University of Toronto
Department of Electrical
F. R. Kschischang
& Computer Engineering
ECE1502F — Information Theory
Final Examination
December 13, 2000
Instructions
You have approximately 2 hours of “inclass” time, followed by five days of “takehome” time to
complete this test.
Complete as much as possible during the inclass time; your grade will be
computed as a weighted average of your “inclass” grade and your “takehome” grade. (Weights
to be determined later.) Answer
all
five [5] questions. All questions have equal value. Show all
steps and present all results clearly. Takehome due date:
Monday, December 18, 2000, 1:00
p.m.
, or earlier. Please hand in to the instructor (SY505) or to his assistant Doreen Lowe (SY 5th
floor reception). All work is to be done independently. Consultation with others is
not
permitted.
Good luck!
1
.
Short Snappers
—the parts of this question all have short answers that require a minimum
of computation. In all cases, justify your answer briefly.
(a) What is
I
(
X
;
X
)?
(b) True or false?:
The capacity achieving input distribution for a discrete memoryless
channel makes the output distribution uniform.
(c) Find the capacity of the channel with channel transition matrix
M
=
1
2
1
4
1
4
1
4
1
2
1
4
1
4
1
4
1
2
.
(d) In the binary erasure channel, let the probability of erasure be
ǫ
. For which values of
ǫ
(if any) is this channel weakly symmetric?
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 Fall '10
 NatashaDevroye

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