  A new polar coding scheme for higher order modulation is presented. The
proposed scheme is based on multi-level coding (MLC) with natural labeling,
where the bit-level corresponding to the sign-bit is generated in dependence on
the previous bit-levels, such that the modulated symbols are distributed
according to a target non-uniform distribution resulting in a shaping gain.
This is realized by replacing the polar encoder in the sign-bit level by a
successive cancellation (SC) decoder, such that the overall complexity is not
increased compared to a conventional MLC scheme with polar codes. Numerical
simulations show significant performance improvements of the proposed approach
compared to conventional transmission schemes with uniform symbol distribution.
By using more complex decoders (e.g. SC list decoder), the proposed scheme
outperforms Gallager's random coding bound.
