  The rate-distortion-perception function (RDPF; Blau and Michaeli, 2019) has
emerged as a useful tool for thinking about realism and distortion of
reconstructions in lossy compression. Unlike the rate-distortion function,
however, it is unknown whether encoders and decoders exist that achieve the
rate suggested by the RDPF. Building on results by Li and El Gamal (2018), we
show that the RDPF can indeed be achieved using stochastic, variable-length
codes. For this class of codes, we also prove that the RDPF lower-bounds the
achievable rate
