Asymptotic Analysis and Optimization Design of Physical Layer Systematic Rateless Codes

In this paper, we first provide the asymptotic analysis of systematic version of Luby transform (LT) and Raptor codes over binary input additive white Gaussian noise (BIAWGN) channel using discretized density evolution (DDE). We then use a DDE-based optimization approach to obtain optimized output degree distributions for the systematic Raptor (SR) codes of various realized code-rates. We finally provide the decoding thresholds and simulation results showing that our optimized SR codes largely outperform the traditional SR codes in BIAWGN channel.