Bridging tree-packing and network coding: An information flow approach

We present an information flow formulation that bridges network coding and tree packing (routing) and that is useful even if a suboptimal tree packing mechanism is used. We provide a system interpretation of our formulation from a network operators perspective. We study the trade-off between transmission cost and the cost of coding in a multicast session over coded packet networks. Our formulation is also useful to determine the maximal uncoded rate that can be delivered to terminals without incurring additional transmission costs with respect to the optimal network coding solution. We present numerical results illustrating the trade-off between transmission cost and the coding cost, using the fraction of rate delivered uncoded to the terminals as a proxy to the coding cost.