Upper bounds and duality relations of the linear deterministic sum capacity for cellular systems

The MAC-BC duality of information theory and wireless communications is an intriguing concept for efficient algorithm design. However, no concept is known so far for the important cellular channel. To make progress on this front, we consider in this paper the linear deterministic cellular channel. In particular, we prove duality of a network with two interfering MACs in each cell and a network with two interfering BCs in each cell. The operational region is confined to the weak interference regime. First, achievable schemes as well as upper bounds will be provided. These bounds are the same for both channels. We will show, that for specific cases the upper bound corresponds to the achievable scheme and hence establishing a duality relationship between them.