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Introduction to rate-distortion theory

2. content. We will give an introduction to Rate Distortion theorySome examples will be included. Han Vinck 2012. 3. Fundamental quantity in Information theory . entropy The minimum average number of binary digits needed tospecify a source output (message) uniquely is called SOUR

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Introduction to rate-distortion theory

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    1. Introduction to rate-distortion theory A.J. Han Vinck University of Essen May 2012

    2. 2 content We will give an introduction to Rate Distortion theory Some examples will be included Han Vinck 2012

    3. 3 Fundamental quantity in Information theory Han Vinck 2012

    4. 4 Recall: Express everything in bits 0 and 1 Han Vinck 2012

    5. 5 Han Vinck 2012

    6. 6 model Han Vinck 2012

    7. 7 Rate Distortion Theory Han Vinck 2012 The distortion is a part of the problem The set of representatives is fixed The distortion is a part of the problem The set of representatives is fixed

    8. 8 Han Vinck 2012

    9. 9 Source representation Han Vinck 2012

    10. 10 Source representation I( X; X‘ ) = H(X) – H(X|X‘) = H(X‘) – H(X‘|X) H(X‘) = I( X; X‘ ) + H(X‘|X) (now H(X‘|X) ? 0) Hence, minimizing I(X;X‘) for all possible transitions X ? X‘ giving an average distortion D gives a lower bound R(D) for the representation of X‘ Han Vinck 2012

    11. 11 Formal definition The rate distortion function for X and X‘ is formally defined as Han Vinck 2012

    12. 12 Example 1 Han Vinck 2012

    13. 13 Example 1: explanation Han Vinck 2012

    14. 14 Example 2: binary source Han Vinck 2012

    15. 15 Han Vinck 2012

    16. 16 Example 2 Han Vinck 2012

    17. 17 quantization Han Vinck 2012

    18. 18 Quantization for Gaussian X with mean 0 Han Vinck 2012

    19. 19 Quantization for uniformly distributed X with mean 0 Han Vinck 2012

    20. 20 Han Vinck 2012

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