Due to the unequal error protection (UEP) property of both the irregular low-density parity-check (LDPC) code and the higher-order modulation, bit mapping is proposed as a joint optimization of the LDPC coded-modulation scheme. In this paper, we discuss the bit mapping optimization performed by employing an additional DEMUX following the given bit interleaver, and then apply it to the second generation digital video broadcasting system for cable (DVB-C2). The extrinsic information transfer (EXIT) chart technique is adopted to analyze the influence of bit mapping on the iterative decoding process. Based on the EXIT-chart analysis, an optimization method is proposed to design the DEMUX for performance improvement. As an example, we re-design the DEMUX for the DVB-C2 system with reduced DEMUX width. The superior performance of the optimized DEMUX is verified by the bit error rate (BER) simulation.