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This paper proposes a joint JPEG-block coding system (JJBC) based on BCJR decoding with expurgating trellis that maintains an acceptable image quality over AWGN and wireless channels. The joint design of JPEG compression and block codes in the transmitter has the advantage of avoiding error propagation and of low decoding complexity over the conventional tandem system with separate optimization of source coding and channel coding. The PSNR performance of the JJBC system is much better than that of the tandem system when the signal to noise ratio is low. Experimental results show that the proposed JJBC system achieves 6 dB (3 dB) reduction at PSNR=20dB, compared to the conventional tandem system, over wireless IEEE 802.11b (AWGN) channels.