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The use of convolutional codes with Viterbi decoding has become commonplace in the design of military communication systems. An important characteristic of the Viterbi decoder is that errors occurring at the output tend to be of a bursty nature. This factor is often neglected in system performance analysis. The union bound and a computer search method are used to obtain the burst error probabilities for a variety of convolutional codes. Examples are given to illustrate the use of these statistics in system performance analysis.