Aufgaben:Exercise 4.Ten: QPSK Channel Capacity - Revision history

Guenter at 09:29, 10 November 2021

2021-11-10T09:29:47Z

Guenter at 09:28, 10 November 2021

2021-11-10T09:28:55Z

Javier at 09:02, 10 November 2021

2021-11-10T09:02:59Z

Noah at 21:21, 1 November 2021

2021-11-01T21:21:00Z

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Guenter at 13:23, 7 October 2021

2021-10-07T13:23:57Z

Noah at 11:59, 4 October 2021

2021-10-04T11:59:09Z

Guenter at 15:38, 27 September 2021

2021-09-27T15:38:46Z

Guenter at 15:37, 27 September 2021

2021-09-27T15:37:24Z

Guenter at 09:39, 16 August 2021

2021-08-16T09:39:53Z

Guenter: Guenter moved page Aufgaben:Aufgabe 4.Zehn: QPSK–Kanalkapazität to Aufgaben:Exercise 4.Ten: QPSK Channel Capacity

2021-08-16T09:35:41Z

Guenter moved page Aufgabe 4.Zehn: QPSK–Kanalkapazität to Exercise 4.Ten: QPSK Channel Capacity

@@ Line 118: / Line 118: @@
+=
 \cdot C_{\rm BPSK}(10 \cdot {\rm lg} \hspace{0.1cm}E_{\rm S}/{N_0} - 3\,{\rm dB}) .$$
-*The&nbsp; <u>proposed solution 1</u>&nbsp; is correct.&nbsp; The second proposal takes into account that with QPSK the energy in one dimension is only  &nbsp;$E_{\rm S}/2$.
+*The&nbsp; <u>proposed solution 1</u>&nbsp; is correct.&nbsp; This takes into account that with QPSK the energy in one dimension is only  &nbsp;$E_{\rm S}/2$.
 {{ML-Fuß}}

@@ Line 67: / Line 67: @@
 {How can &nbsp;$C_{\rm QPSK}( E_{\rm S}/{N_0})$&nbsp; be constructed from &nbsp;$C_{\rm BPSK}( E_{\rm S}/{N_0})$&nbsp;?
-|type="[]"}
+|type="()"}
-+ By doubling: &nbsp; $C_{\rm QPSK}( E_{\rm S}/{N_0}) = 2 \cdot C_{\rm BPSK}( E_{\rm S}/{N_0})$.
++ By doubling: &nbsp; $C_{\rm QPSK}( E_{\rm S}/{N_0}) = 2 \cdot C_{\rm BPSK}( E_{\rm S}/{N_0})$&nbsp; and Additionally by a shift to the right.
-+ Additionally by a shift to the right.
+- By doubling: &nbsp; $C_{\rm QPSK}( E_{\rm S}/{N_0}) = 2 \cdot C_{\rm BPSK}( E_{\rm S}/{N_0})$&nbsp; and Additionally by a shift to the left.
 - $C_{\rm QPSK}( E_{\rm S}/{N_0})$&nbsp; cannot be constructed from &nbsp;$C_{\rm BPSK}( E_{\rm S}/{N_0})$&nbsp;.
@@ Line 110: / Line 109: @@
-'''(4)'''&nbsp; The &nbsp;$C_{\rm QPSK}( E_{\rm B}/{N_0})$ curve can also be constructed from &nbsp;$C_{\rm BPSK}( E_{\rm B}/{N_0})$&nbsp;, namely
+'''(4)'''&nbsp; The &nbsp;$C_{\rm QPSK}( E_{\rm B}/{N_0})$ curve can also be constructed from &nbsp;$C_{\rm BPSK}( E_{\rm B}/{N_0})$, namely
 * on the one hand by doubling:
 :$$C_{\rm BPSK}(10 \cdot {\rm lg} \hspace{0.1cm}E_{\rm S}/{N_0})
@@ Line 119: / Line 118: @@
+=
 \cdot C_{\rm BPSK}(10 \cdot {\rm lg} \hspace{0.1cm}E_{\rm S}/{N_0} - 3\,{\rm dB}) .$$
-*The <u>first two proposed solutions</u> are correct.&nbsp; The second proposal takes into account that with QPSK the energy in one dimension is only  &nbsp;$E_{\rm S}/2$&nbsp;.
+*The&nbsp; <u>proposed solution 1</u>&nbsp; is correct.&nbsp; The second proposal takes into account that with QPSK the energy in one dimension is only  &nbsp;$E_{\rm S}/2$.
 {{ML-Fuß}}

