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The best outer bound on the capacity region of the two-user GaussianInterference Channel (GIC) is known to be the intersection of regions ofvarious bounds including genie-aided outer bounds, in which a genie providesnoisy input signals to the intended receiver. The Han and Kobayashi (HK) schemeprovides the best known inner bound. The rate difference between the best knownlower and upper bounds on the sum capacity remains as large as 1 bit perchannel use especially around $g^2=P^{-1/3}$, where $P$ is the symmetric powerconstraint and $g$ is the symmetric real cross-channel coefficient. In thispaper, 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 techniquethat utilizes noisy observation of interfering signals as genie signals andapplies time sharing to the genie signals at the receivers. A conditionalversion of the worst additive noise lemma is also introduced to derive newcapacity bounds. The resulting upper (outer) bounds on the sum capacity(capacity region) are shown to be tighter than the existing bounds in a certainrange of the moderate interference regime. Using the new upper bounds and theHK 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 realGIC to within $0.104$ bit per channel use in the moderate interference regimeat any signal-to-noise ratio (SNR). We further establish a high-SNRcharacterization of the symmetric real GIC, where the proposed upper bound isat most $0.1$ bit far from a certain HK achievable scheme with Gaussiansignaling 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 thehigh-SNR capacity at least at $g^2=0.25, 0.5$.

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