Polar Coding for Processes With Memory

Eren Şaşoǧlu, Ido Tal

Research output: Contribution to journalArticlepeer-review


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 Arikan 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.

Original languageEnglish
Article number8668049
Pages (from-to)1994-2003
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2019


  • Channels with memory
  • fast polarization
  • mixing
  • periodic processes
  • polar codes
  • rate of polarization

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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