  We consider the inverse boundary value problem for operators of the form
$-\triangle+q$ in an infinite domain
$\Omega=\mathbb{R}\times\omega\subset\mathbb{R}^{1+n}$, $n\geq3$, with a
periodic potential $q$. For Dirichlet-to-Neumann data localized on a portion of
the boundary of the form $\Gamma_1=\mathbb{R}\times\gamma_1$, with $\gamma_1$
being the complement either of a flat or spherical portion of $\partial\omega$,
we prove that a log-type stability estimate holds.
