  A design of rate-compatible polar codes suitable for HARQ communications is
proposed in this paper. An important feature of the proposed design is that the
puncturing order is chosen with low complexity on a base code of short length,
which is then further polarized to the desired length. A practical
rate-matching system that has the flexibility to choose any desired rate
through puncturing or repetition while preserving the polarization is
suggested. The proposed rate-matching system is combined with channel
interleaving and a bit-mapping procedure that preserves the polarization of the
rate-compatible polar code family over bit-interleaved coded modulation
systems. Simulation results on AWGN and fast fading channels with different
modulation orders show the robustness of the proposed rate-compatible polar
code in both Chase combining and incremental redundancy HARQ communications.
