Impulse noise is a major limiting factor to the performance of digital subscriber lines, powerline communication systems, and digital TV. Research has shown that the impulse noise in all those transmission media has very similar statistical properties. Using noise distribution parameters for the specific case of telephone lines, this paper suggests a Bernoulli-Weibull model of impulse noise in the local loop at symbol level. This model is then applied to develop closed-form expressions for the error probability of PAM and single carrier QAM. A novel extension of the distribution of the impulse noise amplitudes to two dimensions is introduced to enable the analysis of two-dimensional modulations, such as QAM. It is shown that earlier noise models, which assume Gaussian distributed impulse amplitudes or Rayleigh distributed powers, produce overly optimistic results for the errors owing to impulse noise in comparison with the Bernoulli-Weibull model presented here. The error performance of multicarrier QAM (DMT) is also evaluated based on the Bernoulli-Weibull model, however this is done numerically owing to the lack of an analytical solution. It is shown that multicarrier QAM performs better than single carrier systems but only for low impulse power and low impulse probability. The analytical framework presented here is also directly applicable to powerline transmission and DVB-T systems as they have very similar impulse noise statistics to those in telephone lines.