  We propose a quantum key distribution scheme that combines a biased basis
choice with the decoy-state method. In this scheme, Alice sends all signal
states in the $Z$ basis and decoy states in the $X$ and $Z$ basis with certain
probabilities, and Bob measures received pulses with optimal basis choice. This
scheme simplifies the system and reduces the random number consumption. From
the simulation result taking into account of statistical fluctuations, we find
that in a typical experimental setup, the proposed scheme can increase the key
rate by at least 45% comparing to the standard decoy-state scheme. In the
postprocessing, we also apply a rigorous method to upper bound the phase error
rate of the single-photon components of signal states.
