Generalized Gaussian Approximation and Its Application in Polar Decoding

How to analyse the block error rate (BLER) of state-of-the-art successive cancellation list (SC-list) decoders has been the most appealing and challenging problem in polar coding theory. In this paper, by investigating the distributions of path metrics for each path at each decoding stage, a generalized Gaussian approximation method is proposed to obtain the distributions of log-likelihood ratio (LLR) messages calculated in a SC-list decoder. Moreover, we also adopt Monte Carlo method to validate the proposed method, based on which a framework to analyze the BLER performance of SC-list decoding is developed. Finally, numerical results show that the proposed generalized Gaussian approximation method approaches the real distribution of LLR messages in practical SC-list decoding.