A bound on Viterbi decoder error burst length

A maximum likelihood (Viterbi) decoder used with a convolutional code on a Gaussian channel produces decoding errors which tend to occur in clusters or bursts. A method is described for deriving an upper bound on the probability of occurrence of error bursts of a given length. The method applies to the optimum convolutional codes found by Odenwalder (1970), for which the codeword weight distribution is partially known. Laboratory measurements of error burst length at signal-to-noise ratios greater than 4 dB indicate that the upper bound is useful for approximating the length of high-probability bursts, but is not precise enough to predict the probability of very long, low-probability bursts.