We consider the construction of polar codes for parallel channels of different reliability. This problem is commonly referred to as compound polar coding in the literature. Different from previous approaches, our idea is to include the channel state into the polarisation procedure and hence polarise the randomness coming from the channels. Using a design criterion based on the minimisation of an upper bound of the block error probability, we propose an explicit construction of the frozen set. A straightforward application of proposed method is polar coding for block fading channels. As a result of matching code
polarisation with fading coefficients, the proposed construction has a better performance than conventional polar or LDPC BICM codes.