In this paper, we proposed a fixed-length robust joint source-channel coding (JSCC) scheme for image transmission over noisy channels. Three channel models are studied: binary symmetric channels (BSC) and additive white Gaussian noise (AWGN) channels for memoryless channels, and Gilbert-Elliott channels (GEC) for bursty channels. We derive, in this research, an explicit operational rate-distortion (R-D) function, which represents an end-to-end error measurement that includes errors due to both quantization and channel noise. In particular, we are able to incorporate the channel transition probability and channel bit error rate into the R-D function in the case of bursty channels. With the operational R-D function, bits are allocated not only among different subsources, but also between source coding and channel coding so that, under a fixed transmission rate, an optimum tradeoff between source coding accuracy and channel error protection can be achieved. This JSCC scheme is also integrated with allpass filtering source shaping to further improve the robustness against channel errors. Experimental results show that the proposed scheme can achieve not only high PSNR performance, but also excellent perceptual quality. Compared with the state-of-the-art JSCC schemes, this proposed scheme outperforms most of them especially when the channel mismatch occurs.