This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on the divergence between the distributions of the source and reconstruction sequences conditioned on the encoder output. The paper considers the case when there is no shared randomness between the encoder and decoder. For discrete memoryless sources, a single-letter characterization of the RDP function is derived, settling a problem that remains open for the marginal metric introduced in Blau and Michaeli (2019). The achievability scheme is based on lossy source coding with a posterior reference map. For continuous valued sources under squared error distortion measure and squared quadratic Wasserstein perception measure, a single-letter characterization is also derived, showing that a noise-adding mechanism at the decoder suffices to achieve the optimal representation. For the case of zero perception loss, the characterization coincides with the results for the marginal metric derived in (2019) and (2020), demonstrating that zero perception loss can be achieved with a 3-dB penalty in the minimum distortion. The results are specialized to Gaussian sources, where the RDP function for vector Gaussian sources is derived and a waterfilling type solution is proposed. The paper also partially characterizes the RDP function for a mixture of vector Gaussians. The RDP tradeoff is characterized for finite alphabet sources and for continuous alphabet sources under squared error distortion measure and squared quadratic Wasserstein perception measure. The paper extends Shannon’s lower bound for the RD tradeoff to the RDP setting and partially characterizes the RDP tradeoff for a Gaussian-mixture source and completely characterizes the tradeoff for a vector Gaussian source. The paper also shows that the MMSE representation can be transformed to representations for other operating points on the RDP tradeoff by adding noise at the decoder. The paper concludes with some concluding remarks.This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on the divergence between the distributions of the source and reconstruction sequences conditioned on the encoder output. The paper considers the case when there is no shared randomness between the encoder and decoder. For discrete memoryless sources, a single-letter characterization of the RDP function is derived, settling a problem that remains open for the marginal metric introduced in Blau and Michaeli (2019). The achievability scheme is based on lossy source coding with a posterior reference map. For continuous valued sources under squared error distortion measure and squared quadratic Wasserstein perception measure, a single-letter characterization is also derived, showing that a noise-adding mechanism at the decoder suffices to achieve the optimal representation. For the case of zero perception loss, the characterization coincides with the results for the marginal metric derived in (2019) and (2020), demonstrating that zero perception loss can be achieved with a 3-dB penalty in the minimum distortion. The results are specialized to Gaussian sources, where the RDP function for vector Gaussian sources is derived and a waterfilling type solution is proposed. The paper also partially characterizes the RDP function for a mixture of vector Gaussians. The RDP tradeoff is characterized for finite alphabet sources and for continuous alphabet sources under squared error distortion measure and squared quadratic Wasserstein perception measure. The paper extends Shannon’s lower bound for the RD tradeoff to the RDP setting and partially characterizes the RDP tradeoff for a Gaussian-mixture source and completely characterizes the tradeoff for a vector Gaussian source. The paper also shows that the MMSE representation can be transformed to representations for other operating points on the RDP tradeoff by adding noise at the decoder. The paper concludes with some concluding remarks.