Multi-level Coding and Multi-stage Decoding for Modulations with Hexagonal Constellation

M-ary Modulation and convolutional encoder are commonly employed in modern wireless systems; the modulation has rectangular constellation and square decision regions, and the encoder is binary based. However, we have demonstrated previously that modulations with hexagonal decision regions are more energy efficient transmission. And we have introduced a system which is compatible with binary data. It provides improved energy efficiency and spectrum utilization and minimizes probability of error, as well as the peak-to-average-power ratio for OFDM systems. Also, we introduce a ternary convolutional encoder. Associated with the mentioned modulation, it outperforms some of the existing conventional schemes, and its computational complexity is comparable to that of a binary decoder with a similar number of states. In this paper, we combine multi-level coding to the hexagonal modulation to provide a system which is capacity-approaching. This concept may be use the ternary convolutional encoder introduced previously related to the constellation used. Here, we work with three different hexagonal constellations which are the 6QAM-H, 8QAM-H, and 12QAM-H, and we design a multilevel coding based on two or three levels. This approach is shown to provide improved probability of error and may be interesting for the further investigations about the multilevel unequal error protection with multistage decoding.