Symbol-Based Belief Propagation Decoder for Multilevel Polar Coded Modulation

In this letter, symbol-based belief propagation decoder is proposed for multilevel polar coded modulation (MLPCM) scheme. Unlike the traditional multi-stage detection (MSD) strategy by decoding polar codes level by level after demapping, we directly calculate the probabilities of symbols and do demapping after the symbol decoding process so as to decrease the decoding delay and improve the performance of MLPCM. The lower bound of frame error rate for MLPCM is also estimated using the union bound technique. Numerical results show that the performance of proposed decoder well matches the estimated bound for pulse amplitude modulation (PAM) modulation and outperforms the MSD strategy about 0.5−1 dB with lower decoding delay, only at the cost of some additional computational complexity, which indicates its effectiveness.