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In many real-world communication systems, the extent of non-Gaussian impulsive noise (IN) rather than Gaussian noise poses practical limits on the achievable system performance. The decoding of IN-corrupted signals is complicated by the fact that accurate IN statistics are typically unavailable at the receiver. Without exploiting the IN statistics, the conventional method is to try to mark the IN-corrupted symbols as erasures preceding a Euclidean metric based decoder. In this work, a novel joint erasure marking and Viterbi algorithm (JEVA) is proposed to decode the convolutionally coded data transmitted over an unknown impulsive noise channel. Based on the Bernoulli-Gaussian IN model, it is empirically demonstrated that JEVA not only can offer significant performance improvement over the conventional separate erasure marking and Viterbi decoding method, but also can almost achieve the optimal performance of the maximum likelihood decoder that fully exploits the perfect knowledge of the IN probability density function. Various implementations of JEVA are proposed to provide different performance-complexity trade-offs.