  In order to eliminate disturbing effects of decoherence, encoding of quantum
information in decoherence-free subspaces has been suggested. We analyze the
benefits of this concept for a quantum register that is realized in a spin
chain in contact with a common bosonic bath. Within a dissipation-less model we
provide explicit analytical results for the average fidelity of plain and
encoded quantum registers. For the investigation of dissipative spin-boson
couplings we employ a master equation of Bloch-Redfield type.
