Analysis and Design of Physical Layer Raptor Codes

In this letter, we first provide the asymptotic analysis of Raptor codes over binary input additive white Gaussian noise channels using discretized density evolution (DDE). We show that the Raptor codes of various realized code-rates using the same output degree distribution perform within 0.4-dB to the Shannon limit. We then prove a necessary condition for the successful decoding of such codes and use it with a DDE-based optimization method to obtain optimized Raptor codes with further improvement in decoding thresholds.