A convolutional decoder includes a first storage, a second storage, a branch metric processor to determine branch metrics for transitions of states from a start step to a last step according to input bit streams, an ACS processor to select maximum likelihood path metrics to determine a survival path according to the branch metrics and to update states of the start step to the first storage and the second storage alternately based on the selection of the maximum likelihood path metrics, and a trace back logic to selectively trace back the survival path based on the states of the start step stored in a selected storage among the first storage and the second storage.