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This paper proposes an irregular mapping technique, where a new labeling searched via modified adaptive binary switch algorithm (ABSA), mixed with a pre-fixed labeling, can provide near-optimal match to a given outer channel code. By using the proposed technique, the bit-interleaved low-density parity-check (LDPC) coded modulation systems with iterative demapping/decoding (BILCM-ID) could achieve near-capacity performance. With a slight modification on the LDPC coded modulation scheme of DVB-T2 standard, the proposed technique can improve the iterative demapping system by exploiting significant iterative gain. The superior performance is verified via extrinsic information transfer (EXIT) chart analysis and bit error rate (BER) simulation.