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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.11862 |
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| _version_ | 1866918493289447424 |
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| author | Wei, Jiahui Kountouris, Marios |
| author_facet | Wei, Jiahui Kountouris, Marios |
| contents | We extend the Rate-Distortion-Perception (RDP) framework to the Rényi information-theoretic regime, utilizing Sibson's $α$-mutual information to characterize the fundamental limits under distortion and perception constraints. For scalar Gaussian sources, we derive closed-form expressions for the Rényi RDP function, showing that the perception constraint induces a feasible interval for the reproduction variance. Furthermore, we establish a Rényi-generalized version of the Strong Functional Representation Lemma. Our analysis reveals a phase transition in the complexity of optimal functional representations: for $0.5<α< 1$, the coding cost is bounded by the $α$-divergence of order $α+1$, necessitating a codebook with heavy-tailed polynomial decay; conversely, for $α> 1$, the representation collapses to one with finite support, offering new insights into the compression of shared randomness under generalized notions of mutual information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11862 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Rényi Rate-Distortion-Perception Function and Functional Representations Wei, Jiahui Kountouris, Marios Information Theory We extend the Rate-Distortion-Perception (RDP) framework to the Rényi information-theoretic regime, utilizing Sibson's $α$-mutual information to characterize the fundamental limits under distortion and perception constraints. For scalar Gaussian sources, we derive closed-form expressions for the Rényi RDP function, showing that the perception constraint induces a feasible interval for the reproduction variance. Furthermore, we establish a Rényi-generalized version of the Strong Functional Representation Lemma. Our analysis reveals a phase transition in the complexity of optimal functional representations: for $0.5<α< 1$, the coding cost is bounded by the $α$-divergence of order $α+1$, necessitating a codebook with heavy-tailed polynomial decay; conversely, for $α> 1$, the representation collapses to one with finite support, offering new insights into the compression of shared randomness under generalized notions of mutual information. |
| title | On the Rényi Rate-Distortion-Perception Function and Functional Representations |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.11862 |