Network Coding in Node-Constrained Line and Star Networks

Line and star networks with both node and edge constraints are studied in the network coding framework. For line networks, the capacity region of the general multiple multicast problem is established. The coding theorem is based on a binary linear coding scheme, while the converse requires new upper bounds that improve on standard cut-based bounds. For star networks, the multiple unicast problem is examined. Capacity upper bounds are derived and a simple linear coding scheme is proposed which is based on the combinatorial optimization problem of cycle packing in directed graphs. The optimality of this scheme is established for a broad class of demands. The connection of node-constrained network coding in star networks, and index coding with side information is discussed and used to partially characterize the optimal linear code for general rates.