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This paper presents a semi-random construction of rate-compatible low-density parity-check (LDPC) codes. We analyze some crucial properties determining the performance of LDPC codes to direct our construction approach. The new parity-check matrices corresponding to lower-rate codes are generated by computer search which is subject to these important properties. The novel construction approach is flexible as we only add new rows with certain constraints to the original parity-check matrix. The simulation results demonstrate that rate-compatible LDPC codes based on this approach work quite well.