On the design of binary polar codes for high-order modulation

In this work, we study the design of polar codes for high-order constellations. We propose a new methodology for selecting polar codes rates in multilevel coding scenarios in order to optimize the overall error performance. We also propose a novel method for the design of polar codes based on the second order statistics of the bit error performance of the equivalent bit channels. This new code design is applied to the proposed multilevel coding scheme as well as to the standard quadrature amplitude modulation (QAM) constellations. We establish the effectiveness of the proposed algorithms through several practical examples.