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, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sub</i>-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 nontrivial 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.