According to some embodiments, a method in a wireless device comprises obtaining a set of information bits for wireless transmission and dividing the set of information bits into one or more subsets of information bits. For each subset, generating extra cyclic redundancy check (CRC) bits using a CRC polynomial capable of generating N CRC bits. The extra CRC bits for each subset comprise less than N CRC bits. The method further comprises: generating a final set of N or less CRC bits for the set of information bits using the CRC polynomial; generating a set of coded bits by encoding the set of information bits for wireless transmission, together with the extra CRC bits and the final set of CRC bits, using a polar encoder; and transmitting the set of coded bits using a wireless transmitter.