An Efficient Ordered Likelihood Decoder for Rate-Compatible Short LDPC codes

This paper proposes a concatenated multi-belief ordered likelihood decoding (MB-OLD) algorithm for rate-compatible (RC) short low-density parity check (LDPC) codes, where the output log-likelihood ratios (LLRs) of belief propagation (BP) are sent to a well-designed bit-flipping decoder, which we called ordered likelihood decoder (OLD). In contrast to conventional ordered statistic decoder (OSD), the test error patterns (TEPs) sequence of OLD is generated from most likely to least likely, where the ordered reliability sequence associated with the most reliable basis (MRB) is approximated as multiple lines, and a stopping criterion (SC) is taken to reduce the decoding complexity. Furthermore, we analyze the LLR behavior of BP decoder in short block-length regimes, and propose an optimal iteration number. Based on these analyses, the output LLRs of BP within the optimal number of iterations are well combined and sent to OLD. Simulation results show that the proposed MB-OLD has the superior decoding performances in terms of error-rate and decoding complexity than its counterparts.