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The paper introduces three new classes of structured regular (n, 2, k) LDPC codes with girth 12, 16, and 20, respectively. These codes are systematically constructed, well structured, and have uniform row and column weights, which make them able to simplify greatly the implementation of LDPC coders. Their large girth improves their decoding performance. Simulation results compare their bit error rate (BER) performance over additive white Gaussian noise (AWGN) channels with randomly constructed LDPC codes. When concatenated with error-correcting codes such as Reed-Solomon codes, LDPC codes with j=2 are promising for data storage and other applications.