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

机译：高斯干扰信道的高SNR容量和新的容量边界

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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 b/channel use, especially around g2=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 moderate interference regime where g2∈ (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∗sym=12log(|g|P+|g|−1(P+1)) characterizes the capacity of the symmetric real GIC to within 0.104 b/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 b far from a certain HK achievable scheme with Gaussian signalling and time sharing for g2∈ (0,1] . In particular, R∗sym is achievable at high SNR by the proposed HK scheme and turns out to be the high-SNR capacity at least at g2=0.25,0.5 . We finally point out that there are two subregimes at high SNR in the weak interference regime, where g2∈(0,1] .
机译：众所周知，两用户高斯干扰信道（GIC）的容量区域上的最佳外边界是各种边界（包括精灵辅助的外边界）的区域的交集，其中，精灵会向预期的接收器提供嘈杂的输入信号。 Han and Kobayashi（HK）计划提供了最著名的内边界。总和容量的最著名下限和上限之间的速率差仍然高达1 b /通道使用，尤其是在g2 = P-1 / 3左右，其中P是对称功率约束，g是对称实数交叉。通道系数。在本文中，我们注意其中g2∈（max（0.086，P−1 / 3），1）的中等干扰机制。我们提出了一种新的上限技术，该技术利用对干扰信号的噪声观测作为精灵信号，并在接收器处将时间共享应用于精灵信号。还引入了最差加性噪声引理的条件版本来推导新的容量边界。在中等干扰范围的特定范围内，总容量（容量区域）上的结果上限（外部）显示为比现有范围更严格。使用新的上限和HK下限，我们显示R * sym = 12log（| g | P + | g | -1（P + 1））将对称真实GIC的容量表征为每通道使用0.104 b在任何信噪比（SNR）下处于中等干扰状态时，我们进一步建立了对称实数GIC的高SNR表征，其中所提出的上限距离具有g2∈（0,1]的具有高斯信号和时间共享的某个HK可实现方案的最大距离为0.1 b。 ∗ sym可以通过提出的HK方案在高SNR下实现，结果证明至少在g2 = 0.25,0.5时是高SNR容量，我们最后指出在弱干扰情况下，在高SNR下有两个子区域，其中g2∈（0,1]

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