a low complexity PC design based on shift registers [@PC_hua] in conjunction with a classical CRC, as proposed in [@PC_CRC], to improve the code design flexibility.

The insertion of an interleaver between the CRC encoder and the polar encoder may have a positive impact on the performance of the code due to the induced change in the number of minimum weight codewords [@conc_polar_cyc]. The interleaver is used to turn the CRC into a distributed CRC, in that a CRC remainder bit is assigned to a bit-channel as soon as all the information bits involved in its parity check have been assigned as well. This feature is used in 5G polar codes to reduce the decoding complexity by early terminating the decoding if an incorrect check is met, providing an additional false alarm rate (FAR) mitigation mechanism [@dist_CRC_aid].

Polar coded modulation
----------------------

If low-order modulation schemes like quadrature phase shift keying (QPSK) are used, the bit-channels polarization is not affected since all modulated symbols have uniform reliability. When larger constellations are used, as envisaged by 5G standard, polar-coded modulation (PCM) [@PCM] can be used to fully exploit the polarization effect at higher-order modulation [@eff_PCM]. However, canonical PCM requires an additional polarization 