Aufgaben:Exercise 2.1: Coding with and without Loss - Revision history

Javier: Text replacement - "code symbol sequence" to "encoded sequence"

2021-08-16T12:07:57Z

Text replacement - "code symbol sequence" to "encoded sequence"

Guenter at 12:08, 10 August 2021

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Noah at 20:30, 6 August 2021

2021-08-06T20:30:14Z

Guenter at 13:14, 7 July 2021

2021-07-07T13:14:10Z

Guenter at 13:12, 7 July 2021

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Guenter at 12:58, 7 July 2021

2021-07-07T12:58:46Z

Guenter at 15:42, 30 June 2021

2021-06-30T15:42:47Z

Noah at 12:44, 28 June 2021

2021-06-28T12:44:49Z

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Guenter at 15:04, 26 June 2021

2021-06-26T15:04:49Z

Guenter: Guenter moved page Aufgaben:Aufgabe 2.1: Codierung mit und ohne Verlust to Aufgaben:Exercise 2.1: Coding with and without Loss

2021-06-26T14:59:44Z

Guenter moved page Aufgabe 2.1: Codierung mit und ohne Verlust to Exercise 2.1: Coding with and without Loss

← Older revision		Revision as of 12:07, 16 August 2021
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−	All these basic coding methods have in common that the source signal  $q(t)$  is represented by a ~~code symbol~~ sequence  $\langle c_\nu \rangle $.  With a digital source  (with or w/o memory)  the source signal  $q(t)$  can be described by the source symbol sequence  $\langle q_\nu \rangle $.	+	All these basic coding methods have in common that the source signal  $q(t)$  is represented by a encoded sequence  $\langle c_\nu \rangle $.  With a digital source  (with or w/o memory)  the source signal  $q(t)$  can be described by the source symbol sequence  $\langle q_\nu \rangle $.

	At the receiver, the sink symbol sequence  $\langle v_\nu \rangle $  or the sink signal  $v(t)$  is obtained from the regenerated symbol sequence  $\langle r_\nu \rangle $.  This is called  "decoding",  sometimes also "signal reconstruction".		At the receiver, the sink symbol sequence  $\langle v_\nu \rangle $  or the sink signal  $v(t)$  is obtained from the regenerated symbol sequence  $\langle r_\nu \rangle $.  This is called  "decoding",  sometimes also "signal reconstruction".

← Older revision		Revision as of 12:08, 10 August 2021
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−	{{quiz-Header\|Buchseite=~~Informationstheorie~~/~~Allgemeine Beschreibung~~	+	{{quiz-Header\|Buchseite=Information_Theory/General_Description
	}}		}}

@@ Line 29: / Line 29: @@
-''Hints:''
+Hints:
 *The exercise belongs to the chapter&nbsp; [[Information_Theory/Allgemeine_Beschreibung|General Description of Source Coding]].
 *The following questions&nbsp; '''(3)'''&nbsp; to&nbsp; '''(6)'''&nbsp; refer to the keywords in the above graphic.

@@ Line 30: / Line 30: @@
 ''Hints:''
-*The exercise belongs to the chapter&nbsp; [[Information_Theory/Allgemeine_Beschreibung|General description of source coding]].
+*The exercise belongs to the chapter&nbsp; [[Information_Theory/Allgemeine_Beschreibung|General Description of Source Coding]].
 *The following questions&nbsp; '''(3)'''&nbsp; to&nbsp; '''(6)'''&nbsp; refer to the keywords in the above graphic.

