Optimal Labeling with Cyclic Gray Codes for Generalized 16PAM Constellations

The mutual information achieved by a pulse-amplitude modulated constellation depends strongly on the symbol labels. In general, these symbols are labeled based on a Gray code mapping, in which neighboring label bit-strings differ by only one bit value. For a 16-symbol constellation, there are numerous such Gray code mappings satisfying this property, each with distinct mutual information performance over SNR. In this paper, we present an investigation of the optimal labeling using cyclic Gray codes for symmetric 16-symbol one-dimensional constellations with uniform symbol probability and non-uniform spacing. These results can be extended to 256-symbol quadrature amplitude modulated constellations with in-phase/quadrature symmetry.