  Our goal in this paper is to investigate ergodicity of white-forced
Kuramoto-Sivashinsky equation (KSE) on the whole line. Under the assumption
that sufficiently many directions of the phase space are stochastically forced,
we can prove that the dynamics is attractive toward a unique invariant
probability measure with polynomial rate of any power. In order to prove this,
we further develop coupling method and establish a sufficiently general
criterion for polynomial mixing. The proof of polynomial mixing for KSE is
obtained by the combination of the coupling criterion and the Foia\c{s}-Prodi
estimate of KSE on the whole line.
