Secure Rate-Distortion-Perception: A Randomized Distributed Function Computation Approach for Realism

Fundamental rate-distortion-perception (RDP) trade-offs arise in applications requiring maintained perceptual quality of reconstructed data, such as neural image compression. When compressed data is transmitted over public communication channels, security risks emerge. We therefore study secure RDP under negligible information leakage over both noiseless channels and broadcast channels, BCs, with correlated noise components. For noiseless channels, the exact secure RDP region is characterized. For BCs, an inner bound is derived and shown to be tight for a class of more-capable BCs. Separate source-channel coding is further shown to be optimal for this exact secure RDP region with unlimited common randomness available. Moreover, when both encoder and decoder have access to side information correlated with the source and the channel is noiseless, the exact RDP region is established. If only the decoder has correlated side information in the noiseless setting, an inner bound is derived along with a special case where the region is exact. Binary and Gaussian examples demonstrate that common randomness can significantly reduce the communication rate in secure RDP settings, unlike in standard rate-distortion settings. Thus, our results illustrate that random binning-based coding achieves strong secrecy, low distortion, and high perceptual quality simultaneously.