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Duality of Quantum and Classical Error Correction Codes: Design Principles and Examples

Babar, Zunaira, Chandra, Daryus, Nguyen, Hung, Botsinis, Panagiotis, Alanis, Dimitrios, Ng, Soon Xin and Hanzo, Lajos (2018) Duality of Quantum and Classical Error Correction Codes: Design Principles and Examples IEEE Communications Surveys and Tutorials.

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Quantum Error Correction Codes (QECCs) can be constructed from the known classical coding paradigm by exploiting the inherent isomorphism between the classical and quantum regimes, while also addressing the challenges imposed by the strange laws of quantum physics. In this spirit, this paper provides deep insights into the duality of quantum and classical coding theory, hence aiming for bridging the gap between them. Explicitly, we survey the rich history of both classical as well as quantum codes. We then provide a comprehensive slow-paced tutorial for constructing stabilizer-based QECCs from arbitrary binary as well as quaternary codes, as exemplified by the dual-containing and non-dual-containing Calderbank-Shor- Steane (CSS) codes, non-CSS codes and entanglement-assisted codes. Finally, we apply our discussions to two popular code families, namely to the family of Bose-Chaudhuri-Hocquenghem (BCH) as well as of convolutional codes and provide detailed design examples for both their classical as well as their quantum versions.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
Babar, Zunaira
Chandra, Daryus
Botsinis, Panagiotis
Alanis, Dimitrios
Ng, Soon Xin
Hanzo, Lajos
Date : 31 July 2018
Funders : EPSRC
DOI : 10.1109/COMST.2018.2861361
Copyright Disclaimer : © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Uncontrolled Keywords : Channel Coding, Quantum Error Correction, BCH Codes, Convolutional Codes.
Depositing User : Melanie Hughes
Date Deposited : 29 Aug 2018 15:05
Last Modified : 11 Dec 2018 11:24

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