Interference Alignment: From Degrees of Freedom to Constant-Gap Capacity Approximations

• Published in: IEEE transactions on information theory Vol. 59; no. 8; pp. 4855 - 4888
• Main Authors: Niesen, Urs, Maddah-Ali, Mohammad Ali
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-08-2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Approximation methods; Band gap; Capacity approximation; Channel models; Communication channels; Detection, estimation, filtering, equalization, prediction; deterministic model; Electric noise; Exact sciences and technology; Information theory; Information, signal and communications theory; interference alignment; Interference channels; network information theory; Noise; Normal distribution; Receivers; Signal and communications theory; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; X-channel; Parameter estimation; Channel capacity; Gaussian channel; X-channel; Time invariance; network information theory; Capacity approximation; interference alignment; Channel estimation; Deterministic model; Selection criterion; Optimal planning; Deterministic approach; Signal to noise ratio; Information theory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2013.2259140

Interference alignment is a key technique for communication scenarios with multiple interfering links. In several such scenarios, interference alignment was used to characterize the degrees of freedom of the channel. However, these degree-of-freedom capacity approximations are often too weak to make accurate predictions about the behavior of channel capacity at finite signal-to-noise ratios (SNRs). The aim of this paper is to significantly strengthen these results by showing that interference alignment can be used to characterize capacity to within a constant gap. We focus on real, time-invariant, frequency-flat X-channels. The only known solutions achieving the degrees of freedom of this channel are either based on real interference alignment or on layer-selection schemes. Neither of these solutions seems sufficient for a constant-gap capacity approximation. In this paper, we propose a new communication scheme and show that it achieves the capacity of the Gaussian X-channel to within a constant gap. To aid in this process, we develop a novel deterministic channel model. This deterministic model depends on the 1/2 log (SNR) most-significant bits of the channel coefficients rather than only the single most-significant bit used in conventional deterministic models. The proposed deterministic model admits a wider range of achievable schemes that can be translated to the Gaussian channel. For this deterministic model, we find an approximately optimal communication scheme. We then translate this scheme for the deterministic channel to the original Gaussian X-channel and show that it achieves capacity to within a constant gap. This is the first constant-gap result for a general, fully-connected network requiring interference alignment.