On the design of Raptor codes over Gaussian channels

Abstract

We investigate the design of Raptor codes---a class of fountain codes---over Gaussian channels. In this thesis, we prove that there exists no universal choice of input degree distribution or constructing capacity-achieving Raptor codes using mean-LLR, EXIT chart approach. An approach of finding input and output degree distribution jointly is proposed. Through the codes constructed by this approach, we show our approach uniformly outperforms an existing heuristic approach over all Gaussian channels. However, there still exists a gap to channel capacity for Raptor codes constructed by mean-LLR. EXIT chart based approach.