Polar codes in quantum information theory

Abstract

Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our recent results for polar coding in quantum information theory, including applications to classical-quantum multiple access channels, interference channels and compound communication settings, including the first proof of channel coding achieving the Han-Kobayashi rate region of the interference channel without the need of a simultaneous decoder. Moreover we add to the existing framework by extending polar codes to achieve the asymmetric capacity and improving the block error probability for classical-quantum channels. In addition we use polar codes to prove a new achievable rate region for the classical-quantum broadcast channel. We also discuss polar codes for quantum communication over quantum channels and state results towards codes for compound quantum channels in this setting. We conclude by stating a list of interesting open questions to invite further research on the topic.

Master's thesis, Leibniz Universität Hannover, 67 pages, 8 figures, chapter 3 partly based on arXiv:1409.7246

References in corpus (6)

• On Quantum Capacity of Compound Channels
• Classical Capacities of Averaged and Compound Quantum Channels
• Rate-splitting in the presence of multiple receivers
• Polar Coding for the General Wiretap Channel
• One-shot Marton inner bound for classical-quantum broadcast channel
• An Entropy Sumset Inequality and Polynomially Fast Convergence to Shannon Capacity Over All Alphabets