An equalization method and device for equalizing the received vestigial sideband (VSB) signal, utilizes segment-sync symbols, Sato directions, erasure slicers, and variable step-sizes. In addition to stop-and-go (SAG) mode, the directions of Sato errors can also be used for speed up the convergence of tap weights of the equalizer. Erasure slicers can mitigate the effect of decision errors as they are passed through the feedback filter. In time-variant environments, variable step-sizes help the equalizer tracking the variations of the channels; in time-invariant environments, variable step-sizes help ease the fluctuations of the steady-state equalizer tap weights, and therefore yield smaller mean-squared-error and better symbol error rate (SER).