A unified order-theoretic view of the capacity region of the Kuser DM-MAC with general message sets

The multiple access channel with private messages has a single accepted capacity characterization. By contrast, when the same channel is considered with message sources that may be commonly known to multiple transmitters, a plurality of distinct capacity descriptions arises. Two descriptions currently exist in the literature, with the capacity region attained with superposition coding in one description, and without superposition in the other. To unify these descriptions, we highlight the successive nature of superposition coding and recast its analysis and description into the language of order theory. Consequently, we obtain a wide class of capacity descriptions by intermingling coding with, and without, superposition.