  We prove ergodicity of a class of infinite measure preserving systems, called
skew-products. More precisely, we consider systems of the form \[ {T_f}:{[0, 1)
\times \mathbb{R}}\to{[0, 1) \times \mathbb{R}},\quad {T_f(x, t)}:={(T(x),
t+f(x))}, \] 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 ${Leb}_{[0,1)\times \mathbb{R}}$
for a typical choice of parameters of $T$ and $f$.
