The complexity of the Viterbi algorithm can be reduced by linear pre-equalization. The authors introduce a linear preprocessor using the weighted least squares filtering (WLS). The geometric technique of L. Barbosa (see IEEE Trans. Inf. Theory, vol.35, no.2, p.419-27, 1989) is evoked for analytical representation of the complexity reduction by pre-equalization, and for evaluation of error performance. They evaluate the bit error rate of the WLS preprocessor and of the linear preprocessor of Falconer and Magee (see Bell System Tech. Journal, vol.52, no.9, p.1541-62, 1973)