Design of Low-Complexity Coded Modulation Employing High-Order QAM With Systematic Geometric Constellation Shaping

In this work, we investigate the performance of geometric constellation shaping for highorder coded quadrature amplitude modulation (QAM) over an additive white Gaussian noise (AWGN) channel. We focus on a systematic design where a single parameter uniquely determines the entire constellation points according to the truncated Gaussian distribution, and the parameter is optimized based on the resulting mutual information. Our main objective is to combine the proposed systematic geometric shaping with practical coded modulation so as to achieve high bandwidth efficiency with low design/decoding complexity. To this end, we investigate the use of multilevel coding (MLC) under multistage decoding (MSD) as well as bit-interleaved coded modulation (BICM), along with pulse amplitude modulation (PAM) consisting of as much as 128 signal points, i.e., leading to 16 384-ary QAM in the two-dimensional case. Our comparative studies employing the off-the-shelf binary punctured turbo codes show that, as we target higher spectral efficiency, MLC with MSD is more attractive than BICM in view of both bit error rate (BER) performance and decoding complexity. In addition, we introduce new closed-form bounds related to constellation constrained capacity, based on which one can quickly assess the capacity behavior of given discrete PAM constellations.