green codes slides
TRANSCRIPT
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small sensors
Fixed Rate Fixed message size
processor with heat sink
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small sensors
Fixed Rate Fixed message size
processor with heat sink
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small sensors
Fixed Rate Fixed message size
processor with heat sink
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small sensors
Fixed Rate Fixed message size
processor with heat sink
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small sensors
Fixed Rate Fixed message size
processor with heat sink
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small sensors
Fixed Rate Fixed message size
processor with heat sink
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small sensors
Fixed Rate Fixed message size
processor with heat sink
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small sensors
Fixed Rate Fixed message size
processor with heat sink
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! !"# $ $"# % %"# & &"#!'
!#"#
!#
!("#
!(
!&"#
!&
!%"#
!%
!$"#
!$
)*+,-
.*/
$!
1!0),
"02
34566*60758,-95..
:6;*
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! !"# $ $"# % %"# & &"#!'
!#"#
!#
!("#
!(
!&"#
!&
!%"#
!%
!$"#
!$
)*+,-
.*/
$!
1!0),
"02
34566*60758,-95..
:6;*
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! !"# $ $"# % %"# & &"#!'
!#"#
!#
!("#
!(
!&"#
!&
!%"#
!%
!$"#
!$
)*+,-
.*/
$!
1!0),
"02
34566*60758,-95..
:6;*
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! !"# $ $"# % %"# & &"#!'
!#"#
!#
!("#
!(
!&"#
!&
!%"#
!%
!$"#
!$
)*+,-
.*/
$!
1!0),
"02
34566*60758,-95..
:6;*
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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
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Decoder implementation graph
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Y1
Output nodes
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
B1
B2
B3
B4
B5
B6
B7
Information nodes
Decoder implementation graph
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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
Decoder implementation graph
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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
Decoder implementation graph
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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
Decoder implementation graph
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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
Decoder implementation graph
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
Decoder implementation graph
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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! " # $ % &
!#
!%
!'
!"(
!$#
)*+,-.
/*0"!
1)
,
2
.
.
34566*6.758,-95//
Ptotal PT +
log()log
log1
Pe
(C(PT)R)2
R = 1/3
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Encoder Decoder
km mk
Etotal
= mPtotal
= m PT + l # of nodes
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Eper bit =Etotal
k
=PT
R+ l
# of nodes
k
Encoder Decoder
km mk
Etotal
= mPtotal
= m PT + l # of nodes
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Eper bit =Etotal
k
=PT
R+ l
# of nodes
k
PT
R+ l
max{k, m}k
Encoder Decoder
km mk
Etotal
= mPtotal
= m PT + l # of nodes
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!" !#$%" &" $" '" (
!((
!()
!'(
!')
!$(
!$)
!&(
!&)
!!(
*+,-./"0,-"123
45.!)
67
,
8
9:;++5+"42
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!" !#$%" &" $" '" (
!((
!()
!'(
!')
!$(
!$)
!&(
!&)
!!(
*+,-./"0,-"123
45.!)
67
,
8
9:;++5+"42
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!" !#$%" &" $" '" (
!((
!()
!'(
!')
!$(
!$)
!&(
!&)
!!(
*+,-./"0,-"123
45.!)
67
,
8
9:;++5+"42
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!"#$ !"% !"%$ &
!&!!
!%!
!#!
!'!
!(!
!$!
!)!
*+,-
.+/&!
02
34
!151!")
!151!"6
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ln(4)
Pe 0
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l 1CR
l log 1
Pe
gap = CR
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