  In this paper we analyze the polarization of the X-ray radiation coming from
laser--electron X-ray generator (LEXG). We obtain general relations connecting
the polarization state of outgoing X-ray radiation to the polarization state of
laser beam as well as to the parameters of electron beam. We demonstrate that
finite electron beam emittance causes a partial depolarization of initially
fully polarized X-ray radiation even when the laser beam is fully polarized. We
demonstrate with a number of numerical experiments that finite electron beam
emittance can in some cases fundamentally alter the polarization state of X-ray
radiation as compared to the polarization state of X-ray radiation scattered by
electron beam with a zero emittance. Possible applications of polarized LEXG's
radiation are discussed.
