Source-Channel Separation Theorems for Distortion Perception Coding

It is well known that separation between lossy source coding and channel coding is asymptotically optimal under classical additive distortion measures. Recently, coding under a new class of quality considerations, often referred to as perception or realism, has attracted significant attention due to its close connection to neural generative models and semantic communications. In this work, we revisit source-channel separation under the consideration of distortion-perception. We show that when the perception quality is measured on the block level, i.e., in the strong-sense, the optimality of separation still holds when common randomness is shared between the encoder and the decoder; however, separation is no longer optimal when such common randomness is not available. In contrast, when the perception quality is the average per-symbol measure, i.e., in the weak-sense, the optimality of separation holds regardless of the availability of common randomness.