The authors address the problem of computing exact bounds on the path metric differences in maximum-likelihood sequence detectors based upon the Viterbi algorithm. The calculation of the bounds is formulated as a series of linear programming problems. Numerical results are presented for several examples of uncoded and coded partial-response channels of practical interest in digital data recording applications.>

Let eta denote the length of the shortest error event achieving the minimum detection distance of maximum-likelihood signal detection for an impulse response having memory v. A family of impulse responses where eta is of order v/sup 2/ is exhibited. This, in turn, shows that some difficulty can arise in computing the minimum detection distance.>