Methods and apparatuses for relaxed polar coding, including cyclic redundancy check (CRC) aided encoding and belief propagation (BP) decoding for relaxed polar codes in wireless communications, are provided. For example, a method comprises determining: 1) a first set of encoding nodes used for creating CRC bits, 2) a first set of polarization branches, each associated with a respective encoding node of the first set of encoding nodes, and 3) a second set of polarization branches, each of the second set of polarization branches is at least one level higher than a respective polarization branch of the first set of polarization branches. The method also comprises performing polar encoding operation(s) for the second set of polarization branches including relaxation, generating a second set of encoding nodes based on the performed polar encoding operation(s) for the second set of polarization branches, and transmitting polar code bits using the generated second set of encoding nodes.