  This paper presents a novel propagation (BP) based decoding algorithm for
polar codes. The proposed algorithm facilitates belief propagation by utilizing
the specific constituent codes that exist in the factor graph, which results in
an express journey (XJ) for belief information to propagate in each decoding
iteration. In addition, this XJ-BP decoder employs a novel round-trip message
passing scheduling method for the increased efficiency. The proposed method
simplifies min-sum (MS) BP decoder by 40.6%. Along with the round-trip
scheduling, the XJ-BP algorithm reduces the computational complexity of MS BP
decoding by 90.4%; this enables an energy-efficient hardware implementation of
BP decoding in practice.
