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A near-capacity irregular bit-interleaved coded modulation based iterative decoding (Ir-BICM-ID) aided scheme is proposed. The irregular design of the scheme pervades the three basic components of BICM-ID, namely the encoder, the unity-rate precoder and the bit-to-symbol mapper. As a result, irregular BICM-ID schemes constituted by irregular components are created, which are capable of approaching the capacity of coded modulation. This is achieved by creating a marginally open extrinsic information transfer (EXIT) chart tunnel, and exploiting the theorem that the open tunnel's area is characteristic of how closely the scheme operates to the channel's capacity. The proposed Ir-BICM-ID scheme employs irregular convolutional codes (IrCC), irregular unity-rate codes (IrURC) and irregular mappers (IrMapper).