Low complexity joint optimization of QAM gray mapping and non-binary LDPC Coefficients

This work presents a method to figure out all possible combinations of Gray codes necessary for the joint optimization of a non-binary LDPC code associated with high-order modulation. However, the complexity of this earch increases rapidly with the order of modulation due to the growing number of Gray codes. To overcome his limitation, we show how to reduce without any loss the number of Gray codes, thereby simplifying the complexity of the process. In this paper, we introduce all possible sets of 64-QAM (Quadrature Amplitude Modulation) Gray codes, including the construction method and the mapping approach. Then, we generalize our ork for all orders of QAM, revealing an intractable exhaustive research for QAM that may be tackled with he method we propose to reduce the sets number of Gray codes.