Constellation shaping for bit-interleaved polar coded-modulation

In this paper, an architecture of constellation shaping for bit-interleaved polar coded modulation (BIPCM) is proposed. Theoretically, the probability distribution of constellation points should be selected according to a continuous Gaussian distribution over Additive White Gaussian Noise (AWGN) channels, which will help to obtain shaping gain. Based on this probabilistic shaping idea, unequiprobable constellations are designed to increase the mutual information. Under the proposed BIPCM architecture, the mapping method has a larger diversity of bit channels that can help to improve the system performance. The mapping way is performed based on the prefix code, which can meet the above property. Simulation results of 16-ary pulse amplitude modulation (16-PAM) over AWGN channels show that the nonequiprobable constellations provide 0.5dB shaping gain compared to the traditional equiprobable constellations.