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In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over additive white Gaussian noise (AWGN) channels. We present the iterative decoding algorithm of LDPC codes, and we also discuss the encoding methods and the bipartite graph representation of LDPC codes ensemble. Finite-length LDPC code performances are investigated, and the influence of cycle is pointed out. Simulation results show that irregular LDPC codes with variable and check node degree distribution optimized for infinite-length codes are not optimal for finite-length LDPC codes, and the error patterns of both regular and irregular codes are investigated as an effort to improve the performance and design methodology of finite-length LDPC codes.