Turbo-codes quantiques

Abstract : The idea of turbo-codes enables to encode classical information very reliably, but could not be used efficiently until today for the purpose of quantum information encoding. Indeed, there were theoretical obstacles as well as obstacles related to the implementation. About the known quantum version of these codes, no result was known establishing an infinite minimal distance, a property enabling to correct an arbitrary number of errors, and no efficient decoding algorithm was available, since these quantum turbo-codes are said catastrophic, in the sense that certain errors propagate during the decoding and prevent its good functioning. This thesis has enabled to rise to these two challenges, by establishing theoretical conditions so that a quantum turbo-code has an infinite minimal distance, and by displaying a construction such that the iterative decoding works well. It is shown by simulations that the designed class of quantum turbo-codes is efficient for the transmission of quantum information by a depolarizing channel up to a depolarizing rate of p = 0.145. These quantum codes, of constant rate, can be directly used to encode quantum binary information, and can as well be integrated as a module to improve the functioning of other codes such as quantum LDPC.
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Contributor : Mamdouh Abbara <>
Submitted on : Monday, July 8, 2013 - 1:41:49 PM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on : Wednesday, October 9, 2013 - 4:22:51 AM

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Mamdouh Abbara. Turbo-codes quantiques. Théorie de l'information [cs.IT]. Ecole Polytechnique X, 2013. Français. ⟨pastel-00842327⟩

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