An Enhanced Probabilistic Computation Method for the Weight Distribution of Polar Codes

Owning to the explicit structure, Hamming weight distribution (HWD) of polar codes with large length can be recursively computed with that of the short one. In this letter, an enhanced probabilistic computation method is proposed to estimate the HWD of polar codes. Only the uniform distribution assumption for the 1 s in the codeword is used and the exhaustively searched HWD for very short polar code are combined to improve the accuracy of the proposed method. Meanwhile, some characteristics for the HWD of polar codes are discussed and used to avoid the unnecessary calculations. Simulation results show that the estimated HWD matches the exact one well for rate larger than 0.5. With the obtained HWD, the asymptotic performance of polar codes can be accurately estimated in almost the whole rate range.