© 1992 IEEE. In the digital implementations of maximumlikelihood detectors based upon the Viterbi algorithm, bounds on the values of path metric differences are important parameters, and various techniques have been proposed for computing such bounds. This paper addresses the more general problem of characterizing the entire space of path metric differences, achievable from a given initial state, and calculating the probability density for the differences as a function of the distribution of the (noisy) channel output samples. Explicit results are given for two examples of interest in digital recording.