Multi-Cast Channels with Hierarchical Flow

A general network is studied in which messages are relayed from multiple sources to multiple destinations according to a certain hierarchical order. The framework of flow decomposition is used to show the class of regular-order decode-forward index-coding schemes is computable. A shifting algorithm finds encoding/decoding schemes in ${\text{P}}(|\mathcal{N}|){\text{EXP}}(|\mathcal{S}|)$ time that achieve desired rate-vectors, where $\mathcal{N}$ is the set of nodes and $\mathcal{S} \subseteq \mathcal{N}$ is the subset of source nodes in the channel.