Capacity of Two-Way Channels with Symmetry Properties

In this paper, we make use of channel symmetry properties to determine the capacity region of three types of two-way networks: (a) two-user memoryless two-way channels (TWCs), (b) two-user TWCs with memory, and (c) three-user multiaccess/degraded broadcast (MA/DB) TWCs. For each network, symmetry conditions under which Shannon's random coding inner bound is tight are given. For two-user memoryless TWCs, prior results are substantially generalized by viewing a TWC as two interacting state-dependent one-way channels. The capacity of symmetric TWCs with memory, whose outputs are functions of the inputs and independent stationary and ergodic noise processes, is also obtained. Moreover, various channel symmetry properties under which Shannon's inner bound is tight are identified for three-user MA/DB TWCs. The results not only enlarge the class of symmetric TWCs whose capacity region can be exactly determined but also imply that adaptive coding, not improving capacity, is unnecessary for such channels.