Revisiting the rate-distortion theory using smooth max Rényi divergence

This paper clarifies the rate-distortion function for general sources in terms of the smooth max Rényi divergence. To this end, we investigate the fixed-length coding problem with two kinds of distortion criteria. One criterion is the maximum distortion criterion, and the other is the average distortion criterion. We show a new achievability result for the latter criterion and new meta-converse theorems for both criteria, and clarify the rate-distortion functions in terms of the smooth Rényi divergence instead of the spectral mutual information.