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This article studies the degree distribution property of low density parity check (LDPC) codes by Gaussian approximation (GA) and presents an efficient hybrid automatic repeat quest (HARQ) scheme for LDPC-coded orthogonal frequency division multiplexing (OFDM) system. In the scheme, the important bits with large degrees have high retransmission priorities and are mapped to the sub-carriers with better channel quality indicator (CQI) levels in the OFDM system. The new scheme provides more protection to the bits with large degrees and thus contributes more to the decoding process by offering more transmission power. In this way the system performance would be improved. The statistics and simulation results also prove the new scheme.