Polar Codes for the Rayleigh Fading Channel

The application of polar codes for the Rayleigh fading channel is considered. We construct polar codes for the block Rayleigh fading channel with known channel side information (CSI) and for the Rayleigh channel with known channel distribution information (CDI). The construction of polar codes for the Rayleigh fading with known CSI allows them to work with any signal noise ratio (SNR). The rate of the codeword is adapted correspondingly. Polar codes for Rayleigh fading with known CDI suffer a penalty for not having complete information about the channel. The penalty, however, is small, about 1.3 dB. We perform simulations and compare the obtained results with the theoretical limits. We show that they are close to the theoretical limit. We compare polar codes with other good codes and the results show that long polar codes are closer to the limit.