Crystallized Rates Region of the Interference Channel via Correlated Equilibrium with Interference as Noise

TL;DR

This paper introduces a novel approach to characterize the interference channel's rate region using correlated equilibrium and binary power control, simplifying analysis and enabling distributed solution via learning algorithms.

Contribution

It proposes the crystallized rates region concept, utilizing game theory and correlated equilibrium to simplify and optimize interference management in multi-user channels.

Findings

Crystallized rates region formed by 2^n-1 corner points.

Time-sharing convex hull achieves the convexified rates region.

Regret-matching algorithm converges to correlated equilibrium in a distributed manner.

Abstract

Treating the interference as noise in the n-user interference channel, the paper describes a novel approach to the rates region, composed by the time-sharing convex hull of 2^n-1 corner points achieved through On/Off binary power control. The resulting rates region is denoted crystallized rates region. By treating the interference as noise, the n-user rates region frontiers has been found in the literature to be the convex hull of n hyper-surfaces. The rates region bounded by these hyper-surfaces is not necessarily convex, and thereby a convex hull operation is imposed through the strategy of time-sharing. This paper simplifies this rates region in the n-dimensional space by having only an On/Off binary power control. This consequently leads to 2^n-1 corner points situated within the rates region. A time-sharing convex hull is imposed onto those corner points, forming the crystallized rates region. The paper focuses on game theoretic concepts to achieve that crystallized convex hull via correlated equilibrium. In game theory, the correlated equilibrium set is convex, and it consists of the time-sharing mixed strategies of the Nash equilibriums. In addition, the paper considers a mechanism design approach to carefully design a utility function, particularly the Vickrey-Clarke-Groves auction utility, where the solution point is situated on the correlated equilibrium set. Finally, the paper proposes a self learning algorithm, namely the regret-matching algorithm, that converges to the solution point on the correlated equilibrium set in a distributed fashion.