@@ Line 83: / Line 83: @@
 * In line coding, redundancy is added to adapt the transmitted signal to the spectral characteristics of the channel.
 *With channel coding, redundancy is also added specifically, in this case to be able to use it at the receiver for error detection and/or error correction.
-*The aim of source coding, on the other hand, is to reduce redundancy as much as possible in order to be able to store or transmit the information of the message source as efficiently as possible.
+*The aim of source coding is to reduce redundancy as much as possible in order to be able to store or transmit the information of the source as efficiently as possible.
@@ Line 89: / Line 89: @@
 '''(2)'''&nbsp; Correct <u>answer is 3</u>:
 *In line and channel coding, lossy techniques would be counterproductive.
-*In contrast, source coding for analogue input signals (audio, video, etc.) is lossy per se.
+*In contrast, source coding for analog input signals (audio, video, etc.) is lossy per se.
-'''(3)'''&nbsp; The following are line coding methods
+'''(3)'''&nbsp; The following are line coding methods:
 *the 4B3T codes (there are several variants of this, all of which work in blocks),
-*the AMI code (symbolic: &nbsp; At each coding step, a binary character is read in and a ternary character is output).
+*the AMI code (symbol-wise &nbsp; &rArr; &nbsp; at each coding step, a binary character is read in and a ternary character is output).
@@ Line 102: / Line 102: @@
-'''(4)'''&nbsp; In the book "Channel Coding" are dealt with:
+'''(4)'''&nbsp; In the book&nbsp; "Channel Coding"&nbsp; are dealt with:
 *the Hamming codes,
 *the Reed-Solomon codes,
@@ Line 109: / Line 109: @@
-The correct result is accordingly $N_\text{KC}\hspace{0.15cm}\underline{ = 4}$.
+The correct result is accordingly $N_\text{ChC}\hspace{0.15cm}\underline{ = 4}$.
-'''(5)'''&nbsp; In lossless source coding, the receiver can completely reconstruct the message of the source if no transmission error has occurred. <br>Lossless source coding schemes include
+'''(5)'''&nbsp; In lossless source coding, the receiver can completely reconstruct the message of the source if no transmission error has occurred.
 *the Huffman code,
 *the different variants of the Lempel-Ziv algorithm,
-*the so-called run-length codes,
+*the run-length code,
 *the well-known compression programme "Winzip".
-All these procedures can only be used with digital input &nbsp; &rArr; &nbsp;  $N_\text{QC (verlustlos)}\hspace{0.15cm}\underline{ = 4}$.
+All these procedures can only be used with digital input &nbsp; &rArr; &nbsp;  $N_\text{SC (lossless)}\hspace{0.15cm}\underline{ = 4}$.
 '''(6)'''&nbsp; <u>Statements 1 and 3</u> are correct:
-* Only GIF and JPG are applied to pictures.&nbsp; MP3 has been the most widely used audio compression programme for years.
+* Only GIF and JPG are applied to pictures.&nbsp; MP3 has been the most widely used audio compression program for years.
-*The AMR codec and the EFR codec are used for GSM and UMTS.
+*The AMR codec and the EFR codec are used for GSM and UMTS in Mobile Communication.
 {{ML-Fuß}}

