On the capacity of the binary input Gaussian and Rayleigh fading channels

A class of binary-input discrete-time channels with symmetric distribution of the output with respect to the input is considered and the channel capacity is analytically evaluated. The Gaussian and Rayleigh fading channel belong to this class and their capacities are numerically obtained for different quantization of the output. The asymptotic capacities for low signal-to-noise ratio (SNR) are compared and it is shown that the Rayleigh fading channel loses about 1 dB.