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On the Capacity of the $K$-User Cyclic Gaussian Interference Channel

机译：$ K $用户循环高斯干扰信道的容量

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摘要

This paper studies the capacity region of a $K$-user cyclic Gaussian interference channel, where the $k{rm th}$ user interferes with only the $(k-1){rm th}$ user (mod $K$ ) in the network. Inspired by the work of Etkin, Tse, and Wang, who derived a capacity region outer bound for the two-user Gaussian interference channel and proved that a simple Han–Kobayashi power-splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters, this paper shows that a similar strategy also achieves the capacity region of the $K$-user cyclic interference channel to within a constant gap in the weak interference regime. Specifically, for the $K$-user cyclic Gaussian interference channel, a compact representation of the Han–Kobayashi achievable rate region using Fourier–Motzkin elimination is first derived; a capacity region outer bound is then established. It is shown that the Etkin–Tse–Wang power-splitting strategy gives a constant gap of at most 2 bits in the weak interference regime. For the special three-user case, this gap can be sharpened to $1 {{1}over {2}}$ bits by time-sharing of several different strategies. The capacity result of the $K$-user cyclic Gaussian interference channel in the strong interference regime is also given. Further, based on the capacity results, this paper studies the generalized degrees of freedom (GDoF) of the symmetric cyclic interference chan- el. It is shown that the GDoF of the symmetric capacity is the same as that of the classic two-user interference channel, no matter how many users are in the network.
机译：本文研究了$ K $用户循环高斯干扰信道的容量区域，其中$ k {rm th} $用户仅干扰$（k-1）{rm th} $用户（mod $ K $）在网络中。受埃特金（Etkin），谢（Tse）和王（Wang）的启发，他们推导出了两个用户高斯干扰信道的容量区域外边界，并证明了简单的Han-Kobayashi功率分流方案可以将容量扩展到一个容量信道参数的所有值，本文表明，在弱干扰状态下，类似的策略也可以将$ K $用户循环干扰信道的容量区域保持在恒定间隙内。具体来说，对于$ K $用户的循环高斯干扰信道，首先推导了使用傅里叶-莫兹金消除技术得出的Han-Kobayashi可达到的速率区域的紧凑表示。然后建立容量区域外边界。结果表明，在弱干扰状态下，Etkin-Tse-Wang功率分流策略最多可提供2位的恒定间隙。对于特殊的三用户情况，可以通过分时使用几种不同的策略，将此差距扩大到$ 1 {{1} over {2}} $位。还给出了$ K $用户循环高斯干扰信道在强干扰状态下的容量结果。此外，基于容量结果，本文研究了对称循环干扰信道的广义自由度（GDoF）。结果表明，无论网络中有多少个用户，对称容量的GDoF都与经典的两用户干扰信道的GDoF相同。

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