  In this letter, we propose a progressive rate-filling method as a framework
to study agile construction of multilevel polar-coded modulation. We show that
the bit indices within each component polar code can follow a fixed,
precomputed ranking sequence, e.g., the Polar sequence in the 5G standard,
while their allocated rates (i.e., the number of information bits of each
component polar code) can be fast computed by exploiting the target sum-rate
approximation and proper rate-filling methods. In particular, we develop two
rate-filling strategies based on the capacity and the rate considering the
finite block-length effect. The proposed construction methods can be performed
independently of the actual channel condition with ${O\left(m\right)}$ ($m$
denotes the modulation order) complexity and robust to diverse modulation and
coding schemes in the 5G standard, which is a desired feature for practical
systems.
