View source for 2S2122 Activity 3.1

== Problem 1 - The Complete Channel Model (2 pts.) ==

Answer '''comprehensively''' and do the following:

1. Draw the complete channel model. (0.2 pts)

2. What is the source? (0.2 pts)

3. What is the channel? (0.2 pts)

4. What is the receiver? (0.2 pts)

5. What are the encoder and decoder? (0.2 pts)

6. What are codebooks? (0.2 pts)

7. What is coding efficiency? (0.2 pts)

8. What is the maximum capacity of a channel? (0.4 pts)

9. What are symbol rates? (0.4 pts)

10. Where is Waldo? (if we like your answer you get 0.2 pts extra)

== Problem 2 - Review of BSC (2 pts.) ==

1. Draw the BSC channel with correct annotations of important parameters <math> p </math> and <math> \epsilon </math>. (0.1 pts)
2. Fill up the probability table in terms of the important parameters: (0.1 pts each entry)

{| class="wikitable"
|-
! scope="col"| Probability Term
! scope="col"| Function
|-
| style="text-align:center;" | <math> P(s=1) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(s=0) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(r=1|s=0) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(r=0|s=1) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(r=0,s=0) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(r=0,s=1) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(r=1,s=0) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(r=1,s=1) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(r=1) </math>
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> P(r=0) </math>
| style="text-align:center;" | 
|-
|}

3. Fill up the table below with the measures of information. Answer only in terms of <math> p </math> and <math> \epsilon </math> parameters (and of course constants). When necessary you can use "let <math>q </math> be ...". Also, answer with equations that are '''programming friendly'''. Answering the simplified version merits half points for that part. (0.1 pts per term)

{| class="wikitable"
|-
! scope="col"| Information Measure
! scope="col"| Function
|-
| style="text-align:center;" | <math> H(S) </math> 
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> H(R) </math> 
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> H(R|S) </math> 
| style="text-align:center;" | 
|-
| style="text-align:center;" | <math> I(R|S) </math> 
| style="text-align:center;" | 
|-
|}

4. Explain why <math> I(R,S) = 0 </math> when <math> \epsilon = 0.5 </math> regardless of varying the source probability distribution <math> p </math>. (0.2 pts.)
5. Explain what does negative information mean and when can it happen? (0.2 pts.)
6. Explain why <math> I(R,S) < 0 </math> means information from the receiver can short-circuit back to the source. (0.1 pts.)

== The Binary Erasure Channel ==


== Huffman Coding ==