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.

翻译：在需要保持重构数据感知质量的应用中（如神经图像压缩），基础率-失真-感知（RDP）权衡问题随之产生。当压缩数据通过公共通信信道传输时，会引发安全风险。因此，我们研究在无噪信道和具有相关噪声分量的广播信道（BCs）上，在可忽略信息泄露条件下的安全RDP问题。针对无噪信道，刻画了精确的安全RDP可达区域；针对广播信道，推导了内界，并证明该内界对一类更优能力的广播信道是紧致的。进一步表明，在可利用无限公共随机性的条件下，分离式信源信道编码对此精确安全RDP区域是最优的。此外，当编解码器均能访问与信源相关的边信息且信道无噪时，建立了精确RDP区域；若仅解码器在无噪场景下拥有相关边信息，则推导了内界及该区域为精确的特例情况。二元和高斯示例证明：与标准率-失真设置不同，公共随机性可显著降低安全RDP设置中的通信速率。因此，我们的结果表明：基于随机装箱的编码方案能同时实现强保密性、低失真和高感知质量。