  A practical rate-matching system for constructing rate-compatible polar codes
is proposed. The proposed polar code circular buffer rate-matching is suitable
for transmissions on communication channels that support hybrid automatic
repeat request (HARQ) communications, as well as for flexible resource-element
rate-matching on single transmission channels. Our proposed circular buffer
rate matching scheme also incorporates a bit-mapping scheme for transmission on
bit-interleaved coded modulation (BICM) channels using higher order
modulations. An interleaver is derived from a puncturing order obtained with a
low complexity progressive puncturing search algorithm on a base code of short
length, and has the flexibility to achieve any desired rate at the desired code
length, through puncturing or repetition. The rate-matching scheme is implied
by a two-stage polarization, for transmission at any desired code length, code
rate, and modulation order, and is shown to achieve the symmetric capacity of
BICM channels. Numerical results on AWGN and fast fading channels show that the
rate-matched polar codes have a competitive performance when compared to the
spatially-coupled quasi-cyclic LDPC codes or LTE turbo codes, while having
similar rate-dematching storage and computational complexities.
