Aufgaben:Exercise 1.5: HDB3 Coding - Revision history

Guenter at 11:03, 10 November 2022

2022-11-10T11:03:02Z

Hwang at 15:18, 9 November 2022

2022-11-09T15:18:36Z

Hwang at 15:18, 9 November 2022

2022-11-09T15:18:13Z

Guenter at 11:14, 28 October 2022

2022-10-28T11:14:01Z

Guenter at 08:41, 28 October 2022

2022-10-28T08:41:52Z

Guenter at 08:24, 28 October 2022

2022-10-28T08:24:17Z

Guenter at 16:21, 24 October 2022

2022-10-24T16:21:38Z

Hwang at 13:31, 11 October 2022

2022-10-11T13:31:37Z

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Guenter at 12:41, 10 September 2022

2022-09-10T12:41:35Z

Guenter: Guenter moved page Aufgaben:Aufgabe 1.5: HDB3–Codierung to Aufgaben:Exercise 1.5: HDB3 Coding

2022-09-10T12:39:34Z

Guenter moved page Aufgabe 1.5: HDB3–Codierung to Exercise 1.5: HDB3 Coding

@@ Line 50: / Line 50: @@
 $T_{\rm R} \ = \ $ { 125 3% } $\ \rm &micro; s$
-{How is the zero block between bit&nbsp; '''6'''&nbsp; and bit&nbsp; '''10'''&nbsp; coded '''KORREKTUR: encoded'''?<br>Possible input values are&nbsp; $0$,&nbsp; $+1$&nbsp; and&nbsp; $&ndash;1$.
+{How is the zero block between bit&nbsp; '''6'''&nbsp; and bit&nbsp; '''10'''&nbsp; encoded?<br>Possible input values are&nbsp; $0$,&nbsp; $+1$&nbsp; and&nbsp; $&ndash;1$.
 |type="{}"}
 $c_{6} \ = \ $ { 0 3% }
@@ Line 58: / Line 58: @@
 $c_{10} \ = \ $ { 0 3% }
-{How is the zero block between bit&nbsp; '''14'''&nbsp; and bit&nbsp; '''17'''&nbsp; coded '''KORREKTUR: encoded'''?
+{How is the zero block between bit&nbsp; '''14'''&nbsp; and bit&nbsp; '''17'''&nbsp; encoded?
 |type="{}"}
 $c_{14} \ = \ $ { 0 3% }
@@ Line 65: / Line 65: @@
 $c_{17} \ = \ $ { 1 3% }
-{How is the zero block between bit&nbsp; '''20'''&nbsp; and bit&nbsp; '''24'''&nbsp; coded '''KORREKTUR: encoded'''?
+{How is the zero block between bit&nbsp; '''20'''&nbsp; and bit&nbsp; '''24'''&nbsp; encoded?
 |type="{}"}
 $c_{20} \ = \ $ { -1.03--0.97 }

@@ Line 65: / Line 65: @@
 $c_{17} \ = \ $ { 1 3% }
-{How is the zero block between bit&nbsp; '''20'''&nbsp; and bit&nbsp; '''24'''&nbsp; coded?
+{How is the zero block between bit&nbsp; '''20'''&nbsp; and bit&nbsp; '''24'''&nbsp; coded '''KORREKTUR: encoded'''?
 |type="{}"}
 $c_{20} \ = \ $ { -1.03--0.97 }

@@ Line 50: / Line 50: @@
 $T_{\rm R} \ = \ $ { 125 3% } $\ \rm &micro; s$
-{How is the zero block between bit&nbsp; '''6'''&nbsp; and bit&nbsp; '''10'''&nbsp; coded?<br>Possible input values are&nbsp; $0$,&nbsp; $+1$&nbsp; and&nbsp; $&ndash;1$.
+{How is the zero block between bit&nbsp; '''6'''&nbsp; and bit&nbsp; '''10'''&nbsp; coded '''KORREKTUR: encoded'''?<br>Possible input values are&nbsp; $0$,&nbsp; $+1$&nbsp; and&nbsp; $&ndash;1$.
 |type="{}"}
 $c_{6} \ = \ $ { 0 3% }
@@ Line 58: / Line 58: @@
 $c_{10} \ = \ $ { 0 3% }
-{How is the zero block between bit&nbsp; '''14'''&nbsp; and bit&nbsp; '''17'''&nbsp; coded?
+{How is the zero block between bit&nbsp; '''14'''&nbsp; and bit&nbsp; '''17'''&nbsp; coded '''KORREKTUR: encoded'''?
 |type="{}"}
 $c_{14} \ = \ $ { 0 3% }

