A joint routing and coding approach to linear network coding

Adopting a cross-layer approach, in this paper we propose an algorithm for joint routing and network coding. The proposed algorithm jointly assigns routes and designs linear network codes over finite fields to achieve the capacity of the network. The algorithm has a dynamic programming approach where a cost function is used to assign weights to all edges in the network. The cheapest flow is chosen subject to certain encoding constraints in order to achieve the network capacity with network coding while minimizing the network complexity. The effectiveness of the algorithm is demonstrated through carefully chosen examples. We show that the constraints imposed by the joint routing and coding algorithm are necessary for successful decoding at the sinks, and their violation can lead to a failure in achieving the network capacity or an increase in the number of encoding nodes.