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

TL;DR

This paper derives shape-independent bounds on the coupling strengths and information capacities of optimal communication channels, revealing fundamental limits dictated by domain sizes and configurations rather than shapes.

Contribution

It introduces general bounds on communication channel strengths and capacities that are independent of domain shape, highlighting the importance of size and configuration.

Findings

Coupling strengths decay sub-exponentially, not exponentially as previously observed.

Domain size and configuration are key to maximizing communication channels.

Bounds apply broadly to wireless and optical systems, setting fundamental limits.

Abstract

The concept of optimal communication channels shapes our understanding of wave-based communication. Its analysis, however, always pertains to specific communication-domain geometries, 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 always observed rapid, exponential decay of coupling strengths, but our bounds predict a much 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 general wireless and optical communication systems, our bounds reveal fundamental limits to what is possible through engineering the communication domains of electromagnetic waves.