A Novel Probabilistic Shaping Scheme for 16QAM Modulated Polar Codes

A new scheme is proposed for polar codes combined with 16 Quadrature Amplitude Modulation (QAM) modulation to obtain the Probabilistic Shaping (PS) gain. In this paper, a low-complexity Constellation Compression Modulation (CCM) system of polar codes is constructed and the corresponding expansion factor equation is derived by combining the characteristics of the proposed system. In the CCM-12QAM-QPSK scheme, label bits are used to solve the many-to-one (MTO) mapping problem in the CCM, and assist with the demodulation. The polarization channels and the MTO mapping relationship are used to design the corresponding interleaver. Due to the different occurrence probabilities of label bits constellation points, a CCM-12QAM-QPSK-N scheme based on the novel diamond Quadrature Phase Shift Keying (QPSK) constellation diagram is proposed to further obtain the shaping gain. Simulation shows that when the expansion factor is 1.2 and the Bit Error Rate (BER) is 1 × 10⁻⁴ under the additive white Gaussian noise (AWGN) channels, the proposed scheme can obtain about 0.6 and 0.7 dB gain respectively in the superiority of the 16QAM scheme in the same code and information bits length; in addition, the CCM-12QAM-QPSK scheme is close to the performance of 16QAM scheme while getting more information bits, it means the receiver can know more useful information. The CCM-12QAM-QPSK-N scheme further gains at least 0.2 dB while receiving more information bits.