  We study in details decoherence process of a spin register, coupled to a spin
environment. We use recently developed methods of information transfer study in
open quantum systems to analyze information flow between the register and its
environment. We show that there are regimes when not only the register
decoheres effectively to a classical bit string, but this bit string is
redundantly encoded in the environment, making it available to multiple
observations. This process is more subtle than in a case of a single qubit due
to possible presence of protected subspaces: Decoherence free subspaces and, so
called, orthogonalization free subspaces. We show that this leads to a rich
structure of coherence loss/protection in the asymptotic state of the register
and a part of its environment. We formulate a series of examples illustrating
these structures.
