On the High-SNR Capacity of the Gaussian Interference Channel and New Capacity Bounds

The best outer bound on the capacity region of the two-user Gaussian Interference Channel (GIC) is known to be the intersection of regions of various bounds including genie-aided outer bounds, in which a genie provides noisy input signals to the intended receiver. The Han and Kobayashi (HK) scheme provides the best known inner bound. The rate difference between the best known lower and upper bounds on the sum capacity remains as large as 1 bit per channel use especially around $g^2=P^{-1/3}$, where $P$ is the symmetric power constraint and $g$ is the symmetric real cross-channel coefficient. In this paper, we pay attention to the \emph{moderate interference regime} where $g^2\in (\max(0.086, P^{-1/3}),1)$. We propose a new upper-bounding technique that utilizes noisy observation of interfering signals as genie signals and applies time sharing to the genie signals at the receivers. A conditional version of the worst additive noise lemma is also introduced to derive new capacity bounds. The resulting upper (outer) bounds on the sum capacity (capacity region) are shown to be tighter than the existing bounds in a certain range of the moderate interference regime. Using the new upper bounds and the HK lower bound, we show that $R_\text{sym}^*=\frac{1}{2}\log \big(|g|P+|g|^{-1}(P+1)\big)$ characterizes the capacity of the symmetric real GIC to within $0.104$ bit per channel use in the moderate interference regime at any signal-to-noise ratio (SNR). We further establish a high-SNR characterization of the symmetric real GIC, where the proposed upper bound is at most $0.1$ bit far from a certain HK achievable scheme with Gaussian signaling and time sharing for $g^2\in (0,1]$. In particular, $R_\text{sym}^*$ is achievable at high SNR by the proposed HK scheme and turns out to be the high-SNR capacity at least at $g^2=0.25, 0.5$.Comment: Submitted to IEEE Transactions on Information Theory on June 2015, revised on November 2016, and accepted for publication on Feb. 28, 201

Capacity Bounds for the KK-User Gaussian Interference Channel

The capacity region of the $K$-user Gaussian interference channel (GIC) is a long-standing open problem and even capacity outer bounds are little known in general. A significant progress on degrees-of-freedom (DoF) analysis, a first-order capacity approximation, for the $K$-user GIC has provided new important insights into the problem of interest in the high signal-to-noise ratio (SNR) limit. However, such capacity approximation has been observed to have some limitations in predicting the capacity at \emph{finite} SNR. In this work, we develop a new upper-bounding technique that utilizes a new type of genie signal and applies \emph{time sharing} to genie signals at $K$ receivers. Based on this technique, we derive new upper bounds on the sum capacity of the three-user GIC with constant, complex channel coefficients and then generalize to the $K$-user case to better understand sum-rate behavior at finite SNR. We also provide closed-form expressions of our upper bounds on the capacity of the $K$-user symmetric GIC easily computable for \emph{any} $K$. From the perspectives of our results, some sum-rate behavior at finite SNR is in line with the insights given by the known DoF results, while some others are not. In particular, the well-known $K/2$ DoF achievable for almost all constant real channel coefficients turns out to be not embodied as a substantial performance gain over a certain range of the cross-channel coefficient in the $K$-user symmetric real case especially for \emph{large} $K$. We further investigate the impact of phase offset between the direct-channel coefficient and the cross-channel coefficients on the sum-rate upper bound for the three-user \emph{complex} GIC. As a consequence, we aim to provide new findings that could not be predicted by the prior works on DoF of GICs.Comment: Presented in part at ISIT 2015, submitted to IEEE Transactions on Information Theory on July 2015, and revised on January 201

The Approximate Capacity of the Many-to-One and One-to-Many Gaussian Interference Channels

