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arXiv · 2509.10061

Semantic Rate-Distortion Theory with Applications

Yi-Qun Zhao·Zhi-Ming Ma·Geoffrey Ye Li·Shuai Yuan·Tong Ye·Chuan Zhou
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Abstract

Artificial intelligence (AI) is ushering in a new era for communication. As a result, the establishment of a semantic communication framework is putting on the agenda. Based on a realistic semantic communication model, this paper develops a rate-distortion framework for semantic compression. Different from the existing works primarily focusing on decoder-side estimation of intrinsic meaning and ignoring its inherent issues, such as ambiguity and polysemy, we exploit a constraint of conditional semantic probability distortion to effectively capture the essential features of practical semantic exchanges in an AI-assisted communication system. With the help of the methods in rate-distortion-perception theory, we establish a theorem specifying the minimum achievable rate under this semantic constraint and a traditional symbolic constraint and obtain its closed-form limit for a particular semantic scenario. From the experiments in this paper, bounding conditional semantic probability distortion can effectively improve both semantic transmission accuracy and bit-rate efficiency. Our framework bridges information theory and AI, enabling potential applications in bandwidth-efficient semantic-aware networks, enhanced transceiver understanding, and optimized semantic transmission for AI-driven systems.

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Yi-Qun Zhao, Zhi-Ming Ma, Geoffrey Ye Li, Shuai Yuan, Tong Ye, Chuan Zhou. 2025-09-12. Semantic Rate-Distortion Theory with Applications. https://arxiv.org/abs/2509.10061

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