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.
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