Low-Complexity BP-ORBOSD Algorithm for Short 5G LDPC Codes

Belief propagation (BP) combined with ordered statistics decoding (OSD) achieves near-optimal frame error rate (FER) for short LDPC codes, but the extensive re-encoding overhead of OSD limits its practicality. To address this, we propose the BPORBOSD, a low-complexity and high-performance decoder that replaces conventional OSD with the ordered reliability bits OSD (ORBOSD), where the test error patterns are produced by the ORB technique. Moreover, in contrast to conventional BP-OSD, which directly adopts the soft information from standard BP into OSD after BP fails, we employ a modified BP scheme with a normalization factor α to produce soft reliability metrics better suited for ORBOSD. We derive the decoder’s complexity and demonstrate that, in the high-SNR regime, the average decoding complexity of BPORBOSD approaches that of standard BP. Simulation results confirm that BP-ORBOSD achieves FERs close to those of conventional BPOSD and the finite-length bound while significantly reducing the average number of re-encodings.