Bounds on the Coupling Strengths of Communication Channels and their Information Capacities

The concept of optimal communication channels shapes our understanding of wave-based communication. Its analysis typically focuses on specific communication-domain geometries, however, without a general theory of scaling laws or fundamental limits. In this article, we derive shape-independent bounds on the coupling strengths and information capacities of optimal communication channels for any two domains that can be separated by a spherical surface. Previous computational experiments have observed rapid, exponential decay of coupling strengths, but our bounds predict a slower, sub-exponential optimal decay, and specific source/receiver distributions that can achieve such performance. Our bounds show that domain sizes and configurations, and not domain shapes, are the keys to maximizing the number of non-trivial communication channels and total information capacities. Applicable to linear time-invariant (LTI) wireless and optical communication systems, our bounds reveal fundamental limits to what is possible through engineering the communication domains of electromagnetic waves.