Polar coding for fading channels

A polar coding scheme for fading channels is proposed in this paper. More specifically, the focus is on the Gaussian fading channel with a BPSK modulation, where the equivalent channel is modeled as a binary symmetric channel with varying cross-over probabilities. To deal with variable channel states, a coding scheme of hierarchically utilizing polar codes is proposed. In particular, by observing the polarization of different binary symmetric channels over different fading blocks, each channel use corresponding to a different polarization is modeled as a binary erasure channel such that polar codes could be adopted to encode over blocks. It is shown that the proposed coding scheme, without instantaneous channel state information at the transmitter, achieves the capacity of the corresponding fading binary symmetric channel.