Communication through complex media: a novel interdisciplinary paradigm to bridge information theory and multi-scale flow and transport theory - Couch, John (2022)
Molecular communication (MC) is a relatively new type of communication which makes use of particles to transmit information. The movement towards particle transfer is appealing as it broadens the range of what we can communicate through (more) efficiently, such as porous mediums. The applications of MC systems are vast, ranging from medical treatments to industrial problems. In this thesis, we combine fluid mechanics and communication theory with the aim to understand MC in a mathematical framework. This approach is still in its infancy, progressing the idea of combining these two fields, providing a solid mathematical basis which can be used for future research in information transfer. In an effort to step further into work done on the study of transport models, specifically work which took the fluid mechanical perspective of studying transport models, an extension is put forward; introducing ideas from communication theory such as transmission, modulation, reception, and demodulation, to find an optimal way of sending information across a porous medium. We begin here, rethinking what it might mean to have a general modulating function; the idea of allowing for a negative (concentration) signal to transmit information opens up the possibility of using functions which are not used in molecular communication as of yet. This gives rise to the novelty of this report, which is the use of biorthogonal functions. We use a generic transfer function and make use of both the modulating- and demodulating- functions. These functions lead to the idea of using orthogonality conditions to help in the optimization process. The idea of combining transport models with communication theory has the potential to open new avenues of research. We believe this can lead to promising results in the future for molecular communication, and perhaps communication in general.