in the graphic on the details page?
 |type="()"}
-+ Block&ndash;Interleaving,
++ Block interleaving,
-- Random&ndash;Interleaving.
+- Random interleaving.
-{Wieviele Zeilen&nbsp; ($Z$)&nbsp; und Spalten&nbsp; ($S$)&nbsp; hat die obere "Interleaver&ndash;Matrix 1"?
+{How many rows&nbsp; ($Z$)&nbsp; and columns&nbsp; ($S$)&nbsp; does the upper "Interleaver matrix 1" have?
 |type="{}"}
 $Z \ = \ ${ 4 }
 $S \ = \ ${ 3 }
-{Es gelte&nbsp; $\underline{u} = (1001'0001'1101'1101'0010'0111)$. Wie beginnt die verwürfelte Folge&nbsp; $\underline{u}_{\pi}$? <br>&nbsp; &nbsp; ''Hinweis:'' &nbsp; Die Hochkommata dienen nur als Lesehilfe.
+{It holds&nbsp; $\underline{u} = (1001'0001'1101'1101'0010'0111)$. How does the scrambled sequence begin&nbsp; $\underline{u}_{\pi}$? <br>&nbsp; &nbsp; Note: &nbsp; The quotation marks serve only as a reading aid.
 |type="()"}
 - $\underline{u}_{\pi} = (110'100'100'011'111'110'010'001' \text{...}\ )$,
 + $\underline{u}_{\pi} = (101'001'000'111'100'101'011'101'\text{...}\ )$.
-{Die verwürfelte Folge sei&nbsp; $\underline{u}_{\pi} = (100'100'011'101'110'100'100'111)$. Wie lautet die Folge nach dem De&ndash;Interleaving?
+{The scrambled sequence be&nbsp; $\underline{u}_{\pi} = (100'100'011'101'110'100'100'111)$. What is the sequence after deinterleaving?
 |type="()"}
 + $\underline{u} = (1101'0010'0011'1111'1001'0001'\text{...}\ )$,
@@ Line 60: / Line 60: @@
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-[[File:P_ID3041__KC_Z_4_8b_v2.png|right|frame|4×3–Interleaver–Matrix]]
+[[File:P_ID3041__KC_Z_4_8b_v2.png|right|frame|4×3 Interleaver Matrix]]
-'''(1)'''&nbsp; Aus der regelmäßigen Struktur der Funktion $I_{\rm Out}(I_{\rm In})$ erkennt man, dass es sich um einen Blockinterleaver handelt &nbsp;&#8658;&nbsp; <u>Antwort 1</u>.
+'''(1)'''&nbsp; From the regular structure of the function $I_{\rm Out}(I_{\rm In})$ one can see that it is a block interleaver &nbsp;&#8658;&nbsp; <u>Response 1</u>.
-'''(2)'''&nbsp; Der Index "1" wird als erstes Zeichen ausgegeben. Weiter gilt:
+'''(2)'''&nbsp; The index "1" is output as the first character. Further applies:
-* Der Index 5 wird als zweites Zeichen ausgegeben &nbsp;&#8658;&nbsp; $\underline{Z = 4}$.
+* The index 5 is output as the second character &nbsp;&#8658;&nbsp; $\underline{Z = 4}$.
-* Der Index 2 wird als viertes Zeichen ausgegeben &nbsp;&#8658;&nbsp; $\underline{S = 3}$.
+* The index 2 is output as the fourth character &nbsp;&#8658;&nbsp; $\underline{S = 3}$.
-Die obere Grafik zeigt für die 4×3–Interleaver&ndash;Matrix:
+The upper graph shows for the 4×3 interleaver matrix:
-* das spaltenweise Beschreiben (rot),
+* the column by column write (red),
-* das zeilenweise Auslesen (grün).
+* the row by row readout (green).
-[[File:P_ID3042__KC_Z_4_8c_v3.png|right|frame|Zum Interleaving]]
+[[File:P_ID3042__KC_Z_4_8c_v3.png|right|frame|Interleaving]]
-'''(3)'''&nbsp; Richtig ist der <u>der Lösungsvorschlag 2</u>:
+'''(3)'''&nbsp; Correct is <u>the proposed solution 2</u>:
-*Die Matrix wird spaltenweise beschrieben und zeilenweise ausgelesen.
