t - VTU e-Learning Centre
t - VTU e-Learning Centre
t - VTU e-Learning Centre
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H(<br />
x)<br />
<br />
[ P(<br />
x<br />
<br />
<br />
P(<br />
x<br />
0)<br />
log P(<br />
x<br />
<br />
<br />
2)<br />
log P(<br />
x<br />
0)<br />
<br />
<br />
2)<br />
P(<br />
x<br />
<br />
<br />
P(<br />
x<br />
1)<br />
log P(<br />
x<br />
<br />
1)<br />
3)<br />
log P(<br />
x<br />
= - [P log Q + Q log Q + Q log Q + P log P]<br />
2P log P 2Q<br />
log Q <br />
H( x)<br />
<br />
2<br />
2<br />
bits/sym. ----(4)<br />
Step – 2: Calculate H(x/y) = P ( xy)<br />
log P ( x / y)<br />
Note, i & j can take values<br />
<br />
i 1 1 2 2<br />
j 1 2 1 2<br />
H(<br />
x / y)<br />
<br />
[ P(<br />
x<br />
P(<br />
x <br />
P(<br />
x <br />
2,<br />
2,<br />
y <br />
i<br />
1,<br />
y 1)<br />
log p(<br />
x 1 / y 1)<br />
P(<br />
x 1,<br />
y 2)<br />
log p(<br />
x 1 / y 2)<br />
Step – 3: Calculate P(x/y) using,<br />
(i) P(x = 1 / y = 1) =<br />
Where,<br />
Input<br />
X<br />
0<br />
1<br />
2<br />
3<br />
2)<br />
log ( x<br />
j<br />
y 1)<br />
log p(<br />
x 2 / y 1)<br />
P(<br />
x<br />
P(y=1) = P(x=1, y=1) + P(x=2, y=1)<br />
2 / y 2)]<br />
P ( x / y)<br />
<br />
1)<br />
. P(<br />
y 1/<br />
x 1)<br />
P(<br />
y 1)<br />
<br />
3)]<br />
P(<br />
x)<br />
. P(<br />
y / x)<br />
P(<br />
y)<br />
= P(x=1) . P(y=1 / x=1) + P(x=2,) . P(y=1 / x=2)<br />
= Q . p + Q . q<br />
= QP + Q (1 – p)<br />
P(<br />
y 1)<br />
Q<br />
1<br />
p<br />
p<br />
1<br />
0<br />
1<br />
1 – p = q<br />
(1 – p) = q<br />
2<br />
3<br />
Output<br />
Y<br />
. ----(5)
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