In non-cooperative communications, blind recognition of channel codes is the key to recover information from noisy intercepted messages. In this paper, we develop a progressive and iterative approach to reconstruct the paritycheck matrices of large QC-LDPC codes under high bit error rate (BER). Specifically, in order to reduce the impact of noisy bits and improve efficiency for large codes, a novel sparse vector recovery (SVR) method based on sub-matrix sampling is first introduced. Then, SVR is operated iteratively after employing intermediate decoding with the partially reconstructed parity-check matrix on the intercepted messages. At last, the full parity-check matrix is built up progressively. Experimental results on a code of length 16200 show that the maximum bearable BER of the proposed approach to fully reconstruct is around 3E-4, at least 100 times higher than previous works.