  The inherent nature of polar codes being channel specific makes it difficult
to use them in a setting where the communication channel changes with time. In
particular, to be able to use polar codes in a wireless scenario, varying
attenuation due to fading needs to be mitigated. To the best of our knowledge,
there has been no comprehensive work in this direction thus far. In this work,
a practical scheme involving channel inversion with the knowledge of the
channel state at the transmitter, is proposed. An additional practical
constraint on the permissible average and peak power is imposed, which in turn
makes the channel equivalent to an additive white Gaussian noise (AWGN) channel
cascaded with an erasure channel. It is shown that the constructed polar code
could be made to achieve the symmetric capacity of this channel. Further, a
means to compute the optimal design rate of the polar code for a given power
constraint is also discussed.
