On the Design of Polar Codes for Spiral Constellations with Low-latency Shaping

In this paper, we propose a low-latency probabilistically shaped multilevel polar coded modulation (PS-MLPCM) scheme for 6G called parallel PS-MLPCM. The proposed scheme achieves parallel encoding by disregarding the relationship between different bit levels when profiling shaping bits, while the conventional PS-MLPCM scheme has to perform encoding level by level. Additionally, we have found a suitable mapping scheme for the spiral constellations to ensure that the spiral constellations based parallel PS-MLPCM scheme can approach the capacity of additive white Gaussian noise (AWGN) channels. We perform numerical simulation for 64-Spiral and 64-QAM based schemes under both successive cancellation (SC) decoder and cyclic redundancy check aided SC-list (CA-SCL) decoder. The results show that the 64-Spiral based scheme achieves more than 0.8dB shaping gain at high signal-to-noise ratio (SNR). Meanwhile, the 64-Spiral based scheme can outperform the 64- QAM based scheme, especially when SNR is high or CA-SCL decoder is used.