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

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.

Approximate Capacity Region for the Symmetric Gaussian Interference Channel With Noisy Feedback

“…In the case α ≥ 1, the bounds on active in characterizing the capacity region of the symmetric LD IC with noisy feedback. Therefore, the sum capacity in [26,Theorem 1], together with the bounds on the individual rates (22)(23)(24)(25), can lead to the same result as that in Theorem 1. It can be shown that the outer bound in (12f) in [21] is the same as our outer bound in (27) for the symmetric linear deterministic IC with noisy feedback.…”

“…Nevertheless, there is an alternative way to prove this outer bound. In the regime where α < 1, this outer bound is inactive due to the outer bound in (22); in the strong and very strong interference regimes, i.e. α ≥ 1, this outer bound follows from an interesting observation.…”

“…Thus, any outer bound that is applicable to the full feedback model, is also applicable to the noisy feedback model. Thus, for the proof of outer bounds for (22), (23) and (26), please refer to [5]. The outer bound for (24) is a simple cut-set bound [30], that follows from the outer bound…”

Approximate Capacity Region of the Two-User Gaussian Interference Channel With Noisy Channel-Output Feedback

“…Inner and outer bounds on the sum-capacity using the existing connections between channel-output feedback and conferencing transmitters have been presented in [31]. More general channel models, for instance when channel-outputs are fed back to both receivers, have been studied in [7], [32]- [34].…”

When Does Output Feedback Enlarge the Capacity of the Interference Channel?

“…Second, the case in which such observation is noisy corresponds to noisy channel-output feedback (NOF) [16], [17]. Third, the case in which such observation is a linear combination of the channel-outputs from both receivers subject to additive noise corresponds to wireless channeloutput feedback (WOF) [18]. The most general formulation is referred to as general channel-output feedback (GOF) [19]- [22].…”