8/13/2019 m10180[Shannon's Noisy Channel Coding]

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C= maxpX(x) {I(X; Y) |pX(x)} I(X; Y) X Y

R

C

> 0

n

R > C

C0.5

Yi= Xi+ i

Xi

i

2 Xi P

1

n

ni=1

Xi

2 P

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nY= X +

n

1

n

ni=1

i

2

= 1

n

ni=1

(|yi xi|)2

2

n Y n

n2 X (|y x|)2 n2

Xi i Xi

1

n

ni=1

yi

2 P+ 2

|Y| n P+ 2

Y

n (P+ 2)

X Y

n2

n (P+ 2)

M =

n(2+P)

n

n2n

=

1 + P2

n2

n

C= 12 log2

1 + P

2

N02

P W P

2 =

WW

N02 df

= W N0

8/13/2019 m10180[Shannon's Noisy Channel Coding]

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12 log2

1 + P

N0W

2W

C=

2W

2 log2

1 +

P

N0W

bits/trans. x trans./sec

C= Wlog2

1 +

P

N0W

bits

sec

C= 3000log2(1 + 1000)30000bits

sec

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log2

1 +

P

2

n2