Minimizing Transmission Cost for Third-Party Information Exchange with Network Coding

In wireless networks, getting the global knowledge of channel state information (CSI, e.g., channel gain or link loss probability) is always beneficial for the nodes to optimize the network design. However, the node usually only has the local CSI between itself and other nodes, and lacks the CSI between any pair of other nodes. To enable all the nodes to get the global CSI, in this paper, we propose a network-coded third-party information exchange scheme, with an emphasis on minimizing the total transmission cost for ( ) exchanging the CSI among the nodes. We show that for a network of N nodes, if and only if any k nodes (1 ≤ k <; N) send at least (2 : k) packets, a feasible solution exists for third-party information exchange. Formulating the problem of feasible and optimal solutions as an integer linear programming (ILP) problem, we compute the optimal number of packets that must be transmitted by every node. Guided by the necessary and sufficient condition, we construct two practical transmission schemes: fair load (FL) scheme and proportional load (PL) scheme. A deterministic encoding strategy based on XORs coding over GF(2) is further designed to guarantee that with FL or PL scheme, each node finally can decode the complete packets. It is shown that in two specific networks, these two schemes are optimal, achieving the minimum transmission cost. In more general networks, simulation results show that PL is still close to optimal with a high probability. Finally, a distributed transmission protocol is developed, which allows FL and PL schemes to be operated in a distributed and hence scalable manner.