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In this paper, we consider rate compatible puncturing of low density parity check (LDPC) codes. We present a general density evolution-based procedure which finds the optimal puncturing of a based code. We show that puncturing can be performed across a range of rates and code lengths in a manner that produces punctured codes with good thresholds. This allows one to implement a single optimal LDPC code of a low rate that can be punctured across a wide range of rates without loss of threshold performance. Simulation results show that the error floors of the codes do not degrade after puncturing.