Encoder and list decoder of Reed-Solomon kernel based polar codes

In this paper, we propose the encoding and list decoding method of polar codes based on the four-dimensional Reed-Solomon (RS-4) kernel. In specific, an encoding table based method is employed to reduce the computational complexity of both encoder and decoder. In addition, a simplified method to update log-likelihood ratios (LLRs) which employs additions instead of exponential calculations is also proposed to further increase the decoding speed. In addition, we present a method to construct RS-4 polar codes using genie-aided simulations, where the symbol channel capacity is determined by the number of decoding errors. Through simulations, we show the decoding performance of the RS-4 polar codes and compare it with the binary polar codes.