Polar Coding for Processes With Memory
Eren Şaşoğlu, Ido Tal · IEEE Transactions on Information Theory · 2019
We study polar coding for stochastic processes with memory. For example, a process may be defined by the joint distribution of the input and output of a channel. The memory may be present in the channel, the input, or both. We show that the ψ-mixing processes polarize under the standard Arıkan transform, under a mild condition. We further show that the rate of polarization of the low-entropy synthetic channels is roughly O(2-√N), where N is the blocklength. That is, essentially, the same rate as in the memoryless case.