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Generalized index modulation (GIM) which implicitly conveys information by the activated indices is a promising technique for next-generation wireless networks. Due to the prohibitive challenge of bit-to-index combination (IC) mapping optimization, conventional GIM system obtains the bit-to-IC mapping table randomly, which may suffer from some performance loss. To circumvent this issue, we propose a low-complexity graph theory assisted bit-to-IC gray coding for GIM systems by minimizing the average hamming distance (HD) between any two ICs having one different value. Specifically, we decompose and transform the optimization problem into two subproblems using the graph theory, i.e., 1) Select an IC set whose corresponding graph has the minimum degree; 2) Design a bit-to-IC mapping principle to minimize the weight of the selected graph. Low-complexity algorithms are developed to solve the …