1.
A te
and
(a)
(b)
ernary comm
2 occur wit
Find the pr
Suppose th
1? 2? (12)
Solution:
Let X deno
(a)
[
p Y
p Y
⎡
=
⎣
(
1
1
2
=
−
Similar
[
p Y
p Y
⎡
=
⎣
1
2
ε
=
+
[
p Y
=
(b)
Using B
ELEC2
munication
th probabili
robabilities
hat a 1 is ob
ote the input
]
0
=
0
0
X
⎤
=
=
⎦
)
1
0
4
ε
+
⋅
+
rly, we have
]
1
=
1
0
X
⎤
=
=
⎦
(
)
1
1
4
ε
−
+
]
[
2
1
p Y
=
−
Bayes’ Rule
210 Spring
channel is s
ity 1/2, 1/4,
of the outpu
served as an
t and Y den
[
]
0
p X
=
+
1
1
1
4
2
4
ε
=
−
e
[
]
0
p X
=
+
1
1
1
0
4
4
4
⋅
=
+
]
[
0
Y
p Y
=
−
e
g 2011 Ho
shown in Fi
and 1/4, re
ut symbols.
n output. W
Fig.
note the outp
0
p Y
X
⎡
=
⎣
ε
1
p Y
X
⎡
=
⎣
ε
]
1
1
Y
⎛
=
=
−
⎜
⎝
omework 2
ig. 1. Suppo
spectively.
(9)
What is the p
1.
put
[
1
p X
⎤
=
=
⎦
[
1
p X
⎤
=
=
⎦
1
1
2
4
ε
⎞
⎛
−
−
⎟
⎜
⎠
⎝
2 Solution
ose that the
probability t
]
1
p Y
⎡
+
=
⎣
]
1
p Y
⎡
+
=
⎣
1
1
4
4
ε
⎞
+
=
⎟
⎠
n
input symb
that the inpu
0
2
X
⎤
=
⎦
1
2
X
p
⎤
=
⎦
1
4
ols 0, 1,
ut was 0?
[
]
2
p X
=
[
]
2
X
=

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