Abstract-The interference channel achievable rate region is presented when the interference is treated as noise. The formulation starts with the 2−user channel, and then extends the results to the n−user case. The rate region is found to be the convex hull of the union of n power control rate regions, where each power control rate region is upperbounded by a (n − 1)-dimensional hyper-surface characterized by having one of the transmitters transmitting at full power. The convex hull operation lends itself to a time-sharing operation depending on the convexity behavior of those hyper-surfaces. In order to know when to use time-sharing rather than power control, the paper studies the hyper-surfaces convexity behavior in details for the 2−user channel with specific results pertaining to the symmetric channel. It is observed that most of the achievable rate region can be covered by using simple On/Off binary power control in conjunction with time-sharing. The binary power control creates several corner points in the n−dimensional space. The crystallized rate region, named after its resulting crystal shape, is hence presented as the time-sharing convex hull imposed onto those corner points; thereby offering a viable new perspective of looking at the achievable rate region of the interference channel.

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 hypersurfaces 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 regretmatching algorithm, that converges to the solution point on the correlated equilibrium set in a distributed fashion.

Treating the interference as noise, the paper studies the first derivative of the frontiers which trace the achievable rates region of the 2−user interference channel. The achievable rates region in this case was found to be the convex hull of the union of two regions, each is bounded by a log-defined line. Those log-defined lines are characterized by holding one of the transmitters at full power, while the other transmitter sweeps its full power range [1]. Maximizing the sum rates for the 2−user interference channel translates to the study of the first intersection point with lines of slope −1 approaching the rates region from positive infinity. The paper achieves the same result reported in [2], that the maximum sum rates solution is one of three points: one user transmitting with full power while the other user is silent, or both users transmitting at full power simultaneously. The result in [2] is achieved through analysis of the objective function, while the solution presented herein follows from analyzing the first derivative of the rates region frontiers. I. INTRODUCTION The capacity region of a 2−user communication channel has been an open problem for about 30 years [3], [4]. Informationtheoretic bounds through achievable rates region have been proposed, most famously with the Han-Kobayashi bounds [5].The capacity of the Gaussian interference channel under strong interference has been found in [6]. Recent results about the 2−user interference channel to within one bit of capacity have been shown in [7]. This paper is interested in the context when the receiver treats the interference as additive thermal noise and does not employ multiuser detection. Such scenario is encountered in cellular communications, ad hoc and sensor networks, where low-complexity transceivers are preferred.Treating the interference as noise, the achievable rates region for the general n−user interference channel was found in [1] to be the convex hull of the union of n regions; where each region is outer-bounded by a hyper-surface frontier of dimension n−1. Each hyper-surface is characterized by having one of the transmitters transmitting at full power, and the other users sweeping their full range of transmit powers. For the case of 2−user interference channel, the achievable rates region is translated as the union of two regions R 1 and R 2 . Each region R i is outer-bounded by a log-defined line Φ i , which is characterized by having P i = P max and P j =i sweeps its full power range from 0 to P max . Explicitly, the achievable rates region for the 2−user interference channel is:

Multihop relaying in cellular networks is seen as a viable strategy to address the need for higher data rates and better coverage. In this paper, we analyze the system-level performance of multicellular multihop networks in the presence of co-channel interference, and build upon prior work in [1]-[2], which considered multihop relaying in a single-cell setting.Considering an opportunistic hop-count routing algorithm, we study cellular sum capacity under different multiuser scheduling algorithms such as MaxCap, proportional fair, and round robin. We numerically investigate the competing interaction between multihop diversity and multiuser diversity, and discuss the areal diversity aspect as a byproduct of multihop relaying. Finally, we provide further practical design insights on cellular planning through our empirical results on interference statistics in multicellular multihop networks.

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