An Efficient Adaptive Belief Propagation Decoder for Polar Codes

Due to the high parallelism of belief propagation (BP) decoding, it is considered as a promising solution for the decoding latency challenge of long polar codes. However, the error-correction performance of the classical BP decoding is inferior to that of the successive cancellation (SC) and the SC list (SCL) decoding. In this paper, an adaptive BP (ABP) decoding algorithm is proposed to bridge this performance discrepancy. It iteratively adjusts the a priori log-likelihood ratios (LLRs) of error-prone bits, which can be efficiently detected using the frozen and information processing elements (FIPEs). Moreover, a novel low-complexity FIPE-based early termination criterion (ETC) is proposed to further reduce the decoding complexity. It functions when all the frozen bits in the FIPEs are successfully decoded with stable LLR magnitudes. Our numerical results show that for the (1024,512) polar code, the ABP decoding outperforms the classical BP decoding by 0.3 dB at the frame error rate (FER) of 10–<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> over the additive white Gaussian noise (AWGN) channel. It can also achieve up to 78.5% latency reduction over the fast simplified SC (FSSC) decoding, while maintaining the same performance. The proposed ETC also exhibits a lower hardware complexity over the existing G-matrix criterion.