Constant Weight Polar Codes through Periodic Markov Processes
Information Theory
2025-01-22 v1 math.IT
Abstract
Constant weight codes can arise from an input process sampled from a periodic Markov chain. A previous result showed that, in general, polarization does not occur for input-output processes with an underlying periodic Markov chain. In this work, we show that if we fix the initial state of an underlying periodic Markov chain, polarization does occur. Fixing the initial state is aligned with ensuring a constant weight code.
Cite
@article{arxiv.2501.12379,
title = {Constant Weight Polar Codes through Periodic Markov Processes},
author = {Boaz Shuval and Ido Tal},
journal= {arXiv preprint arXiv:2501.12379},
year = {2025}
}