Polynomial Time and Provably Efficient Network Coding Scheme for Lossy Wireless Networks

The network coding problem across multiple unicasts is an open problem. Previously, the capacity region of 2-hop relay networks with multiple unicast sessions and limited feedback was characterized where the coding and decoding nodes are neighbors and packet erasure channels are used. A near-optimal coding scheme that exploits the broadcast nature and the diversity of the wireless links was proposed. However, the complexity of the scheme is hyper exponential as it requires the knowledge of the packets that are received by any subset of the receivers. In this paper, we provide a polynomial time coding scheme and characterize its performance using linear equations. The coding scheme uses random network coding to carefully mix intra and intersession network coding and makes a linear, not exponential, number of decisions. We also provide a linear programming formulation that uses our 2-hop relay network results as a building block in large lossy multihop networks. Through simulations, we verify the superiority of our proposed schemes over state-of-the art.