Compute-and-forward on a line network with random access

Signal superposition and broadcast are important features of the wireless medium. Compute-and-Forward, also known as Physical Layer Network Coding (PLNC), is a technique exploiting these features in order to improve performance of wireless networks. More precisely, it allows wireless terminals to reliably de- code a linear combination of all messages, when a superposition of the messages is received through the physical medium. In this paper, we propose a random PLNC scheme for a local interference line network in which nodes perform random access scheduling. We prove that our PLNC scheme is capacity achieving in the case of one symmetric bi-directional session with terminals on both ends of this line network model. We demonstrate that our scheme significantly outperforms any other scheme. In particular, by eligibly choosing the access rate of the random access scheduling mechanism for the network, the throughput of our PLNC scheme is at least 3.4 and 1.7 times better than traditional routing and plain network coding, respectively.