On duality relations for the discrete memoryless multiple access and broadcast channel

Duality between multiple-access (MAC) and broadcast channels (BC) is an interesting and useful concept in multi-user information theory. While duality relationships have been established for some Gaussian and deterministic channels, the question to what extent and under which conditions duality holds for the case of discrete memoryless channels still remains open. In this paper, we define the notion of weak duality, closely related to the existing duality definitions. We give a sufficient condition and a necessary condition for a BC to be weakly dual to a discrete MAC of a certain type. Exemplarily, we use these conditions to derive a weak duality relation between the binary symmetric BC and this class of discrete MACs.