Polar Coding with Enhanced Channel Polarization under Frequency Selective Fading Channels

Abstract

Polar coding proposed by Arikan attracts attention as a channel coding scheme with low complexity and high error correction capability. In polar codes, the probability that each output bit of a polar decoder is incorrectly decoded differs depending on the positions of the output bits. This is due to the effect of the channel polarization. In polar coding, enhancing the effect of the channel polarization is important, especially when the codeword length is not long enough. In this paper, we propose a polar coding scheme for orthogonal frequency division multiplexing (OFDM) systems under frequency selective fading channels. In our polar coding scheme, the codeword bits are permuted so that the bits stemmed from the frozen bits are allocated to subcarriers causing frequent bit errors. We can regard this permutation as a kind of interleaving that enhances the channel polarization. As a result, the polarization is carried out twice; one is due to polar coding, and the other is due to interleaving based on the channel state. Since the effect of the channel polarization is enhanced, the improvement in bit error rate (BER) performance can be expected. Through computer simulation, we show that the system using the polar code with our interleaving scheme outperforms the system using the polar code with random interleaving.