Multi-user two-way deterministic modulo 2 adder channels — When adaptation is useless

In two-way channels nodes are both sources and destinations of messages, allowing them to "adapt" or "interact" in the sense that their next channel input may be a function of their past received signals. This "adaptation" and how to best exploit it lies at the heart of two-way communication problems, rendering them particularly complex and challenging. It would be useful to know when adaptation is not beneficial from a capacity perspective. Certain examples exist: it is known that for the point- to-point two-way modulo 2 adder channel, and the point-to-point Gaussian two-way channel, adaptation does not increase capacity. In this work we show that the same is true for certain classes of deterministic multi-user two-way channels. In particular, we consider a class of multi-user two-way modulo 2 adder channels, which include the two-way modulo 2 adder MAC/BC channel, the two-way modulo 2 adder interference channel, and the two- way modulo 2 adder Z channel. For all three channel models we obtain the capacity region, which may be achieved using simple time-sharing.