Polar coded modulation with optimal constellation labeling

A practical 2^m-ary polar coded modulation (PCM) scheme is proposed. In the proposed scheme, the bit to symbol mapping of the modulation process is regarded as a part of the channel transform. Theoretically, the performance of the PCM scheme will not be affected by the specific constellation labeling strategy. But we find that, when the code length is practical and finite, the performance can be significantly improved by optimizing the labeling rule. To find the optimal labeling rule efficiently, the search space is reduced by exploiting the symmetry properties of the channels. Simulation results of 8-ary pulse amplitude modulation (8-PAM) over Additive White Gaussian Noise (AWGN) channels show that the proposed PCM scheme can outperform the bit-interleaved turbo coded modulation scheme used in the WCDMA (Wideband Code Division Multiple Access) mobile communication systems by up to 1.5dB.