Bit-interleaved coded modulation with iterative decoding (BICM-ID)is a spectral efficient coded modulation technique to improve the performance of digital communication systems. It has been widely known that for fixed signal constellation, interleaver and error control code, signal mapping plays an important role in determining the error performance of a BICM-ID system. This thesis concentrates on signal mapping designs for BICM-ID systems. To this end, the distance criteria to find the best mapping in terms of the asymptotic performance are first analytically derived for different channel models. Such criteria are then used to find good mappings for various two-dimensional 8-ary constellations. The usefulness of the proposed mappings of 8-ary constellations is verified by both the error floor bound and simulation results. Moreover, new mappings are also proposed for BICM-ID systems employing the quadrature phase shift keying (QPSK) constellation. The new mappings are obtained by considering many QPSK symbols over a multiple symbol interval, which essentially creates hypercube constellations. Analytical and simulation results show that the use of the proposed mappings together with very simple convolutional codes can offer significant coding gains over the conventional BICM-ID systems for all the channel models considered. Such coding gains are achieved without any bandwidth nor power expansion and with a very small increase in the system complexity.

Bit-interleaved coded modulation with iterative decoding (BICM-ID)is a spectral efficient coded modulation technique to improve the performance of digital communication systems. It has been widely known that for fixed signal constellation, interleaver and error control code, signal mapping plays an important role in determining the error performance of a BICM-ID system. This thesis concentrates on signal mapping designs for BICM-ID systems. To this end, the distance criteria to find the best mapping in terms of the asymptotic performance are first analytically derived for different channel models. Such criteria are then used to find good mappings for various two-dimensional 8-ary constellations. The usefulness of the proposed mappings of 8-ary constellations is verified by both the error floor bound and simulation results. Moreover, new mappings are also proposed for BICM-ID systems employing the quadrature phase shift keying (QPSK) constellation. The new mappings are obtained by considering many QPSK symbols over a multiple symbol interval, which essentially creates hypercube constellations. Analytical and simulation results show that the use of the proposed mappings together with very simple convolutional codes can offer significant coding gains over the conventional BICM-ID systems for all the channel models considered. Such coding gains are achieved without any bandwidth nor power expansion and with a very small increase in the system complexity.

In this thesis, a novel iterative receiver and its improved version are proposed for relay-assisted multiuser communications, in which multiple users transmit to a destination with the help of a relay and using fast frequency-hopping modulation. Each user employs a channel encoder to protect its information and facilitate interference cancellation at the receiver. The signal received at the relay is either amplified, or partially decoded with a simple energy detector, before being forwarded to the destination. Under flat Rayleigh fading channels, the receiver at the destination can be implemented non-coherently, i.e., it does not require the instantaneous channel information to demodulate the users’ transmitted signals. The proposed iterative algorithm at the destination exploits the soft outputs of the channel decoders to successively extract the maximum likelihood symbols of the users and perform interference cancellation. The iterative method is successfully applied for both cases of amplify-and-forward and partial decode-and-forward relaying. The error performance of the proposed iterative receiver is investigated by computer simulation. Under the same spectral efficiency, simulation results demonstrate the excellent performance of the proposed receiver when compared to the performance of decoding without interference cancellation as well as the performance of the maximum likelihood multiuser detection previously developed for uncoded transmission. Simulation results also suggest that a proper selection of channel coding schemes can help to support significant more users without consuming extra system resources. In addition, to further enhance the receiver’s performance in terms of the bit error rate, an improved version of the iterative receiver is presented. Such an improved receiver invokes inner-loop iterations between the channel decoders and the demappers in such a way that the soft outputs of the channel decoders are also used to refine the outputs of the demappers for every outer-loop iteration. Simulation results indicate a performance gain of about 2.5dB by using the two-loop receiver when compared to the performance of the first proposed receiver.

La géométrie de l’information est la théorie mathématique qui applique les méthodes de la géométrie différentielle dans le domaine des statistiques et de la théorie de l’information. C’est une technique très prometteuse pour l’analyse et l’illustration des algorithmes itératifs utilisés en communications numériques. Cette thèse porte sur l’application de cette technique ainsi que d’autre technique d’optimisation bien connue, l’algorithme itératif du point proximal, sur les algorithmes itératifs en général. Nous avons ainsi trouvé des interprétations géométriques (basée sur la géométrie de l’information) et proximales (basée sur l’algorithme du point proximal)intéressantes dans le cas d’un algorithme itératif de calcul de la capacité des canaux discrets sans mémoire, l’algorithme de Blahut-Arimoto. L’idée étant d’étendre cette application sur une classe d’algorithmes itératifs plus complexes. Nous avons ainsi choisi d’analyser l’algorithme de décodage itératif des modulations codées à bits entrelacés afin de trouver quelques interprétations et essayer de proposer des liens existant avec le critère optimal de maximum de vraisemblance et d’autres algorithmes bien connus dans le but d’apporter certaines améliorations par rapport au cas classique de cet algorithme, en particulier l’étude de la convergence.Mots-clefs : Géométrie de l’information, algorithme du point proximal, algorithme de Blahut-Arimoto, décodage itératif, Modulations codées à bits entrelacés, maximum de vraisemblance. / Information geometry is a mathematical theory that applies methods of differential geometryin the fields of statistics and information theory. It is a very promising technique foranalyzing iterative algorithms used in digital communications. In this thesis, we apply this technique, in addition to the proximal point algorithm, to iterative algorithms. First, we have found some geometrical and proximal point interpretations in the case of an iterative algorithmfor computing the capacity of discrete and memoryless channel, the Blahut-Arimoto algorithm.Interesting results obtained motivated us to extend this application to a larger class of iterative algorithms. Then, we have studied in details iterative decoding algorithm of Bit Interleaved Coded Modulation (BICM) in order to analyse and propose some ameliorations of the classical decoding case. We propose a proximal point interpretation of this iterative process and find the link with some well known decoding algorithms, the Maximum likelihood decoding.