ECE 5620
Spring 2011
Homework #6: Issued Apr. 1, Due Apr. 22 at 5 p.m.
Complete all eight problems.
1. Problem 5 in Chapter 13 of the text.
2. Problem 6 in Chapter 13 of the text.
3. Problem 9 in Chapter 13 of the text.
4. Show that the arithmetic coding algorithm discussed in class is preﬁxfree.
5. Show that the LempelZiv algorithm discussed in class is preﬁxfree.
6. Consider the arithmetic coding algorithm discussed in class for a binary
valued Markov source with a uniform initial distribution and transition ma
trix
P
=
±
3
/
4
1
/
4
1
/
4
3
/
4
²
.
Thus the realization 0110 is encoded to 0110101.
(a) Determine the encoding of 1101.
(b) Suppose a string of length 4 is encoded to 01110. Determine the origi
nal string.
7. How long is the shortest string with the property that “Without loss of gener
ality, it may be assumed that” (without the quotes) is a phrase in its Lempel
Ziv parsing?
8. Consider the string
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 '08
 WAGNER
 Markov chain

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