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 g2=Pβˆ’1/3g^2=P^{-1/3}, where PP is the symmetric power constraint and gg is the symmetric real cross-channel coefficient. In this paper, we pay attention to the \emph{moderate interference regime} where g2∈(max⁑(0.086,Pβˆ’1/3),1)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 Rsymβˆ—=12log⁑(∣g∣P+∣gβˆ£βˆ’1(P+1))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 0.1040.104 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 0.10.1 bit far from a certain HK achievable scheme with Gaussian signaling and time sharing for g2∈(0,1]g^2\in (0,1]. In particular, Rsymβˆ—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 g2=0.25,0.5g^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

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