Capacity of All Nine Models of Channel Output Feedback for the Two-user Interference Channel

TL;DR

This paper analyzes the capacity regions of nine different feedback architectures in two-user interference channels, providing exact and approximate capacity results for deterministic and Gaussian models, respectively.

Contribution

It derives the exact capacity regions for symmetric deterministic channels and approximate regions for Gaussian channels across all nine feedback architectures.

Findings

In weak interference, all feedback models except one share the same capacity region.

Sum-capacity is identical across all feedback models in the weak interference regime.

In strong interference, feedback models with at least one receiver feeding back to its own transmitter share the same sum-capacity.

Abstract

In this paper, we study the impact of different channel output feedback architectures on the capacity of the two-user interference channel. For a two-user interference channel, a feedback link can exist between receivers and transmitters in 9 canonical architectures (see Fig. 2), ranging from only one feedback link to four feedback links. We derive the exact capacity region for the symmetric deterministic interference channel and the constant-gap capacity region for the symmetric Gaussian interference channel for all of the 9 architectures. We show that for a linear deterministic symmetric interference channel, in the weak interference regime, all models of feedback, except the one, which has only one of the receivers feeding back to its own transmitter, have the identical capacity region. When only one of the receivers feeds back to its own transmitter, the capacity region is a strict subset of the capacity region of the rest of the feedback models in the weak interference regime. However, the sum-capacity of all feedback models is identical in the weak interference regime. Moreover, in the strong interference regime all models of feedback with at least one of the receivers feeding back to its own transmitter have the identical sum-capacity. For the Gaussian interference channel, the results of the linear deterministic model follow, where capacity is replaced with approximate capacity.