+*The matrix is written column by column and read row by row.
-*Nach 12 Bit wird die Matrix gelöscht und die Prozedur beginnt von Neuem.
+*After 12 bits, the matrix is cleared and the procedure starts over.
-*Die Grafik zeigt, dass nun der Lösungsvorschlag 2 richtig ist.
+*The graphic shows that now the solution suggestion 2 is correct.
 <br clear=all>
 [[File:P_ID3043__KC_Z_4_8d_v1.png|right|frame|Zum De–Interleaving]]
-'''(4)'''&nbsp; Richtig ist der <u>der Lösungsvorschlag 1</u>:
+'''(4)'''&nbsp; Correct is <u>the proposed solution 1</u>:
-*Beim De&ndash;Interleaving wird die Matrix zeilenweise beschrieben und spaltenweise ausgelesen.
+*In deinterleaving, the matrix is written row by row and read column by column.
-*Die Grafik zeigt, dass hier der Lösungsvorschlag 1 richtig ist.
+*The graphic shows that here the solution suggestion 1 is correct.

@@ Line 4: / Line 4: @@
 Interleaving is required, for example, for a channel with burst error characteristics in order to distribute the errors within the burst over a sufficiently large area so that they can subsequently be largely corrected (or at least detected).
-For turbo codes based on so-called &nbsp;'''RSC&ndash;Coder'''&nbsp; (<i>Recursive Systematic Convolutional Encoder</i>)&nbsp; &ndash; and only such make sense &ndash; <i>interleaving</i> is essential also with the AWGN channel, because then there are also always (some) input sequences, which deliver only zeros in the output sequence after quite a few ones, and that to infinity &nbsp; &#8658; &nbsp; there are output sequences with very small Hamming weight.
+For turbo codes based on so-called &nbsp;'''RSC encoder'''&nbsp; (<i>Recursive Systematic Convolutional Encoder</i>)&nbsp; &ndash; and only such make sense &ndash; <i>interleaving</i> is essential also with the AWGN channel, because then there are also always (some) input sequences, which deliver only zeros in the output sequence after quite a few ones, and that to infinity &nbsp; &#8658; &nbsp; there are output sequences with very small Hamming weight.
 If the bits of such input sequences are distributed over a wide range in the second coder, the problem can be (largely) eliminated by the interaction of both component decoders in the case of iterative symbol-wise decoding.
@@ Line 19: / Line 19: @@
 \le I_{\rm In} \le I_{\rm max} \hspace{0.05cm}. $$
-In the subtask&nbsp; '''(1)'''&nbsp; it is asked whether this is&nbsp; <i>block interleaving</i>&nbsp; oor&nbsp; <i>random interleaving</i> &nbsp;. Letztere werden im&nbsp; [[Channel_Coding/The_Basics_of_Turbo_Codes#Second_requirement_for_turbo_codes:_Interleaving|"Theorieteil"]]&nbsp; allerdings nur in aller Kürze besprochen.
+In the subtask&nbsp; '''(1)'''&nbsp; it is asked whether this is&nbsp; <i>block interleaving</i>&nbsp; or&nbsp; <i>random interleaving</i> &nbsp;. The latter are discussed in the&nbsp; [[Channel_Coding/The_Basics_of_Turbo_Codes#Second_requirement_for_turbo_codes:_Interleaving|"theory section"]]&nbsp; but only very briefly.
@@ Line 25: / Line 25: @@
-''Hinweis:''
+Hints:
-* Die Aufgabe bezieht sich auf das Kapitel&nbsp; [[Channel_Coding/Grundlegendes_zu_den_Turbocodes| Grundlegendes zu den Turbocodes]].
+* Die Aufgabe bezieht sich auf das Kapitel&nbsp; [[Channel_Coding/The_Basics_of_Turbo_Codes| "The Basics of Turbo Codes"]].
