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The identification of low-density parity-check (LDPC) codes with higher rate over a candidate set is more difficult than that of LDPC encoders with lower rate. For the given soft information on a received sequence, we present a method to compute the average Taylor polynomial of the syndrome posterior probability according to the parity-checks of the candidates. Simulation results show that the proposed method performs as well as the existing works when dealing with lower rate encoders. Meanwhile, our method outperforms the existing works in higher rate encoders identification, with the gain being about 0.5 dB.