Design and optimization of AL-FEC codes: the GLDPC-Staircase codes. (Conception et optimisation de codes AL-FEC : les codes GLDPC- Staircase)

This work is dedicated to the design, analysis and optimization of Application-Level Forward Erasure Correction (AL-FEC) codes. In particular, we explore a class of Generalized LDPC (GLDPC) codes, named GLDPC-Staircase codes, involving the LDPCStaircase code (base code) as well as Reed-Solomon (RS) codes (outer codes). In the first part of this thesis, we start by showing that RS codes having “quasi” Hankel matrix-based construction are the most suitable MDS codes to obtain the structure of GLDPC-Staircase codes. Then, we propose a new decoding type, so-called hybrid (IT/RS/ML) decoding, for these codes to achieve Maximum Likelihood (ML) correction capabilities with a lower complexity. To investigate the impact of the structure of GLDPCStaircase codes on decoding, we propose another construction: they differ on the nature of generated LDPC repair symbols. Afterwards, to predict the capacity approaching GLDPCStaircase codes, we derive an asymptotic analysis based on DE, EXIT functions, and area theorem. Eventually, based on finite length analysis and asymptotic analysis, we tune important internal parameters of GLDPC-Staircase codes to obtain the best configuration under hybrid (IT/RS/ML) decoding. The second part of the thesis benchmarks GLDPC-Staircase codes in various situations. First, we show that these codes are asymptotically quite close to Shannon limit performance and achieve finite length excellent erasure correction capabilities very close to that of ideal MDS codes no matter the objects size: very small decoding overhead, low error floor, and steep waterfall region. Second, we show that these codes outperform Raptor codes, LDPCStaircase codes, other construction of GLDPC codes, and have correction capabilities close to that of RaptorQ codes. Last but not least, we propose a general-methodology to address the problem of the impact of packet scheduling on GLDPC-Staircase codes for a large set of loss channels (with burst loss or not). This study shows the best packet scheduling. All the aforementioned results make GLDPC-Staircase codes an ubiquitous Application-Level FEC (AL-FEC) solution.