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Contribution to the study of the common FFT operator in Software radio context: application to channel coding. (Contribution à l'étude de l'opérateur commun FFT dans le contexte de la Radio logicielle : application au codage de canal)

This thesis addresses the problem of SoftWare Radio and more precisely the parametrization technique where the Common Operator (CO) approach is considered. The frequency processing of cyclic codes and particularly Reed-Solomon (RS) codes is investigated. From the perspective of involving the Fast Fourier transform (FFT) operator, used in several processing like filtering function, (de)modulation OFDM, ..., in the channel coding we have revived a specific class of RS codes defined over GF(Ft). As a first contribution, we have re-designed the FFT in such a way to be reconfigurable and able to provide two functionalities: FFT and FNT. This Dual mode FFT (DMFFT) is implemented on FPGA devices and a memory saving of around 25 % and complexity reduction of around 18 % are obtained in comparison with the Velcro approach where the two operators FFT and FNT are implemented separately. The second contribution is the proposition of two scenarios leading to the realization of an optimized triple mode FFT (TMFFT) able to perform, in addition of the DMFFT functionalities, the finite field transform over GF(2m) allowing the involvement of the classical RS codes in the intended SWR system.