Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
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A natural relationship between weighted bit-flipping (WBF) decoding and belief-propagation-like (BP-like) decoding is explored. This understanding can help us develop WBF algorithms from BP-like algorithms. For min-sum decoding, one can find that its WBF algorithm is the algorithm proposed by Jiang et al. For BP decoding, we propose a new WBF algorithm and show its performance advantage. The proposed WBF algorithms are parallelized to achieve rapid convergence. Two efficient simulation-based procedures are proposed for the optimization of the associated thresholds.