Towards Understanding Weighted Bit-Flipping Decoding

A natural relationship between weighted bit-flipping (WBF) decoding and message-passing decoding is explored. This understanding can help us develop a dual WBF decoding algorithm from one type of message-passing decoding algorithm and vice versa. For min-sum decoding, one can find that its dual WBF algorithm is the algorithm proposed by Jiang et al. For belief-propagation (BP) decoding, we propose a new WBF algorithm and show its performance advantage. For some high-rate low-density parity-check (LDPC) codes of large row weight, it is shown that the WBF algorithm proposed by Liu and Pados performs extraordinarily well. However, its dual message- passing decoding does not work well. Furthermore, we propose a parallel implementation framework for various WBF algorithms. Compared to serial implementations, various WBF algorithms in their parallel form converge significantly faster and often perform better.