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When bode meets shannon: control-oriented feedback communication schemes

机译:当博德遇到香农时:面向控制的反馈通信方案

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摘要

In this paper, we show a general equivalence between feedback stabilization through an analog communication channel, and a communication scheme based on feedback which is a generalization of that of Schalkwijk and Kailath. We also show that the achievable transmission rate of the scheme is given by the Bode's sensitivity integral formula, which characterizes a fundamental limitation of causal feedback. Therefore, we can now use the many results and design tools from control theory to design feedback communication schemes providing desired communication rates, and to generate lower bounds on the channel feedback capacity. We consider single user Gaussian channels with memory and memory-less multiuser broadcast, multiple access, and interference channels. In all cases, the results we obtain either achieve the feedback capacity, when this is known, recover known best rates, or provide new best achievable rates.
机译:在本文中,我们展示了通过模拟通信通道的反馈稳定与基于反馈的通信方案之间的一般等效性,该方案是Schalkwijk和Kailath的概括。我们还表明,该方案可实现的传输速率由Bode的灵敏度积分公式给出,该公式表征了因果反馈的基本局限性。因此,我们现在可以使用控制理论中的许多结果和设计工具来设计提供所需通信速率的反馈通信方案,并在信道反馈容量上产生下限。我们考虑具有内存和无内存多用户广播,多路访问和干扰信道的单用户高斯信道。在所有情况下,我们获得的结果要么达到已知的反馈能力,要么恢复已知的最佳速率,要么提供新的最佳可实现速率。

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