← Older revision		Revision as of 09:02, 10 November 2021
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−	The channel capacities  $C_\text{BPSK}$  and  $C_\text{QPSK}$  simultaneously indicate the maximum code rate  $R_{\rm max}$  an, with which the bit error probability  $p_\text{B} &equiv; 0$  can be asymptotically achieved with BPSK (or QPSK) with suitable channel coding.	+	The channel capacities  $C_\text{BPSK}$  and  $C_\text{QPSK}$  simultaneously indicate the maximum code rate  $R_{\rm max}$ , with which the bit error probability  $p_\text{B} &equiv; 0$  can be asymptotically achieved with BPSK (or QPSK) with suitable channel coding.

	The upper diagram shows the dependence on the parameter  $10 \cdot \lg (E_{\rm B}/{N_0})$  in  $\rm dB$, where  $E_{\rm B}$  indicates the "energy per information bit".		The upper diagram shows the dependence on the parameter  $10 \cdot \lg (E_{\rm B}/{N_0})$  in  $\rm dB$, where  $E_{\rm B}$  indicates the "energy per information bit".

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Inf_Z_4_10.png|right|frame|Kapazitätskurven für BPSK und QPSK]]
+[[File:EN_Inf_Z_4_10_v2.png|right|frame|Kapazitätskurven für BPSK und QPSK]]
 Gegeben sind die AWGN&ndash;Kanalkapazitätsgrenzkurven für die Modulationsverfahren
 * [[Modulation_Methods/Lineare_digitale_Modulationsverfahren#BPSK_.E2.80.93_Binary_Phase_Shift_Keying|Binary Phase Shift Keying]]&nbsp; (BPSK),
@@ Line 99: / Line 99: @@
 :$$C_1( E_{\rm B}/{N_0}) = {1}/{2} \cdot  {\rm log}_2 \hspace{0.1cm} ( 1 + \frac { 2 \cdot R \cdot E_{\rm B}}{N_0}) ,$$
 :$$C_2( E_{\rm B}/{N_0}) =  {\rm log}_2 \hspace{0.1cm} ( 1 + \frac { R \cdot E_{\rm B}}{N_0}) .$$
-[[File:P_ID2959__Inf_A_4_1c.png|right|frame|Vier Kapazitätskurven mit unterschiedlichen Aussagen]]
+[[File:EN_Inf_Z_4_10c_v2.png|right|frame|Vier Kapazitätskurven mit unterschiedlichen Aussagen]]
 Man erkennt aus dieser  Skizze: &nbsp; Richtig sind die <u>Lösungsvorschläge 1, 2 und 4</u>.
 *Die grün&ndash;gestrichelte Kurve &nbsp;$C_1( E_{\rm B}/{N_0})$&nbsp; gilt für den AWGN&ndash;Kanal mit gaußverteiltem Eingang.&nbsp;

← Older revision		Revision as of 11:59, 4 October 2021
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−	{{quiz-Header\|Buchseite=~~Informationstheorie~~/~~AWGN–Kanalkapazität bei wertdiskretem Eingang~~	+	{{quiz-Header\|Buchseite=Information_Theory/AWGN_Channel_Capacity_for_Discrete_Input
	}}		}}

← Older revision		Revision as of 09:39, 16 August 2021
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−	[[Category:Information Theory: Exercises\|^4.3 AWGN ~~& wertdiskreter Eingang~~^]]	+	[[Category:Information Theory: Exercises\|^4.3 AWGN and Value-Discrete Input^]]

← Older revision	Revision as of 09:35, 16 August 2021
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