Polar Code Construction for Gaussian Channels Based on Approximated Error Evolution

To achieve good performance of polar codes, certain information bits with the highest bit error probabilities (BEPs) should be fixed at a binary value and are referred to as frozen bits. The assignment of these frozen bits is called code construction. Although the exact BEPs of the information bits can be obtained by density evolution, it requires prohibitive computational complexity for calculating and storing the densities. To reduce such complexity, this paper proposes a method to approximate these BEPs when Gaussian channels are assumed. Specifically, since every density is associated with a BEP at the corresponding stage of density evolution, the output BEPs can be approximated using the input ones without computing the densities, which results in a drastic reduction of complexity. To demonstrate the effectiveness of the proposed method, computer simulations of orthogonal frequency division multiplexing (OFDM) transmission over both binary input additive white Gaussian noise (BIAWGN) and frequency selective fading channels are conducted. The results show that in both cases, the polar codes constructed using the proposed method can achieve near-optimal block error rate (BLER) while significantly reducing execution time and memory usage.