Finite-length polarization measures for polar coded systems

In this paper, polarization performance of polar code generator matrices is analyzed. We obtain the Bhattacharyya parameters of polarized channels generated by all possible lower-triangular 3 × 3 generator matrices and evaluate the corresponding polarization behavior of polar coded systems via both asymptotical polarization rate exponents and finite-length polarization distance graphs. A ranking of all lower-triangular 3 × 3 generator matrices is also provided.