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The MPEG-4 video coding standard uses variable length codes (VLCs) to encode the indices of intra and inter macroblocks after discrete cosine transform and quantization. Although VLCs can achieve good compression, they are very sensitive to channel errors. Joint source-channel decoding (JSCD) is emerging as an efficient method for dealing with this sensitivity to channel errors. This paper proposes an integrated joint source-channel decoder (I-JSCD) for first order Markov sources coded with Huffman codes and convolutional codes over a binary symmetric channel. The proposed decoder combines the source state space of the Huffman decoder and channel state space of the Viterbi decoder together to construct a joint decoder with a Viterbi-like structure. We applied this I-JSCD to VLCs of both inter and intra macroblocks in MPEG-4 coded video. Experiments indicate that the proposed decoder gives significant improvements (maximum 7 dB) than a separate scheme, where a constrained joint source-channel decoder is concatenated with a Viterbi decoder at the same rate.