On the selection of generator matrices for polar coded communication systems

In this paper, the effects of the generator matrix selection on the polarization performance of polar coded communication systems is analyzed. We consider the problem of calculating the Bhattacharyya parameters for generator matrices of size larger than the standard size 2 × 2 and demonstrate that it is not an easy task to obtain the channel capacities in a recursive fashion, unlike the 2 × 2 generator matrix case. We obtain the polarization performance of all lower triangular generator matrices of size 3 × 3 numerically and obtain comparisons that also take into account asymptotical polarization rate exponents. The comparisons are then used to identify generator matrices that are suitable for finite-length polar coded communication systems.