UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Electrical and Computer Engineering
ECE 242 Winter 2009 Instructor: K. Rose
Homework Assignment #5
(Due on Wednesday 3/4/2009)
Reading: Review Chapters 8 and 9.
Problem # 1. Construct a probability sequence p= (p1, p2, . . .) such that H(p) = ∞
(be creative!).
Problem # 2. In this problem you are to try to construct a uniquely decodable code over
the four-letter alphabet A={0,1,2,3}with prescribed codeword lengths. In the following
matrix the symbol kidenotes the number of words of length iin the putative code.
code 1
code 2
code 3
code 4
k1k2k3k4k5k6
3 3 3 3 4 0
2 7 3 3 5 0
1 7 3 7 4 0
0 7 3 11 3 4
In each of the four cases, construct the required code, or explain why such a code cannot
exist.
Problem # 3. A discrete source with probability distribution
p= (.2, .15, .15, .1, .1, .1, .1, .1)
is to be encoded into a ternary prefix code with minimum average length. Construct two sets
of codewords whose lengths have the same minimum average value, but different variances.
State a reason or reasons why one or the other might be preferable in applications.
Problem # 4. Let p= (.9, .1) be the probability distribution of a discrete memoryless
source. Find the minimum average length (in bits per original symbol) for a prefix code for
p,p2, and p3. Vector coding offers advantages even if the samples are independent.
