In this paper, we present a general framework which describes a class of fast methods of error rate evaluation in the presence of additive noise and intersymbol interference. An analysis of this framework led us to propose a new method based on a Fourier series expansion which does not make use of the moments of the intersymbol interference. Its computing cost is low and it handles various kinds of noise as well as current coherent amplitude or phase modulation techniques.

When seen as a linear system of equations, superresolution appears as a classical problem of numerical analysis. The main property of this problem is its strong ill-condition. Many methods are candidates to invert this system; they differ with many aspects: computational cost, regularization properties, flexibility. A review of these methods is presented with application to a given case.