Random Network Coding over Composite Fields

Random network coding is a method that achieves multicast capacity asymptotically for general networks [1, 7]. In this approach, vertices in the network randomly and linearly combine incoming information in a distributed manner before forwarding it through their outgoing edges. To ensure success, the involved finite field needs to be large enough [2, 7], which can be an obstacle if some inner (intermediate) nodes have less computational power than others. In this work, we analyze what can be achieved if different nodes are allowed to use different finite fields from a selection of fields all contained in some composite extension finite field [3, 5].