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Distortion program-size complexity with respect to a fidelity criterion and rate-distortion function

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2 Author(s)
En-hui Yang ; Dept. of Math., Nankai Univ., Tianjin, China ; Shi-Yi Shen

A novel concept of distortion Kolmogorov-chaitin complexity is proposed. Bearing analogy to ordinary Kolmogorov-Chaitin complexity that represents the information content of a single message, distortion Kolmogorov-Chaitin complexity can be regarded as the amount of information about a single message that must be conveyed in order to reproduce it with a bounded distortion. This explanation is justified by the properties of distortion Kolmogorov-Chaitin complexity and the equivalences between distortion Kolmogorov-Chaitin complexity and the rate-distortion function, which are analogous to those between ordinary Kolmogorov-Chaitin complexity and the Shannon entropy. Some implications for universal almost sure data compression are also discussed

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Information Theory, IEEE Transactions on  (Volume:39 ,  Issue: 1 )