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Successive Refinement for Lossy Compression of Individual Sequences
1The Viterbi Faculty of Electrical and Computer Engineering, Technion-Israel Institute of Technology, Technion City, Haifa 3200003, Israel.
Entropy (Basel, Switzerland)
|April 26, 2025
Summary
This study establishes outer bounds for successive-refinement coding using finite-state machines. Achievability schemes are proposed for both successive-refinement and multiple description coding problems.
Area of Science:
- Information Theory
- Data Compression
- Coding Theory
Background:
- Lossy compression involves representing data with some information loss.
- Successive-refinement coding allows for staged data compression and reconstruction.
- Finite-state machines offer a model for practical compression algorithms.
Purpose of the Study:
- To establish theoretical limits (outer bounds) for successive-refinement coding.
- To develop practical coding schemes for successive-refinement and multiple description coding.
- To analyze compression strategies using finite-state machine encoders.
Main Methods:
- Deriving converse theorems to define achievable rate regions.
- Developing constructive coding schemes for specific compression problems.
- Extending existing methods for memoryless sources to more general cases.
Main Results:
- Established outer bounds for successive-refinement coding with finite-state machines.
- Proposed a straightforward achievability scheme for successive-refinement coding.
- Developed analogous achievability schemes for the multiple description coding problem.
Conclusions:
- The derived bounds provide fundamental limits for practical compression systems.
- The proposed schemes demonstrate the feasibility of successive-refinement and multiple description coding.
- This work advances the understanding of information-theoretic limits in data compression.
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