Identification aveugle de codes correcteurs d'erreurs basés sur des grands corps de Galois et recherche d'algorithmes de type décision souple pour les codes convolutifs

Abstract : In the first part of this thesis, we have focused on the blind identification of non-binary error correcting codes over the Galois field GF(2m). A study of the properties of Galois fields and non-binarycodes has been presented so as to get the essential elements for a blind identification of non-binary codes parameters. From the knowledge of only the received symbols, methods have been developed to identify the code parameters in the case of a noiseless transmission. The relevance of this approach has been highlighted when the parameters of the used Galois field are known bythe receiver. A theoretical study of rank criterion behaviors has been also presented to justify its use by the most existing identification methods. Then, three blind identification methods of the codeword size for binary and non-binary linear codes have been developped in the framework of a noisy transmission. In order to identify a dual code basis, an existing method for binary codes based on the use of a hard decision demodulation has been generalized to non-binary codes. The detection performance of this technique has been improved when an iterative process based on the joint use of a soft-decision demodulator and a soft-decision iterative decoding is introduced. In the second part of this thesis manuscript, a mathematical formalism is proposed in order to investigate the impact of mapping-demapping functions on linear algebra computations and properties over Galois field in the case of non-binary error correcting codes. Finally, this formalism has been exploited to detect or/and correct some digital transmission problems such as a bad synchronization. Finally, we have studied the impact of some mapping-demapping functions on the blind identification ofnon-binary error correcting codes parameters.
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Yasamine Zrelli. Identification aveugle de codes correcteurs d'erreurs basés sur des grands corps de Galois et recherche d'algorithmes de type décision souple pour les codes convolutifs. Autre. Université de Bretagne occidentale - Brest, 2013. Français. ⟨NNT : 2013BRES0097⟩. ⟨tel-02153597⟩

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