A Low-Complexity Method for Evaluating the Distance Spectrum of Polar Codes

Abstract

Different from linear block codes that may use one single generator matrix for different channel conditions, polar codes have different generator matrices for different channel conditions. Few papers investigated polar codes from the view of different distance spectrum associated with different generator matrices. Successive cancellation list (SCL) decoding was proposed to evaluate the distance spectrum of polar codes. However, the large memory requirement of SCL decoding using a large number of survival paths can be beyond the memory constraint of normal computers. One practical method to evaluate the distance spectrum of polar codes with SCL decoding was implemented with the aid of hard disk to store the immediately generated data. In this paper, we modify the algorithm of SCL decoding proposed by Tal and Vardy to largely reduce the time complexity and the required space in hard disk. With this method, we further investigate the distance spectrum of polar codes with length N = 128 and N = 256, respectively.