On Improving the Design of Parity-Check Polar Codes

In this paper, a new design of concatenated polar codes is proposed. By concatenating an outer code with polar codes, the distance spectrum can be improved, leading to enhanced decoding performance of vanilla polar codes. In the 5G New Radio standard, both cyclic redundancy check precoding and systematic single-parity-check precoding schemes are adopted and this combination provides stable decoding performance over a wide range of coding parameters. We focus on the design of single-paritycheck precoded polar codes. For the special systematic pre-coding scheme, code construction depends solely on the selection of information and parity bits from the source bits. Since the conventional parity bit selection criteria can draw weaknesses for some coding parameters, we develop new criteria that enhance the protection of weak source bits under the successive cancelation decoding. The simulation results demonstrate that the proposed design consistently outperforms the conventional one across a wide range of coding parameters. The improvement is more pronounced in short-length codes.