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Contribution à la construction et au décodage des codes polaires

Abstract : In a world of intensive and widespread numeric datafow, the use of error correcting codes has become an essential aspect of telecommunication systems, by allowing to compensate the unavoidable alteration of the messages during the transmission, by means of additionnal redundancy to the initial message. Last family of codes to be discovered, in 2008, polar codes have soon experienced a large interest of the community, due to their ability to achieve the Shannon capacity, namely the theoretical limit of the information rate, defned by Shannon in 1948. Very recently, these codes have been adopted in the fifth generation of cellular mobile communications 5G. This thesis concentrates on the analysis of this family of codes regarding constraints of practical systems, including in 5G, through the two major isues of the construction of the code and the decoding in finite length.After reviewing the definition and the caracterisation of polar codes, and addressing the question of the spectrum distance, this thesis considers the issue of the flexibility of the codes as function of the codelength, using either puncturing or shortening techniques, andd escribes a new method to select the pattern so as to minimize the error rate under succssive cancellation decoding (SC). Secondly, a new bit-fipping decoding algorithm is proposed, improving signifcantly the performance compared to state-of-the-art approach,while offering a reduced average complexity, which stays close to the one of the SC decoder. Thirdly, the issue of the use of polar codes with high order modulation is considered. On the one hand, the case of coded modulations, where a high order modulation is combined with binary codes, is considered throughthe bit-interleaved coded modulation and the multilevel coded modulation, and it is shown that the second one is very well suitable for polar codes. On the other hand, the case of non-binary codes, which can be mapped directly to the constellation, are considered and it is revealed they are able to surpass their binary counterpart at the cost of additionnal decoding complexity.
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Ludovic Chandesris. Contribution à la construction et au décodage des codes polaires. Traitement du signal et de l'image [eess.SP]. Université de Cergy Pontoise, 2019. Français. ⟨NNT : 2019CERG1018⟩. ⟨tel-02861774⟩

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