Refined Parity-Check Polar Codes from PAC Codes with Lower Complexity

As any polarization-adjusted convolutional (PAC) code can be transformed into a parity-check (PC) polar code with the same set of codewords, this paper proposes a new approach for refining PC-Polar codes derived from PAC codes. This approach refines PC-polar codes with simpler PC functions, which makes the decoding more efficient. For successive cancellation list (SCL) decoding of the derived PC-Polar code, we first show that its decoding performance is insensitive to the positions of information bits akin to any PC function if the degree profile of PC functions keeps unchanged. Then, we propose to employ a contiguous use of information bit positions for any PC function. For various short PAC codes, simulation results show that the refined PC-Polar code performs very close to the derived PC-Polar code under SCL decoding, but with a lower complexity in both encoding and decoding.