error control coding for wyner-ziv system application 指 導 教 授:楊 士 萱 報 告 學...
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Error Control Coding for Wyner-Ziv System Applica
tion指 導 教 授:楊 士 萱報 告 學 生:李 桐 照
Outline Distributed Source Coding Introduction Wyner-Ziv System Introduction Turbo Coding Simulation Result Future work
Distributed Source Coding 1/2 (DSC)
Source X
Source Y
Source Encoder X
Source Encoder Y
Joint Source Decoder
XR
YR
XYStatisticallydependent
YXHRR YX ,
YXHRX | XYHRY |
y|xP
1Log,| 2
Xx Yy
yxPYXH
Slepian-Wolf Theorem:
RX
RY
Slepian-Wolf
H(X)H(X|Y)
H(Y|X)
H(Y)Compression of X with
side information Y at the Joint decoder
Achievable rates for distributed compression
RX
RY
RX
RY
Slepian-Wolf
H(X)H(X|Y)
H(Y|X)
H(Y)
Slepian-Wolf
H(X)H(X|Y)
H(Y|X)
H(Y)Compression of X with
side information Y at the Joint decoder
Achievable rates for distributed compression
Distributed Source Coding 2/2 (DSC)
Source X
Source Y
Source Encoder X
Joint Source Decoder
Y|XHXR
YHYR
X
Y
Statisticallydependent
p-1yxP
pyxP X-Y Relationship
p H(X|Y) R(In ideal case)
1% 0.080793 0.125
2% 0.141441 0.25
3% 0.194392 0.25
4% 0.242292 0.25
5% 0.286397 0.5
6% 0.327445 0.5
7% 0.365924 0.5
8% 0.402179 0.5
9% 0.436470 0.5
10% 0.468996 0.5
11% 0.499916 0.5
Wyner-Ziv System
Turbo Coding 1/8
Rate Compatible Punctured Turbo Coding
Turbo Coding 2/8
CA B HGFEDWrite In:
CA B D
GE F H
Write In
Read Out
BA E HDGCFRead Out: CA B HGFED
Read In:
CA B D
GE F H
Read Out
Write In
Write Out:
BA E HDGCF
Interleaver Design:
Block Interleaver Block Deinterleaver
Turbo Coding 3/8
Source Inforamtion
D D
CodeWords
kX
kY
kd
Octal
DG
7
5,1
RSC Code Rate R=1/2
Recursive Systematic Convolutional Codes (RSC):
Turbo Coding 4/8
RSCRate:1/2
RSCRate:1/2
Interleaver
Puncture
kX
kY
1,0kd
krscY .1
krscY .2
10
01
1/311
1/2
2/3
4/5
krscY .1
krscY .2
krscY .1
krscY .2
krscY .1
krscY .2
krscY .1
krscY .2
10
00
01
00
10
00
00
00
01
00
Puncturing Pattern Transmitted SequsnceCode Rate kY
8.28.17.27.16.26.15.25.1
4.24.13.23.12.22.11.21.1
,,,,,,,
,,,,,,,,
rscrscrscrscrscrscrscrsc
rscrscrscrscrscrscrscrsc
YYYYYYYY
YYYYYYYY
4.21.1 , rscrsc YY00
00
8.27.16.25.14.23.12.21.1 ,,,,,,, rscrscrscrscrscrscrscrsc YYYYYYYY
7.25.13.21.1 ,,, rscrscrscrsc YYYY
Punctured:
Turbo Coding 5/8
SISO Decoder 1DePuncturing
kxSystematic
Parity 1 k1,yky
SISO Decoder 2
Interleaver
Parity 2 k2,y
Interleaver
extrinsicL2
extrinsicL1
DeInterleaver
)( kd
)( k2 d
extrinsicL (Deinter)2
extrinsicL1(Inter)
DeInterleaver
DecisionThreshold=0
kd
Turbo Decode:
Turbo Coding 6/8
Soft-In/Soft-Out Decoder
)ˆ(XLxcL
)(XL )(e XL
Channel Values in
A Priori Values in Extrinsic Values Out
A Posteriori Values
Deterctor a Posterori LLR Value: )(x)ˆ( ' XLLXL c
Feedback for the next iteration
Output LLR :
)()ˆ()ˆ( ' XLXLXL e
Soft In Soft Output Decoder (SISO) :
Turbo Coding 7/8
Trellis state diagram
N
k
Nk
k
k
Rd
Rd
d
d
1
1k
|0Pr
|1Prln
nObservatio|0Pr
nObservatio|1Prln) (d
Log-Likelihood Ratio(LLR) :
MAP Decoder :
Turbo Coding 8/8
l ikkik lmlRm 1,,
mlRlm kil i
kk ,,11
lSRmSidmlR kkkkki 1|,,Pr,,
m lkkk
m lkkk
lmlRm
lmlRm
10
11
k,,
,,
lnd
m lk
ekk
m lk
ekk
k
k
kk
kk
mlylm
mlylm
d
d
d
d
,,
,,
ln0Pr
1Prln
0|xPr
1|xPrln
01
11
Simulation Result 1/2
Simulation Result 2/2p H(X|Y) R(In ideal case) R(In reality case)
1% 0.080793 0.125 0.25
2% 0.141441 0.25 0.25
3% 0.194392 0.25 0.5
4% 0.242292 0.25 0.5
5% 0.286397 0.5 0.5
6% 0.327445 0.5 0.5
7% 0.365924 0.5 0.5
8% 0.402179 0.5 0.5
9% 0.43647 0.5 1
10% 0.468996 0.5 1
11% 0.499916 0.5 1
Compression Efficiency Compared
Future work Design Good Turbo Coding :
S-Random Interleaver 8-th~11-th Implementation of RCPT