The Hybrid Decoder of Belief Propagation and Ordered Statistics Decoding for LDPC Codes

To enhance the performance of short low-density parity-check (LDPC) codes, we introduce an innovative hybrid decoder that seamlessly integrates belief propagation (BP) with ordered statistics decoding (OSD). This hybrid approach initially employs BP to decode received vectors until successful or upon reaching specified conditions, either a maximum iteration limit or a trapping iteration threshold, indicating the stagnation of BP’s hard output. Upon these conditions, the decoder transitions to a pre-configured error pattern (PEP) OSD. The PEPOSD phase then pursues a valid result, flexibly utilizing either the received vectors or the soft values of BP as input, contingent upon the signal-to-noise ratio (SNR). Given the minimal error overlap between BP and OSD, simulations reveal that this hybrid decoder achieves a notable gain of 1.5dB over BP and 0.3-0.6dB over PEPOSD, while maintaining comparable complexity to BP alone.