On Probabilistic Weight Distribution of Polar Codes

Polar code is a low-complexity and capacity-achieving code with applications in channel coding, source coding and secrecy. One way to evaluate the error performance of the finite-length polar 'channel' code, for instance, is to use Bonferroni-type (e.g., union bound) bounds requiring the Hamming weight distribution. Currently, there are no low-complexity algorithms for the polar code's spectra. In this paper, we propose a recursive probabilistic weight distribution (PWD) expression for polar codes. As this expression is complex, two polynomial-time approximations and a tree-based approach have been presented for a faster implementation of the PWD method with much accuracy.