In this study, the authors propose a new two‐stage decoding scheme for low‐density parity‐check codes to lower the error‐floor, which consists of the conventional belief propagation (BP) decoding algorithm as the first‐stage decoding and the re‐decodings with manipulated log‐likelihood ratios (LLRs) of variable nodes as the second‐stage decoding. In the first‐stage decoding, an early stopping criterion is proposed for early detection of decoding failure and the candidate set of the variable nodes are determined, which can be partly included in the small trapping sets. In the second‐stage decoding, the scores of the variable nodes in the candidate set are computed by the proposed unreliable path search algorithm and the variable nodes are sorted in ascending order by their scores for the re‐decoding trials. Each re‐decoding trial is performed by BP decoding algorithm with manipulated LLR of a selected variable node in the candidate set one at a time with the second early stopping criterion. The parallel unreliable path search algorithm is also proposed for practical application of the proposed algorithm. Numerical results show that the proposed early stopping criteria and the proposed decoding algorithms for the second‐stage decoding can correct most of the unsuccessfully decoded codewords by the first‐stage decoding in the error‐floor region.

In this paper, two classes of fountain codes, called batched zigzag fountain codes and two-phase batched zigzag fountain codes, are proposed for the symbol erasure channel. At a cost of slightly lengthened code symbols, the involved message symbols in each batch of the proposed codes can be recovered by low complexity zigzag decoding algorithm. Thus, the proposed codes have low buffer occupancy during decoding process. These features are suitable for broadcasting to receivers with limited hardware resources. We also propose a method to obtain degree distributions of code symbols for the proposed codes via ripple size evolution by taking into account the released code symbols from the batches. We also show that the proposed codes outperform Luby transform codes and zigzag decodable fountain codes with respect to intermediate recovery rate and coding overhead when message length is short, symbol erasure rate is low, and available buffer size is limited.