Derivation and optimization of turbo convolutional coding schemes for OFDM and DMT modulations.

Summary The research work presented in this thesis focuses on the study, design and optimization of partially turbo-coded modulation schemes to improve the performance of broadband wireless and wireline digital communication systems based on OFDM and DMT technologies. More specifically, we focus on the search for coding methods that improve the trade-off between performance, complexity, flexibility and backward compatibility with Wi-Fi, WiMAX and DSL standards. Our first attempt aims at improving wireline systems (DSL) via the introduction of an original multi-level coding scheme, called hierarchical trellis coded modulation (HTCM), based on the hierarchical protection of three non-binary levels: the first level using turbo-code and the two remaining levels using trellis coded modulation (TCM). Although it can significantly improve (sometimes by no more than one decibel) the coding gain of a TCM scheme of equivalent complexity, the HTCM structure is not well suited for applications using an external Reed-Solomon (RS) code, such as in DSL. As an alternative, we suggest a scheme formed by the serial concatenation of an RS code and a two-level turbo-coded modulation (TuCM) protecting the first 24-ary level with a turbo-code and leaving the second level unprotected. A thorough optimization of the TuCM core shows that a structure employing the turbo-code of WiMAX systems can achieve a coding gain of 7dB for a bit error rate of 10-7, considering a codeword formed by about 900 subcarriers. A modification of this last structure for wireless applications consists in not using an external RS code and in protecting the second TuCM level with a convolutional code. For example, we propose a structure that combines the convolutional and turbo codes of WiMAX systems, and show that this structure improves the performance/complexity tradeoff of standardized Wi-Fi and WiMAX solutions. The design and optimization of our coding schemes have led to the development of original tools, such as new theoretical bounds on the error rate of multilevel coding schemes, and a new algorithm for estimating the free distance of a turbo code. Finally, we propose a method, called self-protection, to improve the error packet correction capability of a multi-carrier system originally designed to correct isolated errors. The technique effectively combines several classical concepts such as SNR margining, erasure decoding, and a new form of channel interleaving. This method can significantly reduce the latency of more traditional techniques (e.g., channel interleaving or RS coding).