  Berry-Esseen bounds for non-linear functionals of infinite Rademacher
sequences are derived by means of the Malliavin-Stein method. Moreover,
multivariate extensions for vectors of Rademacher functionals are shown. The
results establish a connection to small-ball probabilities and shed new light
onto the relation between central limit theorems on the Rademacher chaos and
norms of contraction operators. Applications concern infinite weighted 2-runs,
a combinatorial central limit theorem and traces of Bernoulli random matrices.
