In this paper, a powerful class of irregular low-density parity check (LDPC) codes based on random construction techniques is presented. The resultant codes have accurate profile with the additional features of making them suitable for incremental redundancy systems. The proposed codes also have low encoding complexity and can be decoded efficiently. Moreover, these codes show better puncturing performance than irregular LDPC codes obtained by other techniques over a wide range of code rates (0.6~0.9) and become more distinctive at higher rates.