Rate-Distortion Limits for Task-Oriented Compression with Side Information

Area of Science:

• Information Theory
• Data Compression
• Machine Learning

Background:

• Task-oriented data compression often involves semantic information influencing observations indirectly.
• Existing models typically lack side information or explicit handling of semantic segments.

Purpose of the Study:

• To analyze the semantic rate-distortion problem with side information and two semantic segments.
• To establish information-theoretic limits for compression rates and distortions.
• To validate theoretical findings with deep learning-based image compression.

Main Methods:

• Characterizing the rate-distortion function for semantic information.
• Deriving rate-distortion functions under specific Markov conditions.
• Implementing and evaluating a deep learning model for classification-oriented lossy image compression.

Main Results:

• The information-theoretic limits for the semantic rate-distortion tradeoff were established.
• Explicit rate-distortion functions were derived for binary classification and Gaussian-correlated scenarios.
• Deep learning validation confirmed the effectiveness of side information on distortion and classification accuracy.

Conclusions:

• The study provides a theoretical framework for semantic rate-distortion with side information.
• Side information significantly enhances both data compression and task performance.
• Semantic segmentation is rational and beneficial in lossy compression tasks.