Rate-Distortion-Perception Tradeoff for Vector Gaussian Sources with Limited Common Randomness: Exact Characterization and Approximate Universality

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 $2ρ^*\approx0.2897$ times the total source variance, whereas the optimal-to-greedy distortion ratio is at least $η^*\approx0.7517$.