MacWilliams Identities for Probabilistic Weight Distribution of Polar Codes

The problem of estimating the probabilistic Hamming weight distribution (HWD) is consider for polar codes. Two previous computationally recursive algorithm are reviewed and extended to the whole rate range. For low code rate, the imprecise assumption of previous works can be rectified by calculating HWD of the corresponding dual code. Based on MacWilliams Identities, the HWD of polar codes can be enumerated. By regarding as concatenation of two subcodes, the high rate one and low rate one, the HWD of medium code rate can be derived. The estimated result yields much accurate asymptotic performance bound.