Towards Weight Distribution-Aware Polar Codes

Abstract: Polar codes are constructed based on the reliability of sub-channels resulting from the polarization effect. However, this information-theoretic construction approach leads to a poor weight distribution. To address this issue, pre-transformed polar codes, such as CRC-polar codes and PAC codes, have been employed. In this paper, we focus on the structure of polar codes without applying any pre-transformations and explore methods, guided by the weight-contribution partial order, to design polar-like codes with enhanced weight distribution, notably without employing any search or optimization algorithms. Numerical results demonstrate improvement over a range of codes both with and without pre-transformation.