A unified bit-to-symbol mapping for generalized constellation modulation

Gray mapping is a well-known way to improve the performance of regular constellation modulation, but it is challenging to be applied directly for irregular alternative. To address this issue, in this paper, a unified bit-to-symbol mapping method is designed for generalized constellation modulation (i.e., regular and irregular shaping). The objective of the proposed approach is to minimize the average bit error probability by reducing the hamming distance (HD) of symbols with larger values of pairwise error probability. Simulation results show that the conventional constellation modulation(i.e., phase shift keying and quadrature amplitude modulation (QAM) with the proposed mapping rule yield the same performance as that of classical gray mapping. Moreover, the recently developed golden angle modulation (GAM) with the proposed mapping method is capable of providing around 1 dB gain over the conventional mapping counterpart and offers comparable performance to QAM with Gray mapping.