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