Multi-Stage Bit-Flipping Decoding Algorithms for LDPC Codes

We present two general multi-stage (MS) bit-flipping (BF) decoding algorithms for low-density parity-check (LDPC) codes. Both algorithms consist of soft-decision (SD) and hard-decision BF decoding parts. In comparison with known MS LDPC decoders, our approach is much simpler as all stages share the same BF structure. The only complexity increase is due to the use of an adaptive stage-switching (SS) mechanism which gives near-optimal SS timing. A new design issue we address is that the first-stage algorithm's parameter has to be re-tuned to achieve the optimal overall performance. The numerical results demonstrate that the proposed decoding methods can significantly improve the error-rate performance of the conventional SD BF decoders.