A PEXIT analysis of belief propagation Polar decoder with approximated LLR

Abstract

Belief propagation decoding of Polar codes suffers from performance degradation if the frozen bits are not appropriately allocated. Particularly, when simplified log-likelihood ratio (LLR) calculations are used to reduce hardware complexity, the conventional frozen bit allocation based on protograph extrinsic information transfer (PEXIT) analysis becomes ineffective due to the inaccurate EXIT function. In this paper, we propose a new EXIT function that takes into account the approximation in the LLR for PEXIT analysis. Simulation results show that PEXIT analysis with the proposed EXIT function is able to represent the degradation of bit error rate (BER) due to the LLR approximation.