Edge profile optimal constellation labeling

Structurally distinct constellation labeling exists within both the Gray code and the set-partitioning paradigm. Different labeling choices within either paradigm can provide different bit error rates, especially at low SNR. This paper demonstrates that symmetric ultracomposite (SU) labeling, an extension of the binary reflected Gray code, provides undominated edge profiles for all standard PSK, PAM and square QAM constellations. (The edge profile lists the minimum distance for each binary symbol error) The SU structure can accomodate either the Gray code or the set-partitioning paradigm. It is the clear labeling choice for standard PSK, PAM and square QAM constellations. An extension of SU labeling provides quasi-SU (QSU) labeling for all 2²ⁿ⁺¹-cross constellations for n>1. QSU labeling satisfies the quasi-Gray property for cross constellations. For cross constellations, set-partitioning and QSU labeling structures are distinct. For 32-cross, QSU labeling has a superior edge profile and is preferred when the trellis does not have parallel branches. Despite its inferior profile, set-partitioned 32-cross is still preferred when the trellis has parallel branches