Polar coding for processes with memory

We study polar coding over channels and sources with memory. We show that ψ-mixing processes polarize under the standard transform, and that the rate of polarization to deterministic distributions is roughly O(2 −√N ) as in the memoryless case, where N is the blocklength. This implies that the error probability guarantees of polar channel and source codes extend to a large class of models with memory, including finite-order Markov sources and finite-state channels.