Equivalence of inner regions for broadcast channel coding

The aim of this paper is to investigate relationship between inner regions for broadcast channel codes transmitting common and private messages. One of the regions is known as the Marton inner region, another region was derived by Gel´fand and Pinsker, and yet another is obtained from the saturation property and collision-resistance property. Although at first glance the Marton inner region appears to be larger than the other regions, they are in fact equivalent.