Decoding of generalised low-density parity-check codes using weighted bit-flip voting

A generalised low-density parity-check code (GLDPC) is a low-density parity-check code in which the constraint nodes of the code´s graph are replaced with component or subcodes other than single parity checks. Gallager´s (1963) bit-flipping algorithm for LDPCs is generalised to the class of GLDPCs with Hamming subcodes. The proposed weighted bit-flip voting (WBFV) method is iterative and uses only the hard decision decoder of the Hamming subcodes. Decoding of Hamming-based GLDPCs using WBFV has been simulated on the binary symmetric channel. Simulation results are presented showing the variation in performance with voting rule, graph construction and block length. In terms of the dependence of coding gains and complexity on the GLDPC block length, the proposed method is found to display a good performance to decoding complexity trade-off. The performance is found to compete well with other more conventional hard decision decoding schemes