An improved construction algorithm of polar codes based on the frozen bits

Abstract

In order to improve the problems that the minimum hamming weight (MHW) of the polar codes of the traditional Gaussian approximation (GA) construction is small and its performance is not good enough, an improved channel construction algorithm of polar codes based on frozen bits is proposed by combining the construction of the Reed-Muller (RM) code to effectively increase the MHW and analyzing the correcting and checking functions of the frozen bits in the successive cancellation list (SCL) decoding. The construction algorithm selects the channel with the smaller row weight corresponding to the information channel in the channel construction stage, and some channels are set as the frozen channels under the proposed frozen channel setting principle. So the proposed construction algorithm not only eliminates the channels with the smaller row weight and optimizes the distance spectrum of polar codes, but also makes full use of the checking ability of the frozen bit in SCL decoding to improve the error correction performance of polar codes. The polar codes constructed by this algorithm are named as FRM-polar codes. The simulation results show that the proposed FRM-polar codes have a larger performance gain than the RM-polar codes and the polar codes constructed by GA under different code-lengths. In addition, the proposed construction algorithm has the same complexity as the construction algorithm of the RM-polar codes.

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