 t - VTU e-Learning Centre

Which are the symbols often used for the channel under discussion and why it is
so?
Input
X
OVER A NOISY CHANNEL ONE CAN NEVER SEND
INFORMATION WITHOUT ERRORS
2. For the discrete binary channel shown find H(x), H(y), H(x/y) & H(y/x) when
P(x=0) = 1/4, P(x=1) = 3/4 , = 0.75, & = 0.9.
Solution:
What type of channel in this?
H(x) = – i
p
t
i
log p
t
i
= – [P(x=0) log P(x=0) + P(x=1) log P(x=1)]
= – [p log p+ (1–p) log (1–p)]
Where, p = P(x=0) & (1-p) = p(x=1)
Substituting the values, H(x) = 0.8113 bits/sym.
H(y) = – i
0
1
2
3
0
X
(1 –)
(1 –)
Y
1
p
r
i
log p
r
i
= – [P(y=0) log P(y=0) + P(y=1) log P(y=1)]
r t
t
Recall, p 0 p 0 . p 00 p1
p10
1
p
p
1
0
1
1 – p = q
(1 – p) = q
2
3
0
1
Output
Y