Capacity of a class of multicast tree networks

We consider a class of single-source multicast discrete memoryless tree networks in which the root node is the source, each parent node in the graph has at most one noisy child node and any number of noiseless child nodes, and subsets of leaf nodes are destinations. For this class of multicast tree networks, lower and upper bounds on the capacity are presented and these two bounds are shown to meet when each set of nodes forming a destination is included in a disjoint subtree. Our result generalizes our previous work on the single-destination case, in which a combination of decode-forward (DF) and compress-forward (CF) at noisy relays is shown to be optimal. For generalization to multicast, we develop a robust coding scheme where codebook constructions and relay operations are independent for each node and do not depend on the network topology.