Capacity Region of the Finite-State Multiple-Access Channel With and Without Feedback

The capacity region of the finite-state multiple-access channel (FS-MAC) with feedback that may be an arbitrary time-invariant function of the channel output samples is considered. We characterize both an inner and an outer bound for this region, using Massey's directed information. These bounds are shown to coincide, and hence yield the capacity region, of indecomposable FS-MACs without feedback and of stationary and indecomposable FS-MACs with feedback, where the state process is not affected by the inputs. Though “multiletter” in general, our results yield explicit conclusions when applied to specific scenarios of interest. For example, our results allow us to do the following. Identify a large class of FS-MACs, that includes the additive $\bmod \,2$ noise MAC where the noise may have memory, for which feedback does not enlarge the capacity region.