A Modified Min-Sum Algorithm for Quantized LDPC Decoders

It is well known that for decoding low-density parity-check (LDPC) codes, the attenuated min-sum algorithm (AMSA) and the offset min-sum algorithm (OMSA) can outperform the conventional min-sum algorithm (MSA) at low signalto-noise-ratios (SNRs). In this paper, we demonstrate that, for quantized LDPC decoders, although the MSA achieves better high SNR performance than the AMSA and OMSA, each of the MSA, AMSA, and OMSA all suffer from a relatively high error floor. Therefore, we propose a novel modification of the MSA for decoding quantized LDPC codes with the aim of lowering the error floor. Compared to the quantized MSA, the proposed modification is also helpful at low SNRs, where it matches the waterfall performance of the quantized AMSA and OMSA. The new algorithm is designed based on the assumption that trapping/absorbing sets (or other problematic graphical objects) are the major cause of the error floor for quantized LDPC decoders, and it aims to reduce the probability that these problematic objects lead to decoding errors.