[Withdrawn / Under Revision] Beyond Gray Mapping

Gray mapping has long served as the standard symbol-to-bit assignment in quadrature amplitude modulation (QAM). However, in high-order constellations such as 4096-QAM and non-square cross constellations such as 512-QAM and 2048-QAM, strict adherence to Gray mapping meets structural limits due to geometric boundary constraints and non-uniform log-likelihood ratio (LLR) distributions under forward error correction (FEC). This paper presents a non-Gray constellation mapping optimization framework, referred to as Optimized Permutation Standards (OPS). Simulation evaluations over additive white Gaussian noise (AWGN) channels demonstrate that the optimized mappings achieve bit error rate (BER) reductions of 99.97% for 4096-QAM and 98.44% / 98.50% for 512-QAM / 2048-QAM cross constellations compared to conventional Gray codes. Full lookup tables (LUTs) and simulation verification scripts are published for independent verification.