  A rate-distortion-perception (RDP) tradeoff has recently been proposed by
Blau and Michaeli and also Matsumoto. Focusing on the case of perfect realism,
which coincides with the problem of distribution-preserving lossy compression
studied by Li et al., a coding theorem for the RDP tradeoff that allows for a
specified amount of common randomness between the encoder and decoder is
provided. The existing RDP tradeoff is recovered by allowing for the amount of
common randomness to be infinite. The quadratic Gaussian case is examined in
detail.
