Polar Coding for Processes with Memory

2016/02/04 by Sasoglu, Eren, Tal, Ido · 3 citations
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1602.01870

Abstract

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 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.

Cited by

• Polar Codes for Erasure and Unital Classical-Quantum Markovian Channels
• Last-Pair Swapping Polar Codes: A Structure to Improve Polarization under Finite-State Modulation
• Polarization Decomposition and Its Applications

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