Ergodicity of skew-products over typical IETs

We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \[ {T_f}:{[0, 1) × R}→{[0, 1) × R}, {T_f(x, t)}:={(T(x), t+f(x))}, \] where T is an interval exchange transformation and f is a piece-wise constant function with a finite number of discontinuities. We show that such system is ergodic with respect to Leb[0,1)× R for a typical choice of parameters of T and f.