8
Capacity of the Gaussian Channel
Consider the following additive noise channel
Yi = Xi + Zi ,
where the Zi are i.i.d., zero-mean, variance N Gaussian random variables representing the noise and the
EE 647
Solution to Homework # 1
Georghiades
Given: September 9, 2004
Due: September 16, 2004.
1. Solve problem 2 in Chapter 2 of the textbook.
Solution: Let Y = g (X ) for some function g and dene the
EE 647
Solution to Homework # 2
Georghiades
Given: September 17, 2004
Due: September 28, 2004.
1. Solve problem 6 in Chapter 2 of the textbook.
Solution:
Clearly, the if part is true since knowledge o
EE 647
Solution to Homework # 3
Georghiades
Given: September 28, 2004
Due: October 5, 2004.
1. Solve problem 2 in Chapter 3 of the textbook.
Solution: We have
1
lim [p(X n )] n =
n
lim 2log[p(X
n
1
=
EE 647
Solution to Test # 1
Georghiades
Given: October 26, 2004
Closed book, close notes, one formula sheet allowed.
1
1. (15%) Consider a memoryless source with symbols having probabilities 1 , 4 ,
2
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Chapter 3
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