Design and Performance Evaluation of Polar Coding for BICM Systems With Phase Noise

This letter addresses the issue of polar coding design for bit-interleaved coded modulation (BICM) systems over the phase noise channel. Specifically, the existence of phase reference error (PRE) due to the imperfect phase estimation is considered. The generalized mutual information (GMI) for BICM systems with the PRE considered is first analyzed, using the exact statistical information of the received amplitude and phase, which is a foundation for the coding and decoding. Then based on the calculated average GMI per bit layer for a given PRE variance and signal-to-noise ratio (SNR), we can iteratively calculate the reliabilities of the polarized subchannels to construct polar codes. Finally, the superior performance of the phase noise-matched polar design is verified by comparing it with that of the channel-mismatched design, with 8-ary constellations used for simplicity. In addition, the comparison of the decoding performance between successive cancellation (SC) and successive cancellation list (SCL) algorithms is provided. Detailed numerical results on both frame error rate and bit error rate are given with respect to different PRE variances and SNR values. Note that this proposed scheme can be generalized to arbitrary two-dimensional high-order constellations.