Paper 2025/1612

Low-Latency Rate-Distortion-Perception Trade-offs Through Randomized Distributed Function Computations

Abstract

Semantic communication systems focus on the transmission of meaning rather than the exact reconstruction of data, reshaping communication network design to achieve transformative efficiency in latency-sensitive and bandwidth-limited scenarios. Within this context, we investigate the rate-distortion-perception (RDP) problem for image compression, which plays a central role in producing perceptually realistic outputs under rate constraints. By employing the randomized distributed function computation (RDFC) framework, we derive an achievable non-asymptotic RDP region that captures the finite blocklength trade-offs among rate, distortion, and perceptual quality, aligning with the objectives of semantic communications. This region is further generalized to include either side information or a secrecy requirement, the latter ensuring strong secrecy against eavesdroppers through physical-layer security mechanisms and maintaining robustness in the presence of quantum-capable adversaries. The main contributions of this work are: (i) achievable bounds for non-asymptotic RDP regions subject to realism and distortion constraints; (ii) extensions to cases where side information is available at both the encoder and decoder; (iii) achievable, nonasymptotic RDP bounds with strong secrecy guarantees; (iv) characterization of the asymptotic secure RDP region under a perfect realism constraint; and (v) demonstrations of significant rate reductions and the effects of finite blocklengths, side information, and secrecy constraints. These findings offer concrete guidelines for the design of low-latency, secure, and high-fidelity image compression and generative modeling systems that generate realistic outputs, with relevance for, e.g., privacy-critical applications.