The capacity region of two-way collision networks

The collision channel without feedback is a system with multiple source nodes and a single destination node, where coordination among the source nodes and feedback from the destination node are not available. Its capacity region was first derived by Massey and Mathys. We generalize their model by introducing multiple destination nodes and relay nodes. In this paper, we consider linear collision networks in which the nodes lie on a straight line. The two nodes at the ends want to exchange data through the relay nodes in the middle. An outer bound on achievable rates is derived. By using a simple network code, we can show that all points within the outer bound are indeed achievable, and thus obtain the capacity region.