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Duality of quantum and classical error correction codes: design principles and examples

Duality of quantum and classical error correction codes: design principles and examples
Duality of quantum and classical error correction codes: design principles and examples
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.
1553-877X
Babar, Zunaira
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Chandra, Daryus
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Nguyen, Hung Viet
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Botsinis, Panagiotis
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Alanis, Dimitrios
f540b99b-e7e6-475c-be3c-d8e63fd90e2a
Ng, Soon
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
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Babar, Zunaira
23ede793-1796-449d-b5aa-93a297e5677a
Chandra, Daryus
a2f091a8-9772-4633-8e3b-d3220b10a2ec
Nguyen, Hung Viet
6f5a71ef-ea98-49e0-9be7-7f5bb9880f52
Botsinis, Panagiotis
d7927fb0-95ca-4969-9f8c-1c0455524a1f
Alanis, Dimitrios
f540b99b-e7e6-475c-be3c-d8e63fd90e2a
Ng, Soon
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1

Babar, Zunaira, Chandra, Daryus, Nguyen, Hung Viet, Botsinis, Panagiotis, Alanis, Dimitrios, Ng, Soon and Hanzo, Lajos (2018) Duality of quantum and classical error correction codes: design principles and examples. IEEE Communications Surveys & Tutorials. (doi:10.1109/COMST.2018.2861361).

Record type: Article

Abstract

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.

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Accepted/In Press date: 22 July 2018
e-pub ahead of print date: 31 July 2018

Identifiers

Local EPrints ID: 422635
URI: https://eprints.soton.ac.uk/id/eprint/422635
ISSN: 1553-877X
PURE UUID: d4b7e85b-e1e0-4963-8dbc-23fd9895a78e
ORCID for Zunaira Babar: ORCID iD orcid.org/0000-0002-7498-4474
ORCID for Daryus Chandra: ORCID iD orcid.org/0000-0003-2406-7229
ORCID for Hung Viet Nguyen: ORCID iD orcid.org/0000-0001-6349-1044
ORCID for Soon Ng: ORCID iD orcid.org/0000-0002-0930-7194
ORCID for Lajos Hanzo: ORCID iD orcid.org/0000-0002-2636-5214

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Date deposited: 27 Jul 2018 16:30
Last modified: 14 Mar 2019 01:55

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