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
1
11
8 , 16 , 16 .
(a) Design a binary Human code for
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
= 2lim n
n
i=1
n
1
)] n
log p(Xi )
= 2H (X ) a.e.
(assumi
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 of X completely determines Y . We prove
the only if part
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 Markov chain X X
Y = g (X ). Then, by the signal proc
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 Xi represent the signal. It is assumed that the noise a