MIMO高斯信道下公共随机性生成的最优信号处理及其在识别中的应用
Optimal Signal Processing for Common Randomness Generation over MIMO Gaussian Channels with Applications in Identification
AI总结：
本文研究在Gaussian信道上单向通信生成公共随机性的问题，推导了SISO和MIMO Gaussian信道的CR容量，并探讨了其在提升信道识别容量及CR辅助安全识别方案中的应用。
摘要：
公共随机性（Common Randomness, CR）作为一种资源，在现有的实际通信系统中尚未得到普遍利用。在CR生成框架中，发送方和接收方均旨在生成一个双方均可观察的公共随机变量，理想情况下具有低错误概率。这种CR的可用性使得我们能够实现相关随机协议，从而带来更快、更高效的算法。先前的工作主要集中在容量受限的完美信道上的CR生成。在我们的工作中，我们考虑了在Gaussian信道上通过单向通信，从相关有限源的独立同分布（i.i.d.）样本生成CR的问题。我们首先推导了单输入单输出（SISO）Gaussian信道的CR容量。该结果随后被用于推导多输入多输出（MIMO）情况下的CR容量。CR在识别方案中扮演着关键角色，因为它可能允许信道识别容量的显著增加。在识别框架中，解码器感兴趣的是知道对他具有特殊兴趣的特定消息是否已被发送，而不是知道接收到的消息是什么。在许多新应用中，例如若干机器对机器和人对机器系统以及触觉互联网，这种后香农方案比经典传输更高效。在我们的工作中，我们还考虑了CR辅助的安全识别方案，并开发了相应安全识别容量的下界。
英文摘要：
Common randomness (CR), as a resource, is not commonly exploited in existing practical communication systems. In the CR generation framework, both the sender and receiver aim to generate a common random variable observable to both, ideally with low error probability. The availability of this CR allows us to implement correlated random protocols that can lead to faster and more efficient algorithms. Previous work focused on CR generation over perfect channels with limited capacity. In our work, we consider the problem of CR generation from independent and identically distributed (i.i.d.) samples of a correlated finite source with one-way communication over a Gaussian channel. We first derive the CR capacity for single-input single-output (SISO) Gaussian channels. This result is then used for the derivation of the CR capacity in the multiple-input multiple-output (MIMO) case. CR plays a key role in the identification scheme since it may allow a significant increase in the identification capacity of channels. In the identification framework, the decoder is interested in knowing \emph{whether} a specific message of special interest to him has been sent or not, rather than knowing \emph{what} the received message is. In many new applications, such as several machine-to-machine and human-to-machine systems and the tactile internet, this post-Shannon scheme is more efficient than classical transmission. In our work, we also consider a CR-assisted secure identification scheme and develop a lower bound on the corresponding secure identification capacity.
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