On the capacity of multi-user two-way linear deterministic channels

In multi-user two-way channels nodes are both sources and destinations of messages. This allows for “adaptation” at or “interaction” between the nodes - the next channel inputs may be a function of the past received signals at a particular node. How to best adapt is key to two-way communication problems, rendering them complex and challenging. However, examples exist of channels where adaptation is not beneficial from a capacity perspective; it is known that for the point-to-point two-way modulo 2 adder and Gaussian channels, adaptation does not increase capacity. Recently, it was shown that the two-way modulo-2 additive versions of the multiple-access / broadcast (MAC/BC respectively, in the two directions), the Z channel and the interference channel also have capacity regions equal to two parallel one-way versions of the channels. In this work we show that the same is true for the linear deterministic multi-user two-way channels which approximate their Gaussian counterparts at high SNR, which include the two-way MAC/BC channel, the two-way Z channel, and the two-way interference channel under some adaptation constraints. For all three channel models we obtain the capacity region, which is that of two one-way channels in each direction, which may be achieved without the use of adaptation.