论文标题
Han-Kobayashi地区高斯固定点的稳定性用于Z区域通道
Stability of the Gaussian Stationary Point in the Han-Kobayashi Region for Z-Interference Channels
论文作者
论文摘要
Costa，Nair，Ng和Wang最近猜想是全球优化器，在不平等的不平等中，高斯固定点是全球优化的，如果为此，它将暗示Han-Kobayashi区域对高斯Z-Interference渠道的最佳性。对于某些参数制度，已知该猜想是正确的，但是所有参数的有效性虽然由高斯张力提示，但以前是开放的。在本文中，我们构建了几个反例，表明该猜想可能在某些方案中失败：提出了一个没有赫尔米特多项式扰动的简单结构，在分析上，分布远不及高斯的分布比高斯固定点更好。作为替代方案，我们认为在$ l^2 $或Wasserstein-2公制下沿着测量学的扰动，表明高斯固定点在某个制度中是不稳定的。讨论了与征税定理的稳定性相似。稳定相变点可以根据高斯最大化器的最大特征值来简单地表征。与Holley-trocock原则类似，我们可以证明，在稳定的制度中，高斯固定点在$ l^{\ infty} $ - 与高斯措施相对于$ l^{\ infty} $ - 规范下是最佳的。对于具有恒定功率控制的协议，我们的反例表示Han-Kobayashi地区的高斯次优。允许可变的功率控制，我们表明，汉 - 科巴亚西地区的高斯优化器始终位于稳定的制度中。我们提出了一个修改后的猜想，其有效性将暗示汉·科巴亚西（Han-Kobayashi）在某个制度中绑定的高斯最优性。
The Gaussian stationary point in an inequality motivated by the Z-interference channel was recently conjectured by Costa, Nair, Ng, and Wang to be the global optimizer, which, if true, would imply the optimality of the Han-Kobayashi region for the Gaussian Z-interference channel. This conjecture was known to be true for some parameter regimes, but the validity for all parameters, although suggested by Gaussian tensorization, was previously open. In this paper we construct several counterexamples showing that this conjecture may fail in certain regimes: A simple construction without Hermite polynomial perturbation is proposed, where distributions far from Gaussian are analytically shown to be better than the Gaussian stationary point. As alternatives, we consider perturbation along geodesics under either the $L^2$ or Wasserstein-2 metric, showing that the Gaussian stationary point is unstable in a certain regime. Similarity to stability of the Levy-Cramer theorem is discussed. The stability phase transition point admits a simple characterization in terms of the maximum eigenvalue of the Gaussian maximizer. Similar to the Holley-Stroock principle, we can show that in the stable regime the Gaussian stationary point is optimal in a neighborhood under the $L^{\infty}$-norm with respect to the Gaussian measure. For protocols with constant power control, our counterexamples imply Gaussian suboptimality for the Han-Kobayashi region. Allowing variable power control, we show that the Gaussian optimizers for the Han-Kobayashi region always lie in the stable regime. We propose an amended conjecture, whose validity would imply Gaussian optimality of the Han-Kobayashi bound in a certain regime.
