A semi-continuous version of the Berger-Yeung problem

We present a continuous dual of multiterminal source encoding with one distortion criterion (the “Berger-Yeung (1989) problem”). A continuous source X is encoded with “high resolution” (D_x→0), with the aid of a “helper,” i.e., a correlated discrete or continuous source Y, that is encoded separately subject to some arbitrary distortion criterion D_y. We find the asymptotic form of the set of achievable coding rates R(D_x, D_y) of the X- and Y-encoders as D_x→0. Two extreme cases of our result provide high-resolution interpretations to the classical work of Wyner (1975, 1978), Ahlswede (1975), Korner (1975), and Ziv (1976) on source coding with side information