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Differential chaotic bit-interleaved coded modulation (DC-BICM) system can achieve coding gain from channel code without loss of bandwidth in the differential chaos shift keying (DCSK) system, but the current DC-BICM system using the belief propagation decoding algorithm has high decoding complexity, which brings burdens to resource-limited applications. In this letter, a novel collaborative design framework based on joint coding and decoding optimization is proposed for the DC-BICM system over multipath Rayleigh channels. Firstly, the column-weight-based (CWB) shuffled scheduling decoding is introduced into the DC-BICM system to lower the decoding complexity, called shuffled-based DC-BICM system. Then, a CWB extrinsic information transfer (CWB-EXIT) algorithm is developed for the theoretical analysis of this system. With the CWB-EXIT algorithm, a low-storage protograph low-density parity-check …