Conjectures on the Size of Constellations Constructed from Direct Sums of PSK Kernels

摘要

A general equation is given for the size of complex constellations constructed from the direct sum of PSK-like constellation primitives. The equation uses a generating function whose numerator is a power of a 'coordination polynomial'. Conjectures are also given as to the form and value of these coordination polynomials for various PSK. The study has relevance to error-coding, polynomial residue number theory, and the analysis of random walks.