On the Construction of Generator Matrices for Relaxed Polar Codes
Guiping Li, Jianjun Mu, Lei Liu, Xiaohang Liu · 2018
Relaxed polar codes can reduce the complexities of the encoding and decoding of original polar codes by relaxing the polarization of some sub-channels which are polarized to be sufficiently good or sufficiently bad in the process of polarization. In this paper, we first consider the construction of relaxed polar codes to compute the error probabilities of sub-channels by using Gaussian approximation, and then propose a construction algorithm of generator matrices for relaxed polar codes. Simulations show that the indices of the information sub-channels chosen using the proposed method for relaxed polar codes are almost in accordance with that of the information sub-channels using the method of Gaussian approximation (GA) for full polar codes. And also, relaxed polar codes constructed by using the proposed algorithm can obtain almost the same performance as original polar codes under the reduced encoding and decoding complexities.