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Polar codes were first proposed by E. Arıkan in 2009 and have received significant attention in recent years. Successive-cancellation (SC) and belief-propagation (BP) decoding algorithms have been applied by some researchers to polar codes. However, unlike SC-based decoders, the performance optimization of BP-based decoders has not been fully explored yet, especially in regard to the impact of the number of iterations on the decoding complexity. In this paper, a novel early stopping criterion based on partial frozen bits for belief-propagation polar code decoders is designed. The proposed criterion is based on the fact that some of the frozen bits that are known to the decoders have a higher average error probability than the information bits and can be used to terminate the decoding. Furthermore, the hardware architecture of the BP-based polar code decoder with the proposed stopping criterion is presented. The simulation results show that the proposed early stopping criterion greatly reduces the number of iterations of BP-based polar code decoders without any performance loss and reduces the hardware complexity from <inline-formula> <tex-math notation="LaTeX">$O\left ({NlogN }\right)$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$O\left ({N }\right)$ </tex-math></inline-formula> compared with state-of-the-art design.

Simplified Early Stopping Criterion for Belief-Propagation Polar Code Decoder Based on Frozen Bits