Multicast packing for coding across multiple unicasts

We consider the problem of inter-session network coding for multiple unicast flows over directed acyclic graphs. Our approach consists of the following steps: (i) The unicast flows are partitioned into multiple disjoint subsets of unicast flows; (ii) each subset of unicast flows is mapped to a multicast flow, and linear network codes are constructed for these multicast flows. These linear network codes collectively serve as a linear network code for the original multiple unicast flows, which we refer to as multicast-packing code (MPC). We formulate a linear program to evaluate the performance of MPC for a given partition of the unicast flows. We also propose a practical algorithm, using simulated annealing, for finding such a partition. Using simulations, we demonstrate the benefits of the multicast packing code in terms of achievable common rate and cost, as well as the efficiency of the partitioning algorithm in terms of running time.