@@ Line 23: / Line 23: @@
-The graph above shows the binary signal&nbsp; $q(t)$&nbsp; and the signal&nbsp; $a(t)$&nbsp; after AMI coding.&nbsp; The HDB3 signal,&nbsp; which you are to determine in the course of this exercise,&nbsp; is denoted by&nbsp; $c(t)$.&nbsp;
+The graph above shows the binary signal&nbsp; $q(t)$&nbsp; and the signal&nbsp; $a(t)$&nbsp; after AMI coding.&nbsp; The HDB3 signal is denoted by&nbsp; $c(t)$.&nbsp;
@@ Line 50: / Line 50: @@
 $T_{\rm R} \ = \ $ { 125 3% } $\ \rm &micro; s$
-{How is the zero block between bit&nbsp; '''6'''&nbsp; and bit&nbsp; '''10'''&nbsp; coded?
+{How is the zero block between bit&nbsp; '''6'''&nbsp; and bit&nbsp; '''10'''&nbsp; coded?<br>Possible input values are&nbsp; $0$,&nbsp; $+1$&nbsp; and&nbsp; $&ndash;1$.
 |type="{}"}
 $c_{6} \ = \ $ { 0 3% }

@@ Line 78: / Line 78: @@
 {{ML-Kopf}}
-'''(1)'''&nbsp; The total data rate of the $32$ channels at $64 \ \rm kbit/s$ each results in
+'''(1)'''&nbsp; The total data rate of the&nbsp; $32$&nbsp; channels at&nbsp; $64 \ \rm kbit/s$&nbsp; each results in
 :$$R_{\rm B} \underline{ = 2.048 \ \rm Mbit/s}.$$
-'''(2)'''&nbsp; The bit duration is $T_{\rm B} = 1/R_{\rm B} \underline{ = 0.488 \ \rm &micro; s}$.
+'''(2)'''&nbsp; The bit duration is&nbsp; $T_{\rm B} = 1/R_{\rm B} \underline{ = 0.488 \ \rm &micro; s}$.
-*One byte (8 bits) of each channel is transmitted per frame. It follows that:
+*One byte (8 bits) of each channel is transmitted per frame.&nbsp; It follows that:
 :$$T_{\rm R} = 32 \cdot 8 \cdot T_{\rm B} \hspace{0.15cm}\underline{= 125 \,{\rm &micro; s}}\hspace{0.05cm}.$$
-'''(3)'''&nbsp; By time $t = 6T$, a "+'''1'''" has occurred exactly once in the AMI-encoded signal$a(t)$.
+'''(3)'''&nbsp; By time&nbsp; $t = 6T$,&nbsp; a&nbsp; "+'''1'''"&nbsp; has occurred exactly once in the AMI-encoded signal&nbsp; $a(t)$.
 [[File:EN_Bei_A_1_5e.png|right|frame|Relationship between AMI code and HDB3 code]]
-*Because of $a_{5} = –1$, in the HDB3 code "'''0 0 0 0'''" is replaced by (see diagram)
+*Because of&nbsp; $a_{5} = –1$,&nbsp; in the HDB3 code&nbsp; "'''0 0 0 0'''"&nbsp; is replaced by&nbsp; (see diagram)
 :$$\underline{c_{6} = 0, \hspace{0.2cm}c_{7} = 0, \hspace{0.2cm}c_{8} = 0, \hspace{0.2cm}c_{9} = -1} \hspace{0.05cm}.$$
 '''(4)'''&nbsp; Up to and including $a_{13}$, there are three times a "+1" &nbsp; &rArr; &nbsp;  odd number. Because of $a_{12} = +1$, this zero block is replaced as follows:
 :$$ \underline{c_{14} = 0, \hspace{0.2cm}c_{15} = 0, \hspace{0.2cm}c_{16} = 0, \hspace{0.2cm}c_{17} = +1} \hspace{0.05cm}.$$
-'''(5)'''&nbsp; In the AMI encoded signal, "+1" occurs exactly four times up to and including $a_{19}$ &nbsp; &rArr; &nbsp; even number.
+'''(5)'''&nbsp; In the AMI-encoded signal,&nbsp; "+1"&nbsp; occurs exactly four times up to and including&nbsp; $a_{19}$&nbsp; &nbsp; &rArr; &nbsp; even number.
-*Because of $a_{19} = +1$, the substitution according to rule 2 in the information section is:
+*Because of&nbsp; $a_{19} = +1$,&nbsp; the substitution according to rule 2 in the information section is:
 :$$\underline{c_{20} = -1, \hspace{0.2cm}c_{21} = 0, \hspace{0.2cm}c_{22} = 0, \hspace{0.2cm}c_{23} = -1} \hspace{0.05cm}.$$
-*The zero symbol $a_{24}$ remains unchanged: $\underline{c_{24} = 0}$.
+*The zero symbol&nbsp; $a_{24}$&nbsp; remains unchanged: $\underline{c_{24} = 0}$.
 {{ML-Fuß}}

