Low Complexity Construction of Polar Codes with BP Decoder over Medium to High SNR Region
Hui Wang, S. Gan · 2023
In this paper, we focus on the low-complexity construction method of polar codes with belief propagation (BP) decoder over additive white Gaussian noise (AWGN) channels. Firstly, the zero-noise BP decoding analysis method is proposed to determine the reliability of each bit channel via recursively calculating log-likelihood ratios (LLRs) of nodes from right to left in the factor graph. The final LLR can comprehensively reflect the structural characteristics of each bit channel. Then, the zero-noise LLR criterion based construction is introduced to select the frozen bit indices. Specifically, the lower the LLR value, the higher the priority of the corresponding bit selected as the frozen bit. Due to the assumed noise-free environment, the proposed zero-noise LLR criterion based construction is channel-independent. Finally, the simulation results show that, the zero-noise LLR criterion based construction can sort out the critical bit channels to load the frozen bits. When compared with other construction methods for BP decoder, such as the LLR-based bit-swapping construction and the simulation-based bit-swapping construction, the proposed zero-noise LLR criterion based construction not only has the best error correction ability over medium to high signal-to-noise ratio (SNR) region, but also exhibits the lowest construction complexity.