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 (P-LDPC) code is designed for this system, and the column-weight distribution is taken as an important constraint in the collaborative design process. In this way, the storage space used for storing the scheduling order in the CWB shuffled scheduling can be saved, whose size is proportional to code length. Theoretical analysis and simulations show that the shuffled-based DC-BICM system with the low-storage P-LDPC code can achieve lower decoding complexity, less storage requirement and better performance than the existing systems.
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