Localization-Based Polar Code Construction with Sublinear Complexity

Abstract

In this paper, a localization-based polar construction method is proposed to directly find the set of synthetic channels for information bits given a code configuration. Taking advantage of the partial order of polar codes, only a small number of synthetic channels need to be ordered, which scales as $\mathcal{O} (N/\log_2^{3/2}{N})$, resulting in a sublinear complexity to construct a polar code. Specifically, a practical method is put forward first to fast construct a group-based partial order diagram. A local area in the diagram with adaptive boundaries is then identified. By ordering the synthetic channels within the local area and combining selected ones with all the synthetic channels beyond the local area, the final set of synthetic channels for information bits are determined. Simulation results demonstrate how to adapt the boundary settings to different rate matching schemes and code configurations, and validate the effectiveness of the proposed method compared with the density evolution based methods.