Implementation of Polar Codes Over Multipath Rayleigh Fading Channel Using Channel Transformation

In this manuscript we take a look into the implementation of polar codes over Rayleigh fading multipath channels. For this requirement, we use a channel transformation technique, wherein the channel impulse response vector of the multipath channel is used to create a Toeplitz matrix which is then decomposed. The resultant matrices are used to convert the Rayleigh fading channel into an additive white gaussian noise (AWGN) channel. This enables us to use the standard structure of the polar codes designed for AWGN channels, inclusive of the reliability sequence be used for Rayleigh fading channels with any number of taps. Simulation results show bit error rates of the order of 10
^-7
at bit-energy to noise ratio (Eb/N0) in the range of 1.5 to 2 dB.