Recently, Etkin, Tse, and Wang found the capacity region of the two-user Gaussian interference channel to within one bit/s/Hz. A natural goal is to apply this approach to the Gaussian interference channel with an arbitrary number of users. We make progress towards this goal by finding the capacity region of the many-to-one and one-to-many Gaussian interference channels to within a constant number of bits. The result makes use of a deterministic model to provide insight into the Gaussian channel. The deterministic model makes explicit the dimension of signal scale. A central theme emerges: the use of lattice codes for alignment of interfering signals on the signal scale.Comment: 45 pages, 16 figures. Submitted to IEEE Transactions on Information Theor

Capacity Bounds for a Class of Interference Relay Channels

The capacity of a class of Interference Relay Channels (IRC) -the Injective Semideterministic IRC where the relay can only observe one of the sources- is investigated. We first derive a novel outer bound and two inner bounds which are based on a careful use of each of the available cooperative strategies together with the adequate interference decoding technique. The outer bound extends Telatar and Tse's work while the inner bounds contain several known results in the literature as special cases. Our main result is the characterization of the capacity region of the Gaussian class of IRCs studied within a fixed number of bits per dimension -constant gap. The proof relies on the use of the different cooperative strategies in specific SNR regimes due to the complexity of the schemes. As a matter of fact, this issue reveals the complex nature of the Gaussian IRC where the combination of a single coding scheme for the Gaussian relay and interference channel may not lead to a good coding scheme for this problem, even when the focus is only on capacity to within a constant gap over all possible fading statistics.Comment: 23 pages, 6 figures. Submitted to IEEE Transactions on Information Theory (revised version

Real Interference Alignment: Exploiting the Potential of Single Antenna Systems

In this paper, the available spatial Degrees-Of-Freedoms (DOF) in single antenna systems is exploited. A new coding scheme is proposed in which several data streams having fractional multiplexing gains are sent by transmitters and interfering streams are aligned at receivers. Viewed as a field over rational numbers, a received signal has infinite fractional DOFs, allowing simultaneous interference alignment of any finite number of signals at any finite number of receivers. The coding scheme is backed up by a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on non-degenerate manifolds. The proposed coding scheme is proved to be optimal for three communication channels, namely the Gaussian Interference Channel (GIC), the uplink channel in cellular systems, and the $X$ channel. It is proved that the total DOF of the $K$-user GIC is $\frac{K}{2}$ almost surely, i.e. each user enjoys half of its maximum DOF. Having $K$ cells and $M$ users within each cell in a cellular system, the total DOF of the uplink channel is proved to be $\frac{KM}{M+1}$. Finally, the total DOF of the $X$ channel with $K$ transmitters and $M$ receivers is shown to be $\frac{KM}{K+M-1}$.Comment: Submitted to IEEE Transaction on Information Theory. The first version was uploaded on arxiv on 17 Aug 2009 with the following title: Forming Pseudo-MIMO by Embedding Infinite Rational Dimensions Along a Single Real Line: Removing Barriers in Achieving the DOFs of Single Antenna System

The Ergodic Capacity of Phase-Fading Interference Networks

We identify the role of equal strength interference links as bottlenecks on the ergodic sum capacity of a $K$ user phase-fading interference network, i.e., an interference network where the fading process is restricted primarily to independent and uniform phase variations while the channel magnitudes are held fixed across time. It is shown that even though there are $K(K-1)$ cross-links, only about $K/2$ disjoint and equal strength interference links suffice to determine the capacity of the network regardless of the strengths of the rest of the cross channels. This scenario is called a \emph{minimal bottleneck state}. It is shown that ergodic interference alignment is capacity optimal for a network in a minimal bottleneck state. The results are applied to large networks. It is shown that large networks are close to bottleneck states with a high probability, so that ergodic interference alignment is close to optimal for large networks. Limitations of the notion of bottleneck states are also highlighted for channels where both the phase and the magnitudes vary with time. It is shown through an example that for these channels, joint coding across different bottleneck states makes it possible to circumvent the capacity bottlenecks.Comment: 19 page