Rate-Distortion-Perception Function of Bernoulli Vector Sources
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| Format: | Preprint |
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2025
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| _version_ | 1866909462998024192 |
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| author | Vippathalla, Praneeth Kumar Badiu, Mihai-Alin Coon, Justin P. |
| author_facet | Vippathalla, Praneeth Kumar Badiu, Mihai-Alin Coon, Justin P. |
| contents | In this paper, we consider the rate-distortion-perception (RDP) trade-off for the lossy compression of a Bernoulli vector source, which is a finite collection of independent binary random variables. The RDP function quantifies in a way the efficient compression of a source when we impose a distortion constraint that limits the dissimilarity between the source and the reconstruction and a perception constraint that restricts the distributional discrepancy of the source and the reconstruction. In this work, we obtain an exact characterization of the RDP function of a Bernoulli vector source with the Hamming distortion function and a single-letter perception function that measures the closeness of the distributions of the components of the source. The solution can be described by partitioning the set of distortion and perception levels $(D,P)$ into three regions, where in each region the optimal distortion and perception levels we allot to the components have a similar nature. Finally, we introduce the RDP function for graph sources and apply our result to the Erdős-Rényi graph model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_12348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rate-Distortion-Perception Function of Bernoulli Vector Sources Vippathalla, Praneeth Kumar Badiu, Mihai-Alin Coon, Justin P. Information Theory In this paper, we consider the rate-distortion-perception (RDP) trade-off for the lossy compression of a Bernoulli vector source, which is a finite collection of independent binary random variables. The RDP function quantifies in a way the efficient compression of a source when we impose a distortion constraint that limits the dissimilarity between the source and the reconstruction and a perception constraint that restricts the distributional discrepancy of the source and the reconstruction. In this work, we obtain an exact characterization of the RDP function of a Bernoulli vector source with the Hamming distortion function and a single-letter perception function that measures the closeness of the distributions of the components of the source. The solution can be described by partitioning the set of distortion and perception levels $(D,P)$ into three regions, where in each region the optimal distortion and perception levels we allot to the components have a similar nature. Finally, we introduce the RDP function for graph sources and apply our result to the Erdős-Rényi graph model. |
| title | Rate-Distortion-Perception Function of Bernoulli Vector Sources |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.12348 |