Distributed Source Coding

1. Distributed Source Coding 教師 : 楊士萱 老師 學生 : 李桐照

2. Talk OutLine • Introduction of DSC • Introduction of SWCQ • Conclusion

3. 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)

4. Introduction of DSC

5. 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

6. 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

7. 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

8. Introduction of SWCQ Review of Information Theory Mutual Information

9. 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

10. Introduction of SWCQ Classic Source Coding

11. Introduction of SWCQ Classic Source Coding

12. Introduction of SWCQ Classic Source Coding DSC SWCQ

13. Introduction of SWCQ A Case of SWC

14. Introduction of SWCQ 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)

15. Introduction of SWCQ 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

16. Introduction of SWCQ A Case of SWC RCSCmin =H(X)+H(Y) OurFocus RDSCmin =H(X,Y) RCSCmin>= RDSCmin

17. RY H(Y) H(Y|X) Slepian-Wolf RX H(X) H(X|Y) Introduction of SWCQ The SW Rate Region (for two sources)

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