A construction method of arbitrary-length polar codes

To remove the restriction on code length of polar codes, this paper proposes a construction scheme, called stepwise polar codes, which can generate arbitrary-length polar codes. The stepwise polar codes are generated by sub-polar codes with different code lengths. To improve coding performance, sub-polar codes are united by polarization effect priority algorithm, which can reduce the number of incompletely polarized channels. Then, the construction method of the generator matrix of the stepwise polar code is presented. Furthermore, we prove that the proposed scheme has lower decoding complexity than punctured, multi-kernel polar codes. Simulation results show that the proposed method can achieve similar decoding performance compared with the conventional punctured polar codes, rate-compatible punctured polar code, PC-short and asymmetric polar codes (APC) when code length N=48 and 72, respectively.