Recursive polar code construction for higher-order modulation

In wireless communications, bit-interleaved coded modulation (BICM) with Gray labeling is commonly utilized for the transmission with higher-order modulation. In case of polar codes, BICM performance can be further improved if the coded bits are grouped according to their reliability levels and the interleaving is performed independently at each level. This improvement is achieved due to the faster polarization.In this paper, we propose an efficient divide-and-conquer method to construct polar codes for BICM with quadrature amplitude modulation (QAM). At the first step we decompose the polar design for QAM into several polar code designs for quadrature phase shift keying (QPSK). Next, given the number of information bits to be assigned, we recursively compute their allocations to the polarized subchannels until some predefined length is reached. This allows to utilize the reliability sequences optimized for additive white Gaussian noise (AWGN) channel with QPSK modulation such as 5G New Radio (NR) universal reliability sequence, and enables a low-complexity approach to construct polar codes for several modulation orders. Hence we can take an advantage of the existing designs while providing the performance boost by utilizing the QAM structure in the unified manner.