Digital transmission over copper loops is studied. Models are found of main sources of interference, including near-end crosstalk (NEXT), far-end crosstalk (FEXT), impulse noise (IN) and intersymbol interference (ISI). Importance Sampling theory is introduced, and an explanation is given of how it can be used to efficiently estimate the bit error rate (BER) of the above digital transmission system. Results demonstrate the efficiency of Importance Sampling simulations and the validity of the models for the channel interference. A suboptimal scheme for approaching capacity of the twisted pair is analyzed and its connection to multicarrier modulation is presented. The resulting lower bound on capacity is a significant improvement over what exists in the literature.