Random access in wireless X network: A deterministic view

We study a 2-user symmetric X channel with random access capability for transmitters from a deterministic point of view. Transmitters can work in two modes of operation independent of each other, either active or inactive. There is an independent message from each transmitter to each receiver. It is aimed in this study at maximizing the throughput of this network over the set of rates which can be reliably communicated. To characterize this rate region, an information theoretic outer-bound is derived. Achievability is based on opportunistic signal transmission along with a linear pre-coding scheme. Once the rate region is exactly determined, throughput maximization can be solved as a linear programming problem.