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

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

Practical interference management strategies in Gaussian networks

Increasing demand for bandwidth intensive activities on high-penetration wireless hand-held personal devices, combined with their processing power and advanced radio features, has necessitated a new look at the problems of resource provisioning and distributed management of coexistence in wireless networks. Information theory, as the science of studying the ultimate limits of communication e ciency, plays an important role in outlining guiding principles in the design and analysis of such communication schemes. Network information theory, the branch of information theory that investigates problems of multiuser and distributed nature in information transmission is ideally poised to answer questions about the design and analysis of multiuser communication systems. In the past few years, there have been major advances in network information theory, in particular in the generalized degrees of freedom framework for asymptotic analysis and interference alignment which have led to constant gap to capacity results for Gaussian interference channels. Unfortunately, practical adoption of these results has been slowed by their reliance on unrealistic assumptions like perfect channel state information at the transmitter and intricate constructions based on alignment over transcendental dimensions of real numbers. It is therefore necessary to devise transmission methods and coexistence schemes that fall under the umbrella of existing interference management and cognitive radio toolbox and deliver close to optimal performance. In this thesis we work on the theme of designing and characterizing the performance of conceptually simple transmission schemes that are robust and achieve performance that is close to optimal. In particular, our work is broadly divided into two parts. In the rst part, looking at cognitive radio networks, we seek to relax the assumption of non-causal knowledge of primary user's message at the secondary user's transmitter. We study a cognitive channel model based on Gaussian interference channel that does not assume anything about users other than primary user's priority over secondary user in reaching its desired quality of service. We characterize this quality of service requirement as a minimum rate that the primary user should be able to achieve. Studying the achievable performance of simple encoding and decoding schemes in this scenario, we propose a few di erent simple encoding schemes and explore di erent decoder designs. We show that surprisingly, all these schemes achieve the same rate region. Next, we study the problem of rate maximization faced by the secondary user subject to primary's QoS constraint. We show that this problem is not convex or smooth in general. We then use the symmetry properties of the problem to reduce its solution to a feasibly implementable line search. We also provide numerical results to demonstrate the performance of the scheme. Continuing on the theme of simple yet well-performing schemes for wireless networks, in the second part of the thesis, we direct our attention from two-user cognitive networks to the problem of smart interference management in large wireless networks. Here, we study the problem of interference-aware wireless link scheduling. Link scheduling is the problem of allocating a set of transmission requests into as small a set of time slots as possible such that all transmissions satisfy some condition of feasibility. The feasibility criterion has traditionally been lack of pair of links that interfere too much. This makes the problem amenable to solution using graph theoretical tools. Inspired by the recent results that the simple approach of treating interference as noise achieves maximal Generalized Degrees of Freedom (which is a measure that roughly captures how many equivalent single-user channels are contained in a given multi-user channel) and the generalization that it can attain rates within a constant gap of the capacity for a large class of Gaussian interference networks, we study the problem of scheduling links under a set Signal to Interference plus Noise Ratio (SINR) constraint. We show that for nodes distributed in a metric space and obeying path loss channel model, a re ned framework based on combining geometric and graph theoretic results can be devised to analyze the problem of nding the feasible sets of transmissions for a given level of desired SINR. We use this general framework to give a link scheduling algorithm that is provably within a logarithmic factor of the best possible schedule. Numerical simulations con rm that this approach outperforms other recently proposed SINR-based approaches. Finally, we conclude by identifying open problems and possible directions for extending these results