 *Aber auch in anderen $\rm LNTwww$&ndash;Büchern wird Interleaving behandelt, unter anderem im Buch "Beispiele von Nachrichtensystemen" mit Bezug zum
-:* Standard&nbsp; <i>Digital Subscriber Line</i> (DSL) &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Verfahren_zur_Senkung_der_Bitfehlerrate_bei_DSL#Interleaving_und_De.E2.80.93Interleaving| Interleaving und De&ndash;Interleaving]],
+:* Standard&nbsp; <i>Digital Subscriber Line</i> (DSL) &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Methods_to_Reduce_the_Bit_Error_Rate_in_DSL#Interleaving_und_De.E2.80.93Interleaving| "Interleaving und De&ndash;Interleaving"]],
-:* 2G&ndash;Mobilfunksystem&nbsp; GSM &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Gesamtes_GSM%E2%80%93%C3%9Cbertragungssystem#Komponenten_der_Sprach.E2.80.93_und_Daten.C3.BCbertragung| Komponenten der Sprach&ndash; und Datenübertragung]],
+:* 2G&ndash;Mobilfunksystem&nbsp; GSM &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Entire_GSM_Transmission_System#Komponenten_der_Sprach.E2.80.93_und_Daten.C3.BCbertragung| "Komponenten der Sprach&ndash; und Datenübertragung"]],
-:* 3G&ndash;Mobilfunksystem&nbsp; UMTS &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Nachrichtentechnische_Aspekte_von_UMTS#Kanalcodierung| Kanalcodierung]],
+:* 3G&ndash;Mobilfunksystem&nbsp; UMTS &nbsp; &#8658; &nbsp; [[Examples_of_Communication_Systems/Telecommunications_Aspects_of_UMTS#Kanalcodierung_bei_UMTS| "Kanalcodierung"]],
-:* 4G&ndash;Mobilfunksystem&nbsp; LTE &nbsp; &#8658; &nbsp; [[Mobile_Communications/Die_Anwendung_von_OFDMA_und_SC-FDMA_in_LTE#Funktionsweise_von_SC.E2.80.93FDMA| Funktionsweise von SC&ndash;FDMA]]&nbsp; (im Buch "Mobile Kommunikation").
+:* 4G&ndash;Mobilfunksystem&nbsp; LTE &nbsp; &#8658; &nbsp; [[Mobile_Communications/The_Application_of_OFDMA_and_SC-FDMA_in_LTE#Functionality_of_SC-FDMA| "Funktionsweise von SC&ndash;FDMA"]]&nbsp; (im Buch "Mobile Kommunikation").

@@ Line 4: / Line 4: @@
 Interleaving is required, for example, for a channel with burst error characteristics in order to distribute the errors within the burst over a sufficiently large area so that they can subsequently be largely corrected (or at least detected).
-Für Turbocodes, die auf so genannten &nbsp;'''RSC&ndash;Coder'''&nbsp; (<i>Recursive Systematic Convolutional Encoder</i>)&nbsp; basieren &ndash; und nur solche machen Sinn &ndash; ist <i>Interleaving</i> auch beim AWGN&ndash;Kanal essentiell, da es dann auch stets (einige) Eingangssequenzen gibt, die in der Ausgangsfolge nach etlichen Einsen nur noch Nullen liefern, und zwar bis ins Unendliche &nbsp; &#8658; &nbsp; es gibt Ausgangsfolgen mit sehr kleinem Hamming&ndash;Gewicht.
+For turbo codes based on so-called &nbsp;'''RSC&ndash;Coder'''&nbsp; (<i>Recursive Systematic Convolutional Encoder</i>)&nbsp; &ndash; and only such make sense &ndash; <i>interleaving</i> is essential also with the AWGN channel, because then there are also always (some) input sequences, which deliver only zeros in the output sequence after quite a few ones, and that to infinity &nbsp; &#8658; &nbsp; there are output sequences with very small Hamming weight.
-Verteilt man im zweiten Coder die Bits solcher Eingangssequenzen über einen weiten Bereich, so kann bei iterativer symbolweiser Decodierung das Problem durch das Zusammenspiel beider Komponentendecoder (weitgehend) beseitigt werden.
+If the bits of such input sequences are distributed over a wide range in the second coder, the problem can be (largely) eliminated by the interaction of both component decoders in the case of iterative symbol-wise decoding.
-Man unterscheidet allgemein zwischen
+A general distinction is made between
-* '''Block&ndash;Interleaver''' und
+* '''Block interleaver''' and
-* '''Random&ndash;Interleaver'''.
+* '''Random interleaver'''.
