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For videos transmitted in an error-prone network, it is necessary to protect the source bitstream. Based on our packet loss visibility model, we minimize the end-to-end video quality degradation when transmitted in an AWGN channel using rate-compatible punctured convolutional codes for a given channel rate budget. We transform the original problem into a binary-decision problem, then we solve this integer program by the branch and bound method. Experimental results show that our visibility-based unequal error protection can improve the received video quality compared to equal error protection.