Low-Latency Realism Through Randomized Distributed Function Computations: A Shannon Theoretic Approach

Semantic communication frameworks aim to convey the underlying significance of data rather than reproducing it exactly, a perspective that enables substantial efficiency gains in settings constrained by latency or bandwidth. Motivated by this shift, we study the rate-distortion-perception (RDP) trade-off for image compression, a setting in which reconstructions must be not only accurate but also perceptually faithful. Our analysis is carried out through the lens of randomized distributed function computation (RDFC) framework, which provides a principled means of synthesizing randomness and shaping output distributions. Leveraging this framework, we establish finite-blocklength characterizations of the RDP region, quantifying how communication rate, distortion, and perceptual fidelity interact in non-asymptotic regimes. We further broaden this characterization by incorporating two practically relevant extensions: (i) scenarios in which encoder and decoder share side information, and (ii) settings that require strong secrecy guarantees against adversaries, which might include those with quantum capabilities. Moreover, we identify the corresponding asymptotic region under a perfect realism constraint and examine how side information, finite blocklength effects, and secrecy demands influence achievable performance. The resulting insights provide actionable guidance for the development of low-latency, secure, and realism-aware image compression and generative modeling systems.