Design of Parity-Check Polar Codes Under Belief Propagation List Decoding

In this letter, we consider the parity-check polar (PC-Polar) code design under belief propagation list (BPL) decoding. First, we employ a Monte-Carlo method with BPL decoding to identify unreliable bits, from which parity-check (PC) bits are selected. Then the partial orders of the inner polar code are leveraged to develop a practical correlation metric for designing PC constraints. We also utilize the PC constraints to propose an improved BPL decoding with bit flipping. Simulations show the designed PC-Polar codes outperform state-of-the-art PC-Polar codes under BPL decoding, and the proposed BPLF decoding approaches successive cancellation list (SCL) decoding performance.