Construction and Labeling of Triangular QAM

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.