Partial side information problem: Equivalence of two inner bounds

Consider the two-terminal partial side information problem, where one source is decoded under a distortion measure, while the other acts as a helper. There are two well known inner bounds on the (convex) achievable region: (i) a bound due to Berger et al., and (ii) a suitable specialization of the general Berger-Tung bound. While the former bound admits a simpler description compared to the latter, the latter bound is generally considered more useful because it includes the former. In this backdrop, we show that the above two bounds are in fact equivalent in the sense that their convex hulls coincide. Thus, now one can, without sacrificing generality, make use of the simpler bound in settling the outstanding question of tightness, thereby marking a potential advancement. Further, one can also obtain a new algorithm for numerical simulation of Berger-Tung bound.