  Decoherence is one of the main obstacles in long-distance quantum
communication. Recently, the theoretical work of Fr\"{o}wis and W. D\"{u}r
(Phys. Rev. Lett. \textbf{106}, 110402 (2011)) and the experiment of Lu
\emph{et al.} (Nat. Photon. \textbf{8}, 364 (2014)) both showed that the logic
qubits entanglement say the concatenated Greenberger-Horne-Zeilinger (C-GHZ)
state is more robust under decoherence. In this paper, we describe a protocol
for Bell-state analysis for this logic qubits entanglement. This protocol can
also be extended to the multipartite C-GHZ state analysis. Also, we discuss its
application in the quantum teleportation of a unknown logic qubit and in the
entanglement swapping of logic Bell states. As the logic qubits entanglement is
more robust under decoherence, our protocol shows that it is possible to
realize the long-distance quantum communication based on logic qubits
entanglement.