-Bei <i>Block&ndash;Interleaving</i>&nbsp; füllt man eine Matrix mit&nbsp; $S$&nbsp; Spalten und&nbsp; $Z$&nbsp; Zeilen spaltenweise und liest die Matrix zeilenweise aus. Damit wird ein Informationsblock mit&nbsp; $I_{\rm max} = S \cdot Z$&nbsp; Bit deterministisch verwürfelt.
+In <i>block interleaving</i>&nbsp; one fills a matrix with&nbsp; $S$&nbsp; columns and&nbsp; $Z$&nbsp; rows column by column and reads the matrix row by row. This deterministically scrambles a block of information with&nbsp; $I_{\rm max} = S \cdot Z$&nbsp; bits.
-Rechts sind zwei Interleaver angegeben und zwar in grafischer Form durch die Zuordnung&nbsp; $I_{\rm Out}(I_{\rm In})$. Diese Größen stehen für den "Index der Ausgangsfolge" bzw. für den "Index der Eingangsfolge". Es gilt:
+On the right, two interleavers are indicated and in graphical form by the assignment&nbsp; $I_{\rm Out}(I_{\rm In})$. These quantities represent the "index of the output sequence" and the "index of the input sequence", respectively. It holds:
 :$$1 \le I_{\rm Out} \le I_{\rm max} \hspace{0.05cm}, \hspace{0.5cm}
 \le I_{\rm In} \le I_{\rm max} \hspace{0.05cm}. $$
-In der Teilaufgabe&nbsp; '''(1)'''&nbsp; ist gefragt, ob es sich hierbei um&nbsp; <i>Block&ndash;Interleaving</i>&nbsp; oder um&nbsp; <i>Random Interleaving</i> &nbsp;handelt. Letztere werden im&nbsp; [[Channel_Coding/Grundlegendes_zu_den_Turbocodes#Zweite_Voraussetzung_f.C3.BCr_Turbocodes:_Interleaving|Theorieteil]]&nbsp; allerdings nur in aller Kürze besprochen.
+In the subtask&nbsp; '''(1)'''&nbsp; it is asked whether this is&nbsp; <i>block interleaving</i>&nbsp; oor&nbsp; <i>random interleaving</i> &nbsp;. Letztere werden im&nbsp; [[Channel_Coding/The_Basics_of_Turbo_Codes#Second_requirement_for_turbo_codes:_Interleaving|"Theorieteil"]]&nbsp; allerdings nur in aller Kürze besprochen.

@@ Line 1: / Line 1: @@
 {{quiz-Header|Buchseite=Kanalcodierung/Grundlegendes zu den Turbocodes}}
-[[File:P_ID3032__KC_Z_4_8_v3.png|right|frame|Zur Interleaver–Beschreibung]]
+[[File:P_ID3032__KC_Z_4_8_v3.png|right|frame|Interleaver description]]
-Interleaving&nbsp; (deutsch: &nbsp;<i>Verwürfelung</i>)&nbsp; ist zum Beispiel bei einem Kanal mit Bündelfehlercharakteristik erforderlich, um die Fehler innerhalb des Bündels über einen genügend großen Bereich so zu verteilen, dass diese anschließend weitgehend korrigiert (oder zumindest erkannt) werden können.
+Interleaving is required, for example, for a channel with burst error characteristics in order to distribute the errors within the burst over a sufficiently large area so that they can subsequently be largely corrected (or at least detected).
 Für Turbocodes, die auf so genannten &nbsp;'''RSC&ndash;Coder'''&nbsp; (<i>Recursive Systematic Convolutional Encoder</i>)&nbsp; basieren &ndash; und nur solche machen Sinn &ndash; ist <i>Interleaving</i> auch beim AWGN&ndash;Kanal essentiell, da es dann auch stets (einige) Eingangssequenzen gibt, die in der Ausgangsfolge nach etlichen Einsen nur noch Nullen liefern, und zwar bis ins Unendliche &nbsp; &#8658; &nbsp; es gibt Ausgangsfolgen mit sehr kleinem Hamming&ndash;Gewicht.

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−	[[Category:Channel Coding: Exercises\|^4.3 ~~Grundlegendes zu den Turbocodes~~^]]	+	[[Category:Channel Coding: Exercises\|^4.3 About the Turbo Codes^]]

← Older revision	Revision as of 16:56, 31 October 2022
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