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arXiv · 2501.12348

Rate-Distortion-Perception Function of Bernoulli Vector Sources

Praneeth Kumar Vippathalla·Mihai-Alin Badiu·Justin P. Coon
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Abstract

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.

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Praneeth Kumar Vippathalla, Mihai-Alin Badiu, Justin P. Coon. 2025-01-21. Rate-Distortion-Perception Function of Bernoulli Vector Sources. https://arxiv.org/abs/2501.12348

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