@@ Line 5: / Line 5: @@
 [[File:EN_Bei_A_1_5.png|right|frame|Signals with HDB3 coding]]
-The ISDN primary rate interface is based on the&nbsp; $\rm PCM–System \ 30/32$&nbsp; and offers 30 full-duplex basic channels, plus a signaling channel and a synchronization channel.
+The ISDN primary rate interface&nbsp; $\rm (PRI)$&nbsp; is based on the&nbsp; $\rm PCM\ system \ 30/32$&nbsp; and offers&nbsp;
-Each of these channels, which are transmitted in time division multiplex, has a data rate of&nbsp; $64 \ \rm kbit/s$. A frame consists of one byte (8 bits) of all 32 channels. The duration of such a frame is denoted by&nbsp; $T_{\rm R}$,&nbsp; while&nbsp; $T_{\rm B}$&nbsp; indicates the bit duration.
+*plus a signaling channel
-If four consecutive&nbsp; "'''0'''" symbols occur in the AMI-encoded signal&nbsp; $a(t)$,&nbsp; these are replaced by four other ternary symbols:
+*and a synchronization channel.
-The graph above shows the binary signal&nbsp; $q(t)$&nbsp; and the signal&nbsp; $a(t)$&nbsp; after AMI coding. The HDB3 signal, which you are to determine in the course of this exercise, is denoted by&nbsp; $c(t)$.&nbsp;
+Each of these channels,&nbsp; which are transmitted in time division multiplex,&nbsp; has a data rate of&nbsp; $64 \ \rm kbit/s$.&nbsp; A frame consists of one byte&nbsp; $\rm (8$&nbsp; bits$)$&nbsp; of all&nbsp; $32$&nbsp; channels.&nbsp; The duration of such a frame&nbsp; $($German:&nbsp; "Rahmen"$)$&nbsp; is denoted by&nbsp; $T_{\rm R}$,&nbsp; while&nbsp; $T_{\rm B}$&nbsp; indicates the bit duration.
-''Notes:''
 *The exercise belongs to the chapter&nbsp; [[Examples_of_Communication_Systems/ISDN_Primary_Multiplex_Connection|"ISDN Primary Multiplex Connection"]] .
-*Information about the pseudo-ternary codes can be found in the&nbsp;  [[Digital_Signal_Transmission/Symbolwise_Coding_with_Pseudo-Ternary_Codes|"Symbolwise Coding with Pseudo-Ternary Codes"]]&nbsp; of "Digital Signal Transmission".
+*Information about the pseudo-ternary codes can be found in the section&nbsp;  [[Digital_Signal_Transmission/Symbolwise_Coding_with_Pseudo-Ternary_Codes|"Symbolwise Coding with Pseudo-Ternary Codes"]]&nbsp; of "Digital Signal Transmission".

← Older revision		Revision as of 12:41, 10 September 2022
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−	[[Category:Examples of Communication Systems: Exercises\|^1.3 ~~ISDN–Primärmultiplexanschluss~~	+	[[Category:Examples of Communication Systems: Exercises\|^1.3 ISDN Primary Multiplex Line^]]
−	^]]

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