Rate-Distortion-Perception Tradeoff for Vector Gaussian Sources with Limited Common Randomness: Exact Characterization and Approximate Universality
Abstract
The distortion-rate-common randomness-perception (DRCP) theory characterizes how limited common randomness (CR) improves reconstruction fidelity under perceptual constraints, thereby providing an information-theoretic foundation for generative compression. In this paper, we characterize the DRCP tradeoff for vector Gaussian sources with limited CR under the squared-error distortion measure and the squared Wasserstein-2 perception measure. Specifically, we first establish a generalized reverse waterfilling characterization of globally optimal allocations. Second, we derive an analytical upper bound on the DRCP function through sequential greedy allocation of rate and CR. For fixed rate and CR budgets, the resulting representation is independent of the perception threshold. Finally, we establish its approximate universality through uniform performance guarantees: the achievable distortion exceeds the optimal distortion by at most 2ρ*≈0.2897 times the total source variance, whereas the optimal-to-greedy distortion ratio is at least η*≈0.7517.
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BibTeX
@misc{wang2026ratedistortionperception,
title = {{Rate-Distortion-Perception Tradeoff for Vector Gaussian Sources with Limited Common Randomness: Exact Characterization and Approximate Universality}},
author = {Wentao Wang and Shuo Shao and Ruibin Li and Jingjing Qian and Jun Chen and Bin Xia},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04693},
eprint = {2611.04693},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04693},
}
RIS
TY - UNPB
TI - Rate-Distortion-Perception Tradeoff for Vector Gaussian Sources with Limited Common Randomness: Exact Characterization and Approximate Universality
AU - Wentao Wang
AU - Shuo Shao
AU - Ruibin Li
AU - Jingjing Qian
AU - Jun Chen
AU - Bin Xia
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04693
UR - https://arxiv.org/abs/2611.04693
AB - The distortion-rate-common randomness-perception (DRCP) theory characterizes how limited common randomness (CR) improves reconstruction fidelity under perceptual constraints, thereby providing an information-theoretic foundation for generative compression. In this paper, we characterize the DRCP tradeoff for vector Gaussian sources with limited CR under the squared-error distortion measure and the squared Wasserstein-2 perception measure. Specifically, we first establish a generalized reverse waterfilling characterization of globally optimal allocations. Second, we derive an analytical upper bound on the DRCP function through sequential greedy allocation of rate and CR. For fixed rate and CR budgets, the resulting representation is independent of the perception threshold. Finally, we establish its approximate universality through uniform performance guarantees: the achievable distortion exceeds the optimal distortion by at most 2ρ^*≈0.2897 times the total source variance, whereas the optimal-to-greedy distortion ratio is at least η^*≈0.7517.
ER -