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In this paper we construct two classes of LDPC codes with girth 16 and 20, respectively, based on graphical models. These codes are well-structured, regular, and with column weight j = 2, which greatly simplifies their implementation. The codes with girth g = 16 have code rate r = 1/2. And the codes with girth g = 20 have code rate r = 1/3. Simulation results compare their bit-error-rate (BER) decoding performance in AWGN channels with randomly constructed LDPC codes.