Polar Codes for CQ Channels: Decoding via Belief-Propagation with Quantum Messages
Abstract
This paper considers the design and decoding of polar codes for general classical-quantum (CQ) channels. It focuses on decoding via belief-propagation with quantum messages (BPQM) and, in particular, the idea of paired-measurement BPQM (PM-BPQM) decoding. Since the PM-BPQM decoder admits a classical density evolution (DE) analysis, one can use DE to design a polar code for any CQ channel and then efficiently compute the trade-off between code rate and error probability. We have also implemented and tested a classical simulation of our PM-BPQM decoder for polar codes. While the decoder can be implemented efficiently on a quantum computer, simulating the decoder on a classical computer actually has exponential complexity. Thus, simulation results for the decoder are somewhat limited and are included primarily to validate our theoretical results.
Cite
@article{arxiv.2401.07167,
title = {Polar Codes for CQ Channels: Decoding via Belief-Propagation with Quantum Messages},
author = {Avijit Mandal and S. Brandsen and Henry D. Pfister},
journal= {arXiv preprint arXiv:2401.07167},
year = {2024}
}