  We propose schemes that are efficient when each pair of qubits undergoes some
imperfect collective decoherence with different baths. In the proposed scheme,
each pair of qubits is first encoded in a decoherence-free subspace composed of
two qubits. Leakage out of the encoding space generated by the imperfection is
reduced by the quantum Zeno effect. Phase errors in the encoded bits generated
by the imperfection are reduced by concatenation of the decoherence-free
subspace with either a three-qubit quantum error correcting code that corrects
only phase errors or a two-qubit quantum error detecting code that detects only
phase errors, connected with the quantum Zeno effect again.
