  A framework is proposed that allows for a joint description and optimization
of both binary polar coding and $2^m$-ary digital pulse-amplitude modulation
(PAM) schemes such as multilevel coding (MLC) and bit-interleaved coded
modulation (BICM). The conceptual equivalence of polar coding and multilevel
coding is pointed out in detail. Based on a novel characterization of the
channel polarization phenomenon, rules for the optimal choice of the labeling
in coded modulation schemes employing polar codes are developed. Simulation
results regarding the error performance of the proposed schemes on the AWGN
channel are included.
