Improved Decoder by Partially Permuted Factor Graphs of Polar Codes
Hongji Cui, Kai Niu, Junwei Ren · 2022
We study the structure of the factor graph of polar codes, and propose some improved decoding algorithms for polar codes based on the equivalence of partially permuted factor graphs (PPFG). Different from the previously proposed permuted factor graphs, PPFG proposed in this paper divides the polar code into shorter codewords, each sub-code is permuted into a different factor graph, and finally combined into an equivalent PPFG. We first prove the equivalence of PPFG. Then an algorithm for searching optimal factor graphs is proposed. Finally, we propose a series of algorithms based on PPFG such as optimal PPFG SC/BP, SC parallel list (SCPL) and parallelly permuted SC list (PPSCL). Simulation results show that under the same complexity and delay, the performance of the optimal PPFG SC has a O.25dB gain compared with the original SC decoding algorithm at the code length$N=64$. Algorithms such as SCPL have similar performance to SCL, but SCPL does not require sorting and path expansion.