Multidimensional secure multilevel polarization shift keying

Representations of optical fibre communications in three‐ and four‐dimensional spaces

“…This is due to the fact that the transformations defined by (5)- (8) are not linear nor isomorphic, that is they do not preserve the morphological characteristics of the constellation used in the four-dimensional space. It is also easy to verify that the distances between the two symbols are lower in the three-dimensional spaces than those in the four-dimensional space [13].…”

“…Starting from (5)-(8) and (10)- (13) and reversing the signs of the quadratic terms of the parameters with subscript 1, we obtain the other eight representations that we indicate with S3, T3, R3, P3, S4, T4, R4 and P4…”