Capacity of Two-Way Channels with Symmetry Properties

TL;DR

This paper uses symmetry properties to exactly determine the capacity regions of various two-way channels, showing that under certain conditions, simple coding strategies are sufficient and adaptive coding offers no capacity advantage.

Contribution

It generalizes prior results by identifying symmetry conditions that make the Shannon-type inner bound tight for multiple two-way channel types, including those with memory.

Findings

Capacity regions are exactly determined for symmetric two-user TWCs.

Symmetry conditions under which adaptive coding does not improve capacity are identified.

The results extend to channels with memory and multiuser configurations.

Abstract

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 a Shannon-type random coding inner bound (under independent non-adaptive inputs) 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 the Shannon-type 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 interactive adaptive coding, not improving capacity, is unnecessary for such channels.