Low-Latency Rate-Distortion-Perception Trade-Off: A Randomized Distributed Function Computation Application

Semantic communication systems, which focus on transmitting the semantics of data rather than its exact reconstruction, redefine the design of communication networks for transformative efficiency in bandwidth-limited and latencycritical applications. Addressing these goals, we tackle the rate-distortion-perception (RDP) problem for image compression, a critical challenge in achieving perceptually realistic reconstructions under rate constraints. Formulated within the randomized distributed function computation (RDFC) framework, we establish an achievable non-asymptotic RDP region, providing finite blocklength trade-offs between rate, distortion, and perceptual quality, aligning with semantic communication objectives. We extend this region to also include a secrecy constraint, providing strong secrecy guarantees against eavesdroppers via physical-layer security methods, ensuring resilience against quantum attacks. Our contributions include (i) establishing achievable bounds for non-asymptotic RDP regions under realism and distortion constraints; (ii) extending these bounds to provide strong secrecy guarantees; (iii) characterizing the asymptotic secure RDP region under a perfect realism constraint; and (iv) illustrating significant reductions in rates and the effects of secrecy constraints and finite blocklengths. Our results provide actionable insights for designing low-latency, high-fidelity, and secure image compression systems with realistic outputs, advancing applications, e.g., in privacycritical domains.