Universal Construction for Polar Coded Modulation

Recently, the polarization weight (PW), independent of transmission channel, is proposed to construct the polar codes based on the partial orders (POs) of the polarized bit channels (PBCs). In this paper, we propose a general PW (GPW) to solve the universal construction of the multilevel coding polar-coded modulation (MLC-PCM). In the same way, we first study the POs in the MLC-PCM. For the MLC-PCM, the 2
^m
-ary modulation can be decomposed into m correlated modulated bit channels (MBCs). Then, each MBC group can be further transformed into a series of PBCs by using the conventional channel polarization. Based on this structure of two-stage channel polarization, we find four types of POs. For the PBCs polarized from the same MBCs, we establish two types of POs to indicate the reliability order of some PBCs. Furthermore, for the PBCs polarized from different MBCs, we explore other two types of POs to reveal the relative order of the PBCs. The general PW (GPW), including the influence of the two-stage channel polarization, is defined to construct the polar codes in the MLC-PCM. Finally, the simulation results are given to verify the effectiveness of the proposed GPW in the MLC-PCM.