Perfect Output Feedback in the Two-User Decentralized Interference Channel

TL;DR

This paper characterizes the approximate $ ext{η}$-Nash equilibrium region of the two-user Gaussian interference channel with perfect feedback, showing it is larger than without feedback and close to the capacity outer bound.

Contribution

It provides the first approximation of the $ ext{η}$-NE region with feedback within 1 bit/s/Hz, highlighting feedback's role in enlarging stable rate pairs.

Findings

Feedback enlarges the $ ext{η}$-NE region.

For each rate without feedback, a weakly Pareto superior rate with feedback exists.

An $ ext{η}$-NE configuration can achieve rates within 1 bit/s/Hz of the capacity outer bound.

Abstract

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user Gaussian interference channel (IC) with perfect output feedback is approximated to within $1$ bit/s/Hz and $\eta$ arbitrarily close to $1$ bit/s/Hz. The relevance of the $\eta$-NE region is that it provides the set of rate-pairs that are achievable and stable in the IC when both transmitter-receiver pairs autonomously tune their own transmit-receive configurations seeking an $\eta$-optimal individual transmission rate. Therefore, any rate tuple outside the $\eta$-NE region is not stable as there always exists one link able to increase by at least $\eta$ bits/s/Hz its own transmission rate by updating its own transmit-receive configuration. The main insights that arise from this work are: $(i)$ The $\eta$-NE region achieved with feedback is larger than or equal to the $\eta$-NE region without feedback. More importantly, for each rate pair achievable at an $\eta$-NE without feedback, there exists at least one rate pair achievable at an $\eta$-NE with feedback that is weakly Pareto superior. $(ii)$ There always exists an $\eta$-NE transmit-receive configuration that achieves a rate pair that is at most $1$ bit/s/Hz per user away from the outer bound of the capacity region.