Mapping Selection and Code Construction for 2 is a subset of -ary Polar-Coded Modulation

This paper proposes a mapping strategy and a code construction method for 2 is a subset of -ary polar-coded modulation. In order to find a good mapping for a polar code in an efficient way, we reduce a search space for mapping patterns by exploiting the properties of its polarizing matrix. Once a mapping is selected, the set of unfrozen information bits to define a polar code is automatically determined. Numerical results show that our approach can provide a performance gain of about 0.3\,-\,0.5 dB over a conventional approach using random mapping and the polar code optimized for binary phase-shift keying (BPSK) modulation, when pulse-amplitude modulation (PAM) with Gray labelling is employed.