Quantum Message Passing Convergence and Vanishing Block-Error Probability for Random LDPC Codes
This work proves that a two-stage Belief Propagation with Quantum Messages (BPQM) decoder achieves zero ensemble-average block error probability for random LDPC codes over classical–quantum channels. The decoder uses depth-$l$ BPQM on tree neighborhoods followed by erasure recovery via Gaussian elimination on cyclic neighborhoods, guaranteeing successful decoding as blocklength tends to infinity.