  We discuss the performance of polar codes, the capacity-achieving channel
codes, on wireless communication channel in this paper. By generalizing the
definition of Bhattacharyya Parameter in discrete memoryless channel, we
present the special expression of the parameter for Gaussian and Rayleigh
fading the two continuous channels, including the recursive formulas and the
initial values. We analyze the applications of polar codes with the defined
parameter over Rayleigh fading channel by transmitting image and speech. By
comparing with low density parity-check codes(LDPC) at the same cases, our
simulation results show that polar codes have better performance than that of
LDPC codes. Polar codes will be good candidate for wireless communication
channel.
