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A novel joint source channel distortion model is proposed, which can essentially estimate the average distortion. To improve the precision of the model, the redundancy generated by a forbidden symbol in the arithmetic codes is used to distinguish between the quantization distortion and the channel distortion, all the coefficients from the first error one to the end of the sequence are set to be a value within the variance range of the coefficients instead of zero, then the error propagation coming from the entropy coding can be essentially estimated. Experiment results show that the precision of the model in terms of average peak-signal-to-noise has been improved about 0.5dB compared to classical works. An efficient progressive image transmission system based on the model is developed, and can be used in the wireless communication systems.