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Distributed Source Coding. 教師 : 楊士萱 老師 學生 : 李桐照. Talk OutLine. Introduction of DSC Introduction of SWCQ Conclusion. Introduction of DSC. Distributed Source Coding. Compression of two or more correlated source The source do not communicate with each other

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Distributed source coding

Distributed Source Coding

教師 : 楊士萱 老師 學生 : 李桐照


Talk OutLine

  • Introduction of DSC

  • Introduction of SWCQ

  • Conclusion


Introduction 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)


Introduction of DSC


Introduction of SWCQ

Review of Information Theory

Information

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

Entropy

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


Introduction of SWCQ

Review of Information Theory

Joint Entropy

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

Conditional Entropy

Definition: (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


Introduction of SWCQ

Review of Information Theory

Mutual Information

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


Introduction of SWCQ

Review of Information Theory

Mutual Information


Introduction of SWCQ

Review of Data Compression

Transform Coding:

Take a sequence of inputs and transform them into another sequence in which most of theinformation is contained in only a few elements.

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

Nested quantization: quantization with side info

Slepian-Wolf coding: entropy coding with side info


Introduction of SWCQ

Classic Source Coding


Introduction of SWCQ

Classic Source Coding


Introduction of SWCQ

Classic Source Coding

DSC

SWCQ


A Case of SWC


A Case of SWC

Joint Encoding

Joint Encoding (Y is available when coding X)

  • Code Y at Ry≧ H(Y) : use Y to predict X and then code the difference at Rx≧H(XlY)

  • All together, Rx+Ry≧ H(XlY)+H(Y)=H(X,Y)


A Case of SWC

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


A Case of SWC

RCSCmin =H(X)+H(Y)

OurFocus

RDSCmin =H(X,Y)

RCSCmin>= RDSCmin


RY

H(Y)

H(Y|X)

Slepian-Wolf

RX

H(X)

H(X|Y)

Introduction of SWCQ

The SW Rate Region (for two sources)


Conclusion :

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


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