Distributed Source CodingDistributed Source Coding

教師 教師 : : 楊士萱 老師楊士萱 老師學生 學生 : : 李桐照李桐照

Talk OutLineTalk OutLine•Introduction of DSCIntroduction of DSC

•Introduction of SWCQIntroduction of SWCQ

•ConclusionConclusion

IntroductionIntroduction of DSC of DSC

Distributed Source Coding

Compression of two or more correlated source

•The source do not communicate with each other (hence distributed coding)

•Decoding is done jointly (say at the base station)

Source X

Source Y

Source Encoder X

Source Encoder Y

Joint Decoder

Divination X,Y

IntroductionIntroduction of DSC of DSC

Source X

Source Y

Source Encoder X

Source Encoder Y

Joint Source Decoder

Divination X,Y

Introduction of SWCQIntroduction of SWCQ

Review of Information Theory

Definition: (DMS) I ( P(x) ) = log1/ P(x) = – log P(x) If we use the base 2 logs, the resulting unit of information is call a bit

Definition: (DMS) The Entropy H(X) of a discrete random variable X is defined by

Information

Entropy

p(x)p(x)logH(X)H(p)Xx

2

Introduction of SWCQIntroduction of SWCQ

Review of Information Theory

Definition: (DMS) The joint entropy of 2 RV X,Y is the amount of the information needed on average to specify both their values

Joint Entropy

Xx y

Y)y)logp(X,p(x,Y)H(X,Y

Conditional EntropyDefinition: (DMS) The conditional entropy of a RV Y given another X, expresses how much extra information one still needs to supply on average to communicate Y given that the other party knows X

X)|logp(YE x)|y)logp(yp(x,

x)|x)logp(y|p(yp(x)

x)X|p(x)H(YX)|H(Y

Xx Yy

Xx Yy

Xx

Introduction of SWCQIntroduction of SWCQ

Review of Information Theory

Definition: (DMS) I(X,Y) is the mutual information between X and Y. It is the reduction of uncertainty of one RV due to knowing about the other, or the amount of information one RV contains about the other

Mutual Information

Y)I(X, X)|H(Y -H(Y) Y)|H(X-H(X)

Y)|H(XH(Y) X)|H(YH(X) Y)H(X,

Introduction of SWCQIntroduction of SWCQ

Review of Information Theory

H(YlX)H(XlY) I(X;Y)

H(X) H(Y)

Mutual Information

Y)I(X, X)|H(Y -H(Y) Y)|H(X-H(X)

Y)|H(XH(Y) X)|H(YH(X) Y)H(X,

Introduction of SWCQIntroduction of SWCQ

Review of Data Compression

Transform Coding:Transform Coding:

Take a sequence of inputs and transform them into another Take a sequence of inputs and transform them into another sequence in which most of thesequence in which most of the informationinformation is contained in is contained in

only a few elements. only a few elements.

And, then discarding the elements of the sequence that do not And, then discarding the elements of the sequence that do not contain much information, we can get a large amount of contain much information, we can get a large amount of

compression.compression.Nested quantization: quantization with side info

Slepian-Wolf coding: entropy coding with side info

Source X

Source Y

Source Encoder X

Source Encoder Y

Joint Source Decoder

Divination X,Y

Introduction of SWCQIntroduction of SWCQ

KLT Quantization Entropy Coding

Classic Source Coding

Introduction of SWCQIntroduction of SWCQ

KLT Quantization Entropy Coding

Classic Source Coding

KLT Quantization Syndrome -Based Entropy Coding

Introduction of SWCQIntroduction of SWCQ

KLT Quantization Entropy Coding

Classic Source Coding

KLT Quantization Syndrome -Based Entropy Coding

KLTNested

QuantizationSlepian-Wolf

Coding

SWCQSWCQ

DSC

•Introduction of SWCQIntroduction of SWCQ

A Case of SWC

Source X

Source Y

Source Encoder XRx(rate)

Source Encoder YRy(rate)

Joint Source Decoder

Divination X,Y

Z

W

•Introduction of SWCQIntroduction of SWCQ

A Case of SWC

Source X

Source Y

Source Encoder XRx(rate)

Source Encoder YRy(rate)

Joint Source Decoder

Divination X,Y

Z

W

Joint Encoding (Y is available when coding X)

Joint Encoding

Source X

Source Y

Source Encoder XRx(rate)

Source Encoder YRy(rate)

Joint Source Decoder

Divination X,Y

Z

W• Code Y at Ry≧ H(Y) : use Y to predict X and th

en code the difference at Rx≧H(XlY) • All together, Rx+Ry≧ H(XlY)+H(Y)=H(X,Y)

•Introduction of SWCQIntroduction of SWCQ

A Case of SWC

Source X

Source Y

Source Encoder XRx(rate)

Source Encoder YRy(rate)

Joint Source Decoder

Divination X,Y

Z

W

Distributed Encoding (Y is not available when coding X)• What is the min rate to code X in this case?• SW Theorem: Still H(XlY)

Separate encoding as efficient as joint encoding

•Introduction of SWCQIntroduction of SWCQ

A Case of SWC

Source XSource Encoder X

Rx(rate)

Source X

Source Y

Source Encoder XRx(rate)

Source Encoder YRy(rate)

Joint Source Decoder

Divination X,Y

Source YSource Encoder Y

Ry(rate)

Our Focus

RCSCmin =H(X)+H(Y)

RDSCmin =H(X,Y)

RCSCmin>= RDSCmin

Introduction of SWCQIntroduction of SWCQ

The SW Rate Region (for two sources) The SW Rate Region (for two sources)

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

ConclusiConclusionon : :

Compression of two or more correlated sources use DSC good than CSC.