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 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

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

Degrees of Freedom of Uplink-Downlink Multiantenna Cellular Networks

An uplink-downlink two-cell cellular network is studied in which the first base station (BS) with $M_1$ antennas receives independent messages from its $N_1$ serving users, while the second BS with $M_2$ antennas transmits independent messages to its $N_2$ serving users. That is, the first and second cells operate as uplink and downlink, respectively. Each user is assumed to have a single antenna. Under this uplink-downlink setting, the sum degrees of freedom (DoF) is completely characterized as the minimum of $(N_1N_2+\min(M_1,N_1)(N_1-N_2)^++\min(M_2,N_2)(N_2-N_1)^+)/\max(N_1,N_2)$, $M_1+N_2,M_2+N_1$, $\max(M_1,M_2)$, and $\max(N_1,N_2)$, where $a^+$ denotes $\max(0,a)$. The result demonstrates that, for a broad class of network configurations, operating one of the two cells as uplink and the other cell as downlink can strictly improve the sum DoF compared to the conventional uplink or downlink operation, in which both cells operate as either uplink or downlink. The DoF gain from such uplink-downlink operation is further shown to be achievable for heterogeneous cellular networks having hotspots and with delayed channel state information.Comment: 22 pages, 11 figures, in revision for IEEE Transactions on Information Theor