This paper presents a new method to design Echo & NEXT cancellers for gigabit and multi-gigabit transceivers by exploiting sparse characteristics of the category-6 (CAT6) unshielded twisted pair (UTP) copper channel. The proposed scheme uses correlation method to estimate the long sparse channel impulse response and identifies the active taps based on an energy threshold. Adaptive filtering is only performed on few active taps. An area saving architecture is also proposed to implement the algorithm. It is shown that the proposed method leads to computational savings of 50% during initial training stage, and 29-66.7% during the steady-state.