Convolutional and tail-biting quantum error-correcting codes

G. David Forney; Markus Grassl; Saikat Guha

doi:10.1109/TIT.2006.890698

Convolutional and tail-biting quantum error-correcting codes

G. David Forney, Markus Grassl, Saikat Guha

Research output: Contribution to journal › Article › peer-review

69 Scopus citations

Abstract

Rate-(n -2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to are constructed as stabilizer codes from classical self-orthogonal rate-1-/n F₄ linear and binary linear convolutional codes, respectively. These codes generally have higher rate and less decoding complexity than comparable quantum block codes or previous quantum convolutional codes. Rate-(n - 2)/n block stabilizer codes with the same rate and error-correction capability and essentially the same decoding complexity are derived from these convolutional codes via tail-biting.

Original language	English (US)
Pages (from-to)	865-880
Number of pages	16
Journal	IEEE Transactions on Information Theory
Volume	53
Issue number	3
DOIs	https://doi.org/10.1109/TIT.2006.890698
State	Published - Mar 2007

Keywords

CSS-type codes
Quantum convolutional codes (QCCs)
Quantum error-correcting codes
Quantum tail-biting codes

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2006.890698

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title = "Convolutional and tail-biting quantum error-correcting codes",

abstract = "Rate-(n -2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to are constructed as stabilizer codes from classical self-orthogonal rate-1-/n F4 linear and binary linear convolutional codes, respectively. These codes generally have higher rate and less decoding complexity than comparable quantum block codes or previous quantum convolutional codes. Rate-(n - 2)/n block stabilizer codes with the same rate and error-correction capability and essentially the same decoding complexity are derived from these convolutional codes via tail-biting.",

keywords = "CSS-type codes, Quantum convolutional codes (QCCs), Quantum error-correcting codes, Quantum tail-biting codes",

author = "Forney, {G. David} and Markus Grassl and Saikat Guha",

note = "Funding Information: Manuscript received November 2, 2005; revised November 7, 2006. The work of S. Guha was supported in part by the U.S. Army Research Office DoD MURI under Grant DAAD-19-00-1-0177. G. D. Forney, Jr. is with the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: forneyd@comcast.net). M. Grassl is with the Institut f{\"u}r Algorithmen und Kognitive Systeme, Univer-sit{\"a}t Karlsruhe (TH), 76128 Karlsruhe, Germany (e-mail: grassl@ira.uka.de). S. Guha is with the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: saikat@mit.edu). Communicated by A. Winter, Associate Editor for Quantum Information Theory. Digital Object Identifier 10.1109/TIT.2006.890698",

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AU - Grassl, Markus

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Convolutional and tail-biting quantum error-correcting codes

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