On Viterbi detector path metric differences

This letter continues the investigation of methods for computing exact bounds on the path metric differences in maximum-likelihood sequence detectors based upon the Viterbi algorithm. New upper and lower estimates for these bounds are presented and recast in terms of a collection of linear programming problems. These estimates improve upon previously proposed linear programming bounds. The estimates are applied to derive exact bounds or provably close to exact bounds for several Viterbi detectors corresponding to coded and uncoded partial-response channels of practical interest in digital magnetic and optical recording.