Polar Coding for Block Fading Channels

In this paper, we consider the problem of polar coding for block fading channels, with emphasis on those with instantaneous channel state information (CSI) at neither the transmitter nor the receiver. Our approach is to decompose a block fading channel of $T_c$ symbols per coherent interval into $T_c$ binary-input sub-channels in a capacity-preserving way, and design a polar code for each of them. For the case when instantaneous CSI is available at the receiver, a random interleaver can be used to enable joint encoding and decoding of all sub-channels so as to enhance the finite length performance. It is shown that our proposed schemes achieve the ergodic capacity of binary-input block fading channels under various CSI assumptions.