Abstract
We propose two algorithms: one is for building and the other for labeling triangular QAM (TQAM) constellations. A root distribution algorithm (also referred as RD) is used to construct TQAM constellations of low average energy. The proposed labeling algorithm, termed the layer labeling algorithm, results in bit-to-symbol mappings that minimize the average Hamming distance between constellation points. The strength of the algorithms lies in their applicability to large constellations, while currently known solutions rely on a manual design of good TQAM constellations. This letter describes the very details of the algorithms and compares the performance, in terms of $BER(E_{b}/N_{0})$ , of the proposed solution with the one that can be found in the literature.
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