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A Coding Theorem for f-Separable Distortion Measures.
1Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study introduces f-separable distortion measures, relaxing traditional assumptions for better modeling of non-linear penalties in data compression. This innovation leads to new rate-distortion functions for stationary ergodic sources.
Area of Science:
- Information Theory
- Data Compression
- Signal Processing
Background:
- Traditional rate-distortion theory relies on separability assumptions.
- Non-linear penalties are common in real-world distortion modeling.
- Existing models may not adequately capture complex distortion behaviors.
Purpose of the Study:
- To introduce and analyze f-separable distortion measures.
- To extend rate-distortion theory beyond traditional separability.
- To model non-linear penalties effectively in information theory.
Main Methods:
- Defining n-letter distortion measures as f-means of single-letter distortions.
- Proving a rate-distortion coding theorem for stationary ergodic sources using f-separable measures.
- Deriving and illustrating rate-distortion functions for these new measures.
Main Results:
- Demonstrated the utility of f-separable distortion measures for non-linear penalties.
- Established a theoretical framework for rate-distortion coding with these measures.
- Provided examples of novel rate-distortion functions.
Conclusions:
- F-separable distortion measures offer a flexible alternative to traditional separable measures.
- The proposed framework advances the understanding of rate-distortion theory for complex distortion models.
- Connections to subadditive distortion measures are explored, broadening theoretical insights.
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