The Belief Propagation (BP) algorithm has the advantages of high-speed decoding and low latency. To improve the block error rate (BLER) performance of the BP-based algorithm, the BP flipping algorithm was proposed. However, the BP flipping algorithm attempts numerous useless flippings for improving the BLER performance. To reduce the number of decoding attempts needed without any loss of BLER performance, in this paper a metric is presented to evaluate the likelihood that the bits would correct the BP flipping decoding. Based on this, a BP-Step-Flipping (BPSF) algorithm is proposed which only traces the unreliable bits in the flip set (FS) to flip and skips over the reliable ones. In addition, a threshold β is applied when the magnitude of the log-likelihood ratio (LLR) is small, and an enhanced BPSF (EBPSF) algorithm is presented to lower the BLER. With the same FS, the proposed algorithm can reduce the average number of iterations efficiently. Numerical results show the average number of iterations for EBPSF-1 decreases by 77.5% when N = 256, compared with the BP bit-flip-1 (BPF-1) algorithm at Eb/N0 = 1.5 dB.
Keywords: belief propagation; bit-flipping; polar code; stepping.