Reconnaissance de codes correcteurs d'erreurs

Abstract : In this thesis, I am interested in the recognition of error correcting codes from a noisy observation. Of these codes, we chose to study in particular convolutional codes and turbo codes. The transmission channel considered in our work is the binary symmetric channel. Based on the work of E. Filiol and J. Barber, I developed an algorithm, devised jointly with N. Sendrier. We've created a new generic method for recognition of convolutional codes (n, k) (k inputs and n outputs). This method improves the state of the art with the exclusive use of binary linear algebra operations in the algorithm. The implementation provides good results, both in terms of execution time as the noise tolerance for any type of convolutional code. The second part consists of the development of a recognition method of turbo-codes. This method relies on assumptions that we are able to recover the first convolutional code using our method of recognition of convolutional code and the second convolutional code (according to the interleaver) has a systematic generator matrix defined by P (D ) / Q (D) (where P (D) and Q (D) are polynomials of the convolutional encoder) of non-zero constant term. This strong but realistic assumption allows us to build a method and an algorithm to find both the interleaver and the polynomials P (D) and Q (D) convolutional code. This algorithm is very fast but is limited when the error rate believes. Moreover, our hypothesis makes it impossible to rebuild turbo punctured codes without changing the algorithm.
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Submitted on : Wednesday, July 21, 2010 - 9:03:29 AM
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Maxime Côte. Reconnaissance de codes correcteurs d'erreurs. Mathématiques [math]. Ecole Polytechnique X, 2010. Français. ⟨pastel-00006125⟩

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