Broadcast channels with cooperation: Capacity and duality for the semi-deterministic case

The semi-deterministic (SD) broadcast channel (BC) where the decoders cooperate via a one-sided link is considered and its capacity region is derived. The direct proof relies on an achievable region for the general BC that is tight for the SD scenario. This achievable region follows by a coding scheme that combines rate-splitting and binning with Marton and superposition coding. The SD-BC is shown to be operationally equivalent to a class of relay-BCs (RBCs) and the correspondence between their capacity regions is established. Furthermore, a dual source coding problem, referred to as the Wyner-Ahlswede-Körner (WAK) problem with one-sided encoder cooperation, is proposed. Transformation principles between the problems are presented and the optimal rate region for the AK problem is stated. The SD-BC capacity and the admissible region of the AK problem are shown to be dual to one another in the sense that the information measures defining the corner points of both regions coincide. Special cases of the two problems are inspected and shown to maintain duality.