Towards Empirical Sandwich Bounds on the Rate-Distortion Function

Rate-distortion (R-D) function, a key quantity in information theory,
characterizes the fundamental limit of how much a data source can be compressed
subject to a fidelity criterion, by any compression algorithm. As researchers
push for ever-improving compression performance, establishing the R-D function
of a given data source is not only of scientific interest, but also sheds light
on the possible room for improving compression algorithms. Previous work on
this problem relied on distributional assumptions on the data source (Gibson,
2017) or only applied to discrete data. By contrast, this paper makes the first
attempt at an algorithm for sandwiching the R-D function of a general (not
necessarily discrete) source requiring only i.i.d. data samples. We estimate
R-D sandwich bounds on Gaussian and high-dimension banana-shaped sources, as
well as GAN-generated images. Our R-D upper bound on natural images indicates
room for improving the performance of state-of-the-art image compression
methods by 1 dB in PSNR at various bitrates.