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 P(|N|)EXP(|S|) time that achieve desired rate-vectors, where N is the set of nodes and S ⊆ N is the subset of source nodes in the channel.