Reduction of the numerical range of the state metrics in a Viterbi decoder

Large state metric differences indicate a strong discrimination between the likelihood of survivor paths. A state metric is called "large" if the state metric of a node in the trellis exceeds the minimum state metric at the given depth in the trellis by more than some constant B that depends on the binary convolutional code. Theorem I formulates a stopping rule that deletes all nodes with a "large" metric, as for any path that runs through such a node and for any received sequence, a detour exists via the node that has minimal state metric such that the resulting path has a smaller metric than the original path. The proof use simultaneous application of tight bounds for maximum state metric differences for the forward and the time reversed convolutional code.<>