This preview shows pages 1–2. Sign up to view the full content.
EE 376B/Stat 376B
Handout #27
Information Theory
Tuesday, June 6, 2006
Prof. T. Cover
Solutions to Homework Set #8
1.
Universal data compression.
Consider three possible source distributions on
X
,
P
a
= (0
.
7
,
0
.
2
,
0
.
1)
,
P
b
= (0
.
1
,
0
.
7
,
0
.
2)
,
P
c
= (0
.
2
,
0
.
1
,
0
.
7)
.
(a) Find the minimum incremental cost of compression
D
*
= min
P
max
θ
D
(
P
θ

P
)
,
the associated mass function
P
= (
p
1
,p
2
,p
3
), and ideal codeword lengths
l
i
=
log(1
/p
i
).
(b) What is the channel capacity of a channel matrix with rows
P
a
, P
b
, P
c
?
Solution: Universal data compression.
Since
D
*
=
C,
where
C
is the capacity of a channel deﬁned by a channel matrix with
rows
P
a
,P
b
,P
c
, and the uniform input distribution
p
*
= (1
/
3
,
1
/
3
,
1
/
3) achieves the
capacity
C
,
D
*
=
C
= log 3

H
(0
.
1
,
0
.
7
,
0
.
2)
≈
.
4282
.
Thus, the cost of not knowing the true source distribution is slightly less than half a
bit per symbol.
2.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 06/10/2008 for the course ECE 376B taught by Professor Tomcover during the Spring '05 term at Stanford.
 Spring '05
 TomCover

Click to edit the document details