Green Codes Slides

8/14/2019 Green Codes Slides

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small sensors

Fixed Rate Fixed message size

processor with heat sink


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small sensors




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small sensors




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small sensors




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small sensors




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small sensors




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small sensors




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small sensors




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! !"# $ $"# % %"# & &"#!'

!#"#

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! !"# $ $"# % %"# & &"#!'

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! !"# $ $"# % %"# & &"#!'

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! !"# $ $"# % %"# & &"#!'

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Encoder Decoder


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Encoder Decoder


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Pe R

Pe exp(mEr(R))


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Pe R

Want a similar analysis for iterative decoding.

Pe exp(mEr(R))


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Y1

Output nodes

Y2

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Y8

Y9

Decoder implementation graph


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Y1

Output nodes

Y2

Y3

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Y7

Y8

Y9

B1

B2

B3

B4

B5

B6

B7

Information nodes



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Y1

Output nodes

Y2

Y3

Y4

Y5

Y6

Y7

Y8

Y9

Helper nodes

B1

B2

B3

B4

B5

B6

B7

Information nodes



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Y1

Output nodes

Y2

Y3

Y4

Y5

Y6

Y7

Y8

Y9

Helper nodes

B1

B2

B3

B4

B5

B6

B7

Information nodes



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Y1

Output nodes

Y2

Y3

Y4

Y5

Y6

Y7

Y8

Y9

Helper nodes

B1

B2

B3

B4

B5

B6

B7

Information nodes



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Y1

Output nodes

Y2

Y3

Y4

Y5

Y6

Y7

Y8

Y9

Helper nodes

B1

B2

B3

B4

B5

B6

B7

Information nodes


l # of nodes


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Y1

Output nodes

Y2

Y3

Y4

Y5

Y6

Y7

Y8

Y9

Helper nodes

B1

B2

B3

B4

B5

B6

B7

Information nodes


l # of nodes

Suffices now to findl


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Bi

a


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Bi

a


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Bi

a


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Bi

a

l

< a

l+1


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Channel needs tobehave atypicallyonly in the decoding neighborhood to cause an error

Bi

a

l

< a

l+1


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l 1

log()

log log1

Pe

(C

R)2

Pe

Pe


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Minimize by optimizing overPtotal PT

PT

Encoder Decoder

km mk

PT + l

PT +

log()log

log 1

Pe

(C(PT)R)2

Ptotal = PT + l

# of nodes

m


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Ptotal PT +

log()log

log1

Pe

(C(PT)R)2

R = 1/3


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Encoder Decoder

km mk

Etotal

= mPtotal

= m PT + l # of nodes


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Eper bit =Etotal

k

=PT

R+ l

# of nodes

k

Encoder Decoder

km mk

Etotal

= mPtotal



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Eper bit =Etotal

k

=PT

R+ l

# of nodes

k

PT

R+ l

max{k, m}k

Encoder Decoder

km mk

Etotal

= mPtotal



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67

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8

9:;++5+"42


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!" !#$%" &" $" '" (

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!" !#$%" &" $" '" (

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!"#$ !"% !"%$ &

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ln(4)

Pe 0


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l 1CR

l log 1

Pe

gap = CR


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