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Based on hidden Markov modelling of the channel output, two decoding strategies are proposed. The first one is a soft\u2010decoder which estimates the source reconstruction vectors directly from a sequence of channel output samples. The second one is a hard\u2010decoder based on joint maximum a posteriori (MAP) probability estimation of channel symbols and channel states. An iterative procedure for designing JSC optimised vector quantisers (VQs) is also proposed. Finally, the design of VQs for wireless channels using a finite\u2010state model is examined. Experimental results are provided for a Gauss\u2010Markov source and flat\u2010fading wireless channels. A comparison with an idealised tandem source\u2010channel coding system is also provided to demonstrate the advantage of the proposed JSC coding approach. 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