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Polar codes are a class of codes proposed currently, which can achieve the capacity of binary symmetric channel with low encoding and decoding algorithm. By generalizing the definition of Bhattacharyya parameter in discrete memoryless channel, we discuss the performance of polar codes on wireless communication channels in this paper. We present the special expressions of the parameters for continuous channels (Gaussian and Rayleigh fading channels), including the recursive formulas and the initial values, and we discuss the construction of polar codes for Gaussian and Rayleigh fading channels. We analyze the application of polar codes with the defined parameter over Rayleigh fading channel by transmitting image signals. The simulation results show that polar codes have better performance than that of low density parity-check codes (LDPC) codes with the same simulation condition. It is shown that polar codes will be a good candidate for wireless communication channels. [ABSTRACT FROM PUBLISHER]