Proof of Non-stationary Channel Polarization

In this paper, we consider the proof of the non-stationary channel polarization theory and its achievability of capacity. First, we construct a multi-channel stochastic process for the non-stationary channel polarization operation. Then based on this stochastic process, we extend Arıkan’s standard martingale proof method on the average channel capacity and average channel Bhattacharyya parameter, by which we have successfully proved the non-stationary channel polarization theory and the achievability of capacity. For those who are familiar with Arıkan’s polarization proofs, our extended proofs will be easy to understand.