Traditional channel capacity based on one-dimensional time domain mismatches the four-dimensional electromagnetic fields, thus it cannot fully exploit the information in the spatial dimensions. Therefore, electromagnetic information theory based on the four-dimensional electromagnetic fields becomes necessary to reveal the fundamental theoretical capacity bound of the communication systems. Existing works on electromagnetic information theory focused on deterministic signals and degrees of freedom, which were unable to derive the capacity due to the lack of entropy definition. In this paper, we first model the communication between two continuous regions by random field. Then, we analyze a special case with parallel linear source and destination to derive the capacity bound. Specifically, for parallel infinite-length source and destination, we analyze the mutual information by spatial spectral density and derive the best current distribution on the source to achieve the maximum mutual information, i.e., the capacity. Then, we analyze the scenario with infinite-length source and finite-length destination. We use Mercer expansion to derive the mutual information between the source and the destination. Finally, for a practical model with finite-length source and destination, we analyze its Mercer expansion and reveal its connection with the infinite-length case. The capacity we analyzed reveals the theoretical limit of the communication rate between two continuous regions.
翻译:以一维时间域为基础的传统频道能力使四维电磁场不匹配,因此无法充分利用空间维度的信息。因此,基于四维电磁场的电磁信息理论对于揭示通信系统的基本理论约束是有必要的。现有的电磁信息理论工作侧重于确定信号和自由度,由于缺乏恒定定义,这些信号和自由度无法产生能力。在本文中,我们首先通过随机字段来模拟两个连续区域之间的通信。然后,我们分析一个具有平行线性源和目的地的特例,以获得能力约束。具体地说,对于平行的无限源和目的地,我们通过空间光谱密度分析相互信息,并从源上获取最佳的当前分布,以取得最大限度的相互信息,即能力。然后,我们用长源和长的目的地来分析情景。我们利用Mercer的扩展来获取源和目的地之间的相互信息。最后,我们分析一个具有定量源和目的地的实用模型,我们分析其Mercer扩展和显示其与无限案例的联系。我们分析了两个连续通信率的理论极限。