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Inf_A_2_1.png|right|frame|Keywords for "coding"]]
+[[File:EN_Inf_A_2_1.png|right|frame|Keywords related to <br>the topic&nbsp; "Coding"]]
 Three types of coding methods are distinguished, namely:
-*Line Coding &nbsp; &rArr; &nbsp; Chapter "Coded and Multilevel Transmission" in the book&nbsp; [[Digital_Signal_Transmission]],
+*Line Coding &nbsp; &rArr; &nbsp; Chapter&nbsp; "Coded and Multilevel Transmission"&nbsp; in the book&nbsp; "[[Digital_Signal_Transmission]]",
-*Channel Coding &nbsp; &rArr; &nbsp; &nbsp; [[Channel_Coding]] book,
+*Channel Coding &nbsp; &rArr; &nbsp; &nbsp;  book&nbsp; "[[Channel_Coding]]",
-*Source Coding &nbsp; &rArr; &nbsp; Chapter "Source Coding - Data Compression" in the book&nbsp; [[Information_Theory]].
+*Source Coding &nbsp; &rArr; &nbsp; Chapter&nbsp; "Source Coding - Data Compression"&nbsp; in the book&nbsp; "[[Information_Theory]]".
-All these basic coding methods have in common that the source signal &nbsp; $q(t)$&nbsp; is represented by a code symbol sequence&nbsp; $\langle c_\nu \rangle $&nbsp;.&nbsp; With a digital source&nbsp; (with or without memory)&nbsp; the source signal&nbsp; $q(t)$&nbsp; can also be described by the source symbol sequence&nbsp; $\langle q_\nu \rangle $&nbsp;.
+All these basic coding methods have in common that the source signal&nbsp; $q(t)$&nbsp; is represented by a code symbol sequence&nbsp; $\langle c_\nu \rangle $.&nbsp; With a digital source&nbsp; (with or w/o memory)&nbsp; the source signal&nbsp; $q(t)$&nbsp; can be described by the source symbol sequence&nbsp; $\langle q_\nu \rangle $.
-At the receiver, the sink symbol sequence&nbsp; $\langle v_\nu \rangle $&nbsp; or the sink signal&nbsp; $v(t)$&nbsp; is obtained from the regenerated symbol sequence&nbsp; $\langle r_\nu \rangle $&nbsp; gewonnen.&nbsp; This is called  <i>decoding</i>, sometimes also <i>signal reconstruktion</i>.
+At the receiver, the sink symbol sequence&nbsp; $\langle v_\nu \rangle $&nbsp; or the sink signal&nbsp; $v(t)$&nbsp; is obtained from the regenerated symbol sequence&nbsp; $\langle r_\nu \rangle $.&nbsp; This is called&nbsp;  "decoding",&nbsp; sometimes also "signal reconstruction".
 All the terms listed on the right belong to one of the three disciplines listed above, between which there is a certain affinity, but which are quite different in terms of objective and mathematical handling.
-A further distinguishing feature in coded transmission is:
+A further distinguishing feature in&nbsp; "coded transmission"&nbsp; is:
-* One speaks of a <i>lossless coding procedure</i>, if after decoding&nbsp; $\langle v_\nu \rangle  = \langle q_\nu \rangle$&nbsp; applies.&nbsp; Otherwise, the coding procedure is <i>lossy</i>.
+* One speaks of a&nbsp; "lossless coding procedure", if after decoding&nbsp; $\langle v_\nu \rangle  = \langle q_\nu \rangle$&nbsp; applies.&nbsp; <br>Otherwise, the coding procedure is called&nbsp; "lossy".
 * The prerequisite for this classification is error-free transmission: &nbsp; $\langle r_\nu \rangle  = \langle c_\nu \rangle$.
@@ Line 30: / Line 30: @@
 ''Hints:''
-*The task belongs to the chapter&nbsp; [[Information_Theory/Allgemeine_Beschreibung|General description of source coding]].
+*The exercise belongs to the chapter&nbsp; [[Information_Theory/Allgemeine_Beschreibung|General description of source coding]].
-*The following questions&nbsp; '''(3)'''&nbsp; to&nbsp; '''(6)'''&nbsp; refer to the keywords in the above diagram.
+*The following questions&nbsp; '''(3)'''&nbsp; to&nbsp; '''(6)'''&nbsp; refer to the keywords in the above graphic.
@@ Line 40: / Line 40: @@
 {In which coding procedures is redundancy added?
 |type="[]"}
-+ Procedure for line coding,
++ Line coding  methods,
-+ Channel coding method,
++ Channel coding methods,
-- Source coding method.
+- Source coding methods.
 {Which coding methods can be lossy?
 |type="[]"}
-- Line coding method,
+- Line coding methods,
-- Channel coding method,
+- Channel coding methods,
-+ Source coding method.
++ Source coding methods.
-{How many of the terms given in the diagram are counted as line coding?
+{How many of the terms given in the chart are counted as&nbsp; "Line Coding"?
 |type="{}"}
 $N_\text{LC} \ = \ $ { 2 }
-{How many of the terms in the graph are counted as channel coding?
+{How many of the terms in the graph are counted as&nbsp; "Channel Coding"?
 |type="{}"}
-$N_\text{KC}\ =  \ $ { 4 }
+$N_\text{ChC}\ =  \ $ { 4 }
-{How many of the terms given in the graph are counted as lossless source coding?
+{How many of the terms given in the graph are counted as&nbsp; "lossless Source Coding"?
 |type="{}"}
-$N_\text{QC (lossless)} \ =  \ $ { 4 }
+$N_\text{SC (lossless)} \ =  \ $ { 4 }

← Older revision		Revision as of 15:04, 26 June 2021
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−	[[Category:Information Theory: Exercises\|^2.1 ~~Allgemeine Beschreibung~~^]]	+	[[Category:Information Theory: Exercises\|^2.1 General Description^]]