A Multi-Hop Framework For Multi-Source Multi-Relay All-Cast Channels

The decode-forward region is characterized for general multi-source, multi-relay, all-cast channels. This region depends on the sequences of nodes that forward each message, the encoding delays in each sequence, and the messages decoded at each node. The assumption of causality creates necessary conditions on the encoding delays since nodes cannot forward messages they have not decoded. Flow decompositions are introduced to describe these dependencies. Every rate vector in the decode-forward region corresponds to a set of flow decompositions. The conditions derived from causality impose some structure on otherwise arbitrary sets of flow decompositions. Given this structure, there exists an equivalent set of flow decompositions that recovers the same region in a causal manner.