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In real-time video applications, where unreliable networks are commonplace, corrupted video packets can adversely affect visual quality. In this paper, we present a novel maximum likelihood approach to performing video error correction. Rather than discarding corrupted video packets, the method estimates the likeliest syntactically valid video slice content based on these packets. First, we present the mathematical foundations that enable solution of the problem at the slice level. Then, we present a simplified solution operating at the syntax element level. The method's performance is evaluated using the H.264 baseline profile. Unlike error concealment methods, we correct the errors in the bit stream, instead of reconstructing missing pixels. Simulation results show that the method yields improved visual quality. Furthermore, the proposed approach is computationally simpler than state-of-the-art error concealment methods.