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This paper proposes a serially concatenated system with an outer convolutional channel encoder and an inner chaos-based coded modulator. With the help of the principles of symbolic dynamics, the chaotic modulation can be described in terms of a trellis. Owing to this, we show that the resulting system can be designed and analyzed following developments made for serially concatenated channel codes (SCCCs) or bit-interleaved coded-modulation systems. We show how the iterative decoding algorithm used in this concatenated framework can be analyzed through the well-known extrinsic information transfer chart device and how the bit error rate can be bounded using the transfer function of the convolutional channel encoder. Comparison with a related SCCC system in both additive white Gaussian noise and frequency-nonselective fading channels shows that this kind of chaos-based systems keeps the potential advantages of coded-modulation-based systems. We are thus confident that the principles shown here can lead to the design of competitive chaotic discrete communication systems.