On the Corner Points of the Capacity Region of a Two-User Gaussian Interference Channel

This work considers the corner points of the capacity region of a two-user Gaussian interference channel (GIC). In a two-user GIC, the rate pairs where one user transmits its data at the single-user capacity (without interference), and the other at the largest rate for which reliable communication is still possible are called corner points. This paper relies on existing outer bounds on the capacity region of a two-user GIC that are used to derive informative bounds on the corner points of the capacity region. The new bounds refer to a weak two-user GIC (i.e., when both cross-link gains in standard form are positive and below 1), and a refinement of these bounds is obtained for the case where the transmission rate of one user is within $\varepsilon > 0$ of the single-user capacity. The bounds on the corner points are asymptotically tight as the transmitted powers tend to infinity, and they are also useful for the case of moderate SNR and INR. Upper and lower bounds on the gap (denoted by $\Delta$) between the sum-rate and the maximal achievable total rate at the two corner points are derived. This is followed by an asymptotic analysis analogous to the study of the generalized degrees of freedom (where the SNR and INR scalings are coupled such that $\frac{\log(\text{INR})}{\log(\text{SNR})} = \alpha \geq 0$), leading to an asymptotic characterization of this gap which is exact for the whole range of $\alpha$. The upper and lower bounds on $\Delta$ are asymptotically tight in the sense that they achieve the exact asymptotic characterization. Improved bounds on $\Delta$ are derived for finite SNR and INR, and their improved tightness is exemplified numerically.Comment: Submitted to the IEEE Trans. on Information Theory in July 17, 2014, and revised in April 5, 2015. Presented in part at Allerton 2013, and also presented in part with improved results at ISIT 201

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

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.Comment: submitted to IEEE Transactions on Information Theory, results improved by deriving capacity region of all 9 canonical feedback models in two-user interference channe

At Every Corner: Determining Corner Points of Two-User Gaussian Interference Channels

The corner points of the capacity region of the two-user Gaussian interference channel under strong or weak interference are determined using the notions of almost Gaussian random vectors, almost lossless addition of random vectors, and almost linearly dependent random vectors. In particular, the "missing" corner point problem is solved in a manner that differs from previous works in that it avoids the use of integration over a continuum of SNR values or of Monge-Kantorovitch transportation problems

On the Capacity Region of the Two-user Interference Channel with a Cognitive Relay

This paper considers a variation of the classical two-user interference channel where the communication of two interfering source-destination pairs is aided by an additional node that has a priori knowledge of the messages to be transmitted, which is referred to as the it cognitive relay. For this Interference Channel with a Cognitive Relay (ICCR) In particular, for the class of injective semi-deterministic ICCRs, a sum-rate upper bound is derived for the general memoryless ICCR and further tightened for the Linear Deterministic Approximation (LDA) of the Gaussian noise channel at high SNR, which disregards the noise and focuses on the interaction among the users' signals. The capacity region of the symmetric LDA is completely characterized except for the regime of moderately weak interference and weak links from the CR to the destinations. The insights gained from the analysis of the LDA are then translated back to the symmetric Gaussian noise channel (GICCR). For the symmetric GICCR, an approximate characterization (to within a constant gap) of the capacity region is provided for a parameter regime where capacity was previously unknown. The approximately optimal scheme suggests that message cognition at a relay is beneficial for interference management as it enables simultaneous over the air neutralization of the interference at both destinations

Achievable and Crystallized Rate Regions of the Interference Channel with Interference as Noise

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.Comment: 28 pages, 12 figures, to appear in IEEE Transactions of Wireless Communicatio

Gaussian Multiple Access via Compute-and-Forward

Lattice codes used under the Compute-and-Forward paradigm suggest an alternative strategy for the standard Gaussian multiple-access channel (MAC): The receiver successively decodes integer linear combinations of the messages until it can invert and recover all messages. In this paper, a multiple-access technique called CFMA (Compute-Forward Multiple Access) is proposed and analyzed. For the two-user MAC, it is shown that without time-sharing, the entire capacity region can be attained using CFMA with a single-user decoder as soon as the signal-to-noise ratios are above $1+\sqrt{2}$. A partial analysis is given for more than two users. Lastly the strategy is extended to the so-called dirty MAC where two interfering signals are known non-causally to the two transmitters in a distributed fashion. Our scheme extends the previously known results and gives new achievable rate regions.Comment: to appear in IEEE Transactions on Information Theor