Augmented Belief-Propagation Decoding of Low-Density Parity-Check Codes

We propose an augmented belief-propagation (BP) decoder for low-density parity-check (LDPC) codes which can be used on memoryless or intersymbol-interference (ISI) channels. The proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the BP decoder. The augmented decoder is a multistage iterative decoder, where at each stage, the original channel messages on select symbol nodes are replaced by saturated messages. The key element of the proposed method is the symbol-selection process, which is based on the appropriately defined subgraphs of the code graph and/or the reliability of the information received from the channel. We demonstrate by examples that this decoder can be implemented to achieve substantial gains (compared with the standard locally operating BP decoder) for short LDPC codes decoded on both memoryless and ISI Gaussian channels. Using the Margulis code example, we also show that the augmented decoder reduces the error floors. Finally, we discuss types of BP decoding errors and relate them to the augmented BP decoder.