Enhanced BP decoding schemes of polar codes

Abstract

In this paper, two decoding schemes for polar codes based on the belief propagation (BP) algorithm are proposed. The basic idea of the proposed schemes, called “interleaved BP” (I-BP) and “multiple-candidates BP” (M-BP), is to construct multiple candidates with different reliability values from the received signal and to decode each candidate by a BP decoder. Then, the output of the BP decoder that meets the stopping criterion or the maximum likelihood (ML) rule is chosen as the decoded data. Simulation results show that both the proposed polar decoders outperform the one based only on a single conventional BP decoder. In conjunction with each of the proposed schemes, a feedback structure is also proposed to achieve more performance gain. The proposed feedback structure takes as input the output of each BP decoder, and enhances the a posteriori information of reliable bits and flips unreliable bits. Then, the processed information is fed back into its corresponding decoder. Simulation results show that the performance gain of the proposed schemes with this feedback, compared to the ones without the feedback, may be as large as 1 dB at a frame-error rate 10 − 2 on frequency selective channels and 2 dB at a frame-error rate of 0.07 on doubly selective channels.