EXIT Functions for LT and Raptor Codes, and Asymptotic Ranks of Random Matrices

In this paper we propose a notion of EXIT functions for LT-codes and Raptor codes, and discuss some of their useful properties that can be used to design good codes. We will further use these results to derive interesting conclusions on ranks of random matrices. New expressions for the asymptotic ranks of certain classes of random binary matrices are derived and the results are compared to previously known bounds and results.