Performance of low-density parity-check codes with 16-ary MR-CMD-PSK modulations

In this paper, we present the results of our investigation concerning the performance of low-density parity-check (LDPC) codes associated with high spectral efficiency 16-ary multi-ring constant-modulus-difference phase-shift keying (MR-CMD-PSK) modulations on a complex additive white Gaussian noise (AWGN) channel. 16-ary MR-CMD-PSK modulations consist of 4R-CMD-QPSK, 2R-CMD-8PSK and 16PSK, and we propose one method of determining the reliability for each bit in these three modulations. The performance curves of hard-decision and soft-decision decoding algorithms for different modulation modes are offered, and the uncoded modulation performance curves for different modulations are also given for the purpose of comparison incidentally.