This project was made to probe various modulation schemes, with the hope of exploring more complicated schemes which scale quickly with respect to the amount of resources present.
A resource in this context is a communications channel, and $\mathcal{O}(n \log (n))$ growth rate is known to exist through Permutation Modulation. This is a faster growth rate than linear - so I attempted to see if a scheme growing as $\mathcal{O}(n^{(1 + \epsilon)})$ is possible through using a graph (the combinatoric structure, that is).
Despite really trying, two terms of work and a 50 page limit was nowhere near enough to fully explore the field. Rather than moping around and being unhappy I didn’t find graph modulation, I’m putting this document here to show the conditions that graph modulation doesn’t exist in.
Hopefully, this will help someone, somehow.
The interested reader is directed to the document here.
If anyone spots anything interesting, please let me know! I’d be really excited to hear any thoughts and would be happy to discuss other thoughts I have (I tried a lot more than